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Class 11 • Physics
Motion in 2D & Vectors
Chapter-3
206 Questions
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53 Easy152 Medium1 Hard
Practice Questions
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1
MediumAiims2018
Assertion The maximum height of projectile is always 25% of the maximum range. Reason For maximum range, projectile should be projected at 90°.
Options:
A) Both Assertion and Reason are correct, Reason is the correct explanation of Assertion
B) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C) Assertion is correct and Reason is incorrect
D) Assertion is incorrect and Reason is correct
2
MediumCOMEDK2025
The square of resultant of two equal electric field vectors is three times their product. Angle between them is
Options:
A) \frac{\pi}{5}
B) \frac{\pi}{6}
C) \frac{\pi}{8}
D) \frac{\pi}{3}
3
MediumAiims2017
Assertion : When $\theta=45^{\circ} or 135^{\circ}, the value of R remains the same, only the sign changes. Reason : R=\frac{u^2 \sin 2 \theta}{g}
Options:
A) Both assertion and reason are true and reason is the correct explanation of assertion
B) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false
D) Both assertion and reason are false.
4
MediumCOMEDK2024
If $\alpha, \beta and \gamma are the angles between the vectors \overrightarrow{\mathrm{P}}, \overrightarrow{\mathrm{Q}}, and \overrightarrow{\mathrm{R}} and \alpha=90^{\circ} as shown in figure. the product of (\vec{Q} \times \vec{R}) \cdot \vec{Q}$ is equal to
Options:
A)
R Q^2 \sin \theta \cos \theta
B)
R Q^2 \cos \theta
C)
R Q^2 \sin\theta
D) Zero
5
MediumJEE Mains2026
A boy throws a ball into air at 45^{\circ} from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is \_\_\_\_ m. $ \left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)
Options:
A) 20
B) 25
C) 10
D) 15
6
MediumCOMEDK2023
The sides of a parallelogram are represented by vectors $\vec{p}=5 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}} and \vec{q}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$. Then, the area of the parallelogram is
Options:
A) \sqrt{684}$ sq units
B) \sqrt{72}$ sq units
C) 171 sq units
D) 72 sq units
7
MediumJEE Mains2026
A projectile is thrown upward at an angle 60^{\circ} with the horizontal. The speed of the projectile is 20 \mathrm{~m} / \mathrm{s} when its direction of motion is 45^{\circ} with the horizontal. The initial speed of the projectile is \_\_\_\_ \mathrm{m} / \mathrm{s}.
Options:
A) 20 \sqrt{3}
B) 20 \sqrt{2}
C) 40
D) 40 \sqrt{2}
8
MediumCOMEDK2022
The resultant of two forces acting at an angle of 120$^\circ$ is 10 kg-W and is perpendicular to one of the forces. That force is
Options:
A) \frac{10}{\sqrt3}$ kg-W
B) 10$ kg-W
C) 20\sqrt3$ kg-W
D) 10\sqrt3$ kg-W
9
MediumJEE Mains2026
A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are ______ and ______ respectively.
Options:
A) 20 s and 100 m
B) 40 s and 100 m
C) 40 s and 200 m
D) 40 s and 0 m
10
MediumCOMEDK2020
A particle starts moving from point (2, 10, 1). Displacement for the particle is $8\widehat i - 2\widehat j + \widehat k$. The final coordinates of the particle is
Options:
A) (10, 8, 2)
B) (8, 10, 2)
C) (2, 10, 8)
D) (8, 2, 10)
11
MediumJEE Mains2025
Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. T_1 and T_2 are the total flying times of first and second ball, respectively, then the ratio of T_1 and T_2 is
Options:
A) 2 : 1
B) \sqrt{2} : 1
C) 2 \sqrt{2} : 1
D) 4 : 1
12
MediumJEE Mains2025
Two particles are located at equal distance from origin. The position vectors of those are represented by \vec{A}=2 \hat{i}+3 n \hat{j}+2 \hat{k} and \bar{B}=2 \hat{i}-2 \hat{j}+4 p \hat{k}, respectively. If both the vectors are at right angle to each other, the value of n^{-1} is ________ .
Options:
13
EasyJEE Mains2025
A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where the object was released is : (use acceleration due to gravity g = 10 m/s2 and neglect air resistance)
Options:
A) 7.2 km
B) 2\sqrt{5} km
C) 2\sqrt{2} km
D) 4 km
14
MediumJEE Mains2024
The resultant of two vectors $\vec{A} and \vec{B} is perpendicular to \vec{A} and its magnitude is half that of \vec{B}. The angle between vectors \vec{A} and \vec{B} is _________^\circ$.
Options:
15
EasyJEE Mains2025
Two projectiles are fired from ground with same initial speeds from same point at angles \left(45^{\circ}+\right. \alpha) and \left(45^{\circ}-\alpha\right) with horizontal direction. The ratio of their times of flights is
Options:
A) \frac{1+\tan \alpha}{1-\tan \alpha}
B) \frac{1+\sin 2 \alpha}{1-\sin 2 \alpha}
C) \frac{1-\tan \alpha}{1+\tan \alpha}
D) 1
16
MediumJEE Mains2024
If $\vec{a} and \vec{b} makes an angle \cos ^{-1}\left(\frac{5}{9}\right) with each other, then |\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}| for |\vec{a}|=n|\vec{b}| The integer value of \mathrm{n}$ is _________.
Options:
17
MediumJEE Mains2025
A particle is projected with velocity u so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as \frac{n u^2}{25 g}, where value of n is: (Given, ' g ' is the acceleration due to gravity.)
Options:
A) 6
B) 12
C) 18
D) 24
18
MediumJEE Mains2024
Three vectors $\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}} and \overrightarrow{\mathrm{OR}} each of magnitude \mathrm{A} are acting as shown in figure. The resultant of the three vectors is \mathrm{A} \sqrt{x}. The value of x$ is _________.
Options:
19
MediumJEE Mains2025
The angle of projection of a particle is measured from the vertical axis as \phi and the maximum height reached by the particle is \mathrm{h}_{\mathrm{m}}. Here \mathrm{h}_{\mathrm{m}} as function of \phi can be presented as
Options:
A)
B)
C)
D)
20
EasyJEE Mains2024
For three vectors $\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k}), \vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k}) and \vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k}), if \vec{A} \cdot(\vec{B} \times \vec{C})=0, then value of x$ is ________.
Options:
21
MediumJEE Mains2025
A river is flowing from west to east direction with speed of 9 \mathrm{~km} \mathrm{~h}^{-1}. If a boat capable of moving at a maximum speed of 27 \mathrm{~km} \mathrm{~h}^{-1} in still water, crosses the river in half a minute, while moving with maximum speed at an angle of 150^{\circ} to direction of river flow, then the width of the river is :
Options:
A) 112.5 m
B) 75 m
C) 300 m
D) 112.5 \times \sqrt{3} \mathrm{~m}
22
EasyJEE Mains2024
A vector has magnitude same as that of $\vec{A}=3 \hat{i}+4 \hat{j} and is parallel to \vec{B}=4 \hat{i}+3 \hat{j}. The x and y components of this vector in first quadrant are x and 3 respectively where x=$ _________.
Options:
23
MediumJEE Mains2025
Two projectiles are fired with same initial speed from same point on ground at angles of (45^\circ - \alpha) and (45^\circ + \alpha), respectively, with the horizontal direction. The ratio of their maximum heights attained is :
Options:
A) \frac{1+\sin\alpha}{1-\sin\alpha}
B) \frac{1+\sin2\alpha}{1-\sin2\alpha}
C) \frac{1-\tan\alpha}{1+\tan\alpha}
D) \frac{1-\sin2\alpha}{1+\sin2\alpha}
24
EasyJEE Mains2023
If $\overrightarrow P = 3\widehat i + \sqrt 3 \widehat j + 2\widehat k and \overrightarrow Q = 4\widehat i + \sqrt 3 \widehat j + 2.5\widehat k then, the unit vector in the direction of \overrightarrow P \times \overrightarrow Q is {1 \over x}\left( {\sqrt 3 \widehat i + \widehat j - 2\sqrt 3 \widehat k} \right). The value of x$ is _________.
Options:
25
EasyJEE Mains2025
The position vector of a moving body at any instant of time is given as \overrightarrow{\mathrm{r}}=\left(5 \mathrm{t}^2 \hat{i}-5 \mathrm{t} \hat{j}\right) \mathrm{m}. The magnitude and direction of velocity at t=2 s is,
Options:
A) 5 \sqrt{17} \mathrm{~m} / \mathrm{s}, making an angle of \tan ^{-1} 4 with - ve Y axis
B) 5 \sqrt{15} \mathrm{~m} / \mathrm{s}, making an angle of \tan ^{-1} 4 with + ve X axis
C) 5 \sqrt{17} \mathrm{~m} / \mathrm{s}, making an angle of \tan ^{-1} 4 with + ve X axis
D) 5 \sqrt{15} \mathrm{~m} / \mathrm{s}, making an angle of \tan ^{-1} 4 with - ve Y axis
26
EasyJEE Mains2023
Vectors $a\widehat i + b\widehat j + \widehat k and 2\widehat i - 3\widehat j + 4\widehat k are perpendicular to each other when 3a + 2b = 7, the ratio of a to b is {x \over 2}. The value of x$ is ____________.
Options:
27
MediumJEE Mains2025
An object of mass ' m ' is projected from origin in a vertical xy plane at an angle 45^{\circ} with the \mathrm{x}- axis with an initial velocity \mathrm{v}_0. The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [ g is acceleration due to gravity]
Options:
A) \frac{m v_o{ }^3}{2 \sqrt{2} g} along negative z-axis
B) \frac{m v_o^3}{2 \sqrt{2} g} along positive z-axis
C) \frac{m v_o^3}{4 \sqrt{2} g} along positive z-axis
D) \frac{m v_o^3}{4 \sqrt{2} g} along negative z-axis
28
EasyJEE Mains2022
If the projection of $2 \hat{i}+4 \hat{j}-2 \hat{k} on \hat{i}+2 \hat{j}+\alpha \hat{k} is zero. Then, the value of \alpha$ will be ___________.
Options:
29
EasyJEE Mains2025
A ball of mass 100 g is projected with velocity 20 \mathrm{~m} / \mathrm{s} at 60^{\circ} with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is
Options:
A) 20 J
B) 5 J
C) 15 J
D) zero
30
EasyJEE Mains2022
If $\vec{A}=(2 \hat{i}+3 \hat{j}-\hat{k})\, \mathrm{m} and \vec{B}=(\hat{i}+2 \hat{j}+2 \hat{k}) \,\mathrm{m}. The magnitude of component of vector \vec{A} along vector \vec{B} will be ____________ \mathrm{m}$.
Options:
31
MediumJEE Mains2024
The angle of projection for a projectile to have same horizontal range and maximum height is :
Options:
A) \tan ^{-1}\left(\frac{1}{2}\right)
B) \tan ^{-1}(2)
C) \tan ^{-1}\left(\frac{1}{4}\right)
D) \tan ^{-1}(4)
32
MediumJEE Mains2021
Three particles P, Q and R are moving along the vectors $\overrightarrow A = \widehat i + \widehat j, \overrightarrow B = \widehat j + \widehat k and \overrightarrow C = - \widehat i + \widehat j respectively. They strike on a point and start to move in different directions. Now particle P is moving normal to the plane which contains vector \overrightarrow A and \overrightarrow B . Similarly particle Q is moving normal to the plane which contains vector \overrightarrow A and \overrightarrow C . The angle between the direction of motion of P and Q is {\cos ^{ - 1}}\left( {{1 \over {\sqrt x }}} \right)$. Then the value of x is _______________.
Options:
33
EasyJEE Mains2024
The co-ordinates of a particle moving in $x-y plane are given by : x=2+4 \mathrm{t}, y=3 \mathrm{t}+8 \mathrm{t}^2$. The motion of the particle is :
Options:
A) uniform motion along a straight line.
B) non-uniformly accelerated.
C) uniformly accelerated having motion along a straight line.
D) uniformly accelerated having motion along a parabolic path.
34
EasyJEE Mains2021
If $\overrightarrow P \times \overrightarrow Q = \overrightarrow Q \times \overrightarrow P , the angle between \overrightarrow P and \overrightarrow Q is \theta(0^\circ < \theta < 360^\circ). The value of '\theta' will be ___________^\circ$.
Options:
35
HardJEE Mains2024
Projectiles A and B are thrown at angles of $45^{\circ} and 60^{\circ} with vertical respectively from top of a 400 \mathrm{~m} high tower. If their ranges and times of flight are same, the ratio of their speeds of projection v_A: v_B is : [Take g=10 \mathrm{~ms}^{-2}$]
Options:
A) 1: 2
B) \sqrt{2}: 1
C) 1: \sqrt{2}
D) 1: \sqrt{3}
36
MediumJEE Mains2020
The sum of two forces $\overrightarrow P and \overrightarrow Q is \overrightarrow R such that \left| {\overrightarrow R } \right| = \left| {\overrightarrow P } \right| . The angle \theta (in degrees) that the resultant of 2{\overrightarrow P } and {\overrightarrow Q } will make with {\overrightarrow Q }$ is , ..............
Options:
37
EasyJEE Mains2024
Position of an ant ($\mathrm{S} in metres) moving in \mathrm{Y}-\mathrm{Z} plane is given by S=2 t^2 \hat{j}+5 \hat{k} (where t is in second). The magnitude and direction of velocity of the ant at \mathrm{t}=1 \mathrm{~s}$ will be :
Options:
A) 16 \mathrm{~m} / \mathrm{s} in y$-direction
B) 4 \mathrm{~m} / \mathrm{s} in x$-direction
C) 9 \mathrm{~m} / \mathrm{s} in \mathrm{z}$-direction
D) 4 \mathrm{~m} / \mathrm{s} in y$-direction
38
EasyJEE Mains2024
The angle between vector $\vec{Q} and the resultant of (2 \vec{Q}+2 \vec{P}) and (2 \vec{Q}-2 \vec{P})$ is :
Options:
A)
\tan ^{-1}(\mathrm{P} / \mathrm{Q})
B) 0$^\circ
C)
\tan ^{-1} \frac{(2 \vec{Q}-2 \vec{P})}{2 \vec{Q}+2 \vec{P}}
D)
\tan ^{-1}(2 Q / \mathrm{P})
39
EasyJEE Mains2023
A projectile is projected at $30^{\circ} from horizontal with initial velocity 40 \mathrm{~ms}^{-1}. The velocity of the projectile at \mathrm{t}=2 \mathrm{~s} from the start will be : (Given g=10 \mathrm{~m} / \mathrm{s}^{2}$ )
Options:
A) 20 \sqrt{3} \mathrm{~ms}^{-1}
B) Zero
C) 20 \mathrm{~ms}^{-1}
D) 40 \sqrt{3} \mathrm{~ms}^{-1}
40
EasyJEE Mains2024
If two vectors $\vec{A} and \vec{B} having equal magnitude R are inclined at angle \theta$, then
Options:
A) |\vec{A}+\vec{B}|=2 R \cos \left(\frac{\theta}{2}\right)
B) |\vec{A}-\vec{B}|=2 R \cos \left(\frac{\theta}{2}\right)
C) |\vec{A}-\vec{B}|=\sqrt{2} R \sin \left(\frac{\theta}{2}\right)
D) |\vec{A}+\vec{B}|=2 R \sin \left(\frac{\theta}{2}\right)
41
EasyJEE Mains2023
Two projectiles are projected at $30^{\circ} and 60^{\circ}$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:
Options:
A) 1: \sqrt{3}
B) \sqrt{3}: 1
C) 1 : 3
D) 2: \sqrt{3}
42
EasyJEE Mains2023
A vector in x-y plane makes an angle of 30^{\circ} with y-axis. The magnitude of \mathrm{y}-component of vector is 2 \sqrt{3}. The magnitude of x-component of the vector will be :
Options:
A) \sqrt{3}
B) 2
C) 6
D) \frac{1}{\sqrt{3}}
43
EasyJEE Mains2023
The range of the projectile projected at an angle of 15$^\circ with horizontal is 50 m. If the projectile is projected with same velocity at an angle of 45^\circ$ with horizontal, then its range will be
Options:
A) 50$\sqrt2$ m
B) 100 m
C) 100$\sqrt2$ m
D) 50 m
44
EasyJEE Mains2023
When vector $\vec{A}=2 \hat{i}+3 \hat{j}+2 \hat{k} is subtracted from vector \overrightarrow{\mathrm{B}}, it gives a vector equal to 2 \hat{j}. Then the magnitude of vector \overrightarrow{\mathrm{B}}$ will be :
Options:
A) 3
B) \sqrt{33}
C) \sqrt6
D) \sqrt5
45
EasyJEE Mains2023
The trajectory of projectile, projected from the ground is given by $y=x-\frac{x^{2}}{20}. Where x and y$ are measured in meter. The maximum height attained by the projectile will be.
Options:
A) 10 m
B) 5 m
C) 200 m
D) 10$\sqrt2$ m
46
EasyJEE Mains2023
Two forces having magnitude $A and \frac{A}{2}$ are perpendicular to each other. The magnitude of their resultant is:
Options:
A) \frac{5 A}{2}
B) \frac{\sqrt{5} A}{4}
C) \frac{\sqrt{5} A}{2}
D) \frac{\sqrt{5} A^{2}}{2}
47
EasyJEE Mains2023
Two projectiles A and B are thrown with initial velocities of $40 \mathrm{~m} / \mathrm{s} and 60 \mathrm{~m} / \mathrm{s} at angles 30^{\circ} and 60^{\circ} with the horizontal respectively. The ratio of their ranges respectively is \left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)
Options:
A) 4: 9
B) 2: \sqrt{3}
C) \sqrt{3}: 2
D) 1: 1
48
EasyJEE Mains2023
If two vectors $\overrightarrow P = \widehat i + 2m\widehat j + m\widehat k and \overrightarrow Q = 4\widehat i - 2\widehat j + m\widehat k$ are perpendicular to each other. Then, the value of m will be :
Options:
A) -1
B) 3
C) 1
D) 2
49
EasyJEE Mains2023
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R Assertion A : When a body is projected at an angle $45^{\circ}, it's range is maximum. Reason R : For maximum range, the value of \sin 2 \theta$ should be equal to one. In the light of the above statements, choose the correct answer from the options given below:
Options:
A) Both $\mathbf{A} and \mathbf{R} are correct and \mathbf{R} is the correct explanation of \mathbf{A}
B) \mathbf{A} is true but \mathbf{R}$ is false
C) \mathbf{A} is false but \mathbf{R}$ is true
D) Both $\mathbf{A} and \mathbf{R} are correct but \mathbf{R} is NOT the correct explanation of \mathbf{A}
50
EasyJEE Mains2022
Two vectors $\overrightarrow A and \overrightarrow B have equal magnitudes. If magnitude of \overrightarrow A + \overrightarrow B is equal to two times the magnitude of \overrightarrow A - \overrightarrow B , then the angle between \overrightarrow A and \overrightarrow B $ will be :
Options:
A) {\sin ^{ - 1}}\left( {{3 \over 5}} \right)
B) {\sin ^{ - 1}}\left( {{1 \over 3}} \right)
C) {\cos ^{ - 1}}\left( {{3 \over 5}} \right)
D) {\cos ^{ - 1}}\left( {{1 \over 3}} \right)
51
EasyJEE Mains2023
A child stands on the edge of the cliff $10 \mathrm{~m} above the ground and throws a stone horizontally with an initial speed of 5 \mathrm{~ms}^{-1}. Neglecting the air resistance, the speed with which the stone hits the ground will be \mathrm{ms}^{-1} (given, g=10 \mathrm{~ms}^{-2}$ ).
Options:
A) 20
B) 25
C) 30
D) 15
52
EasyJEE Mains2022
\overrightarrow A is a vector quantity such that |\overrightarrow A | = non-zero constant. Which of the following expression is true for \overrightarrow A $ ?
Options:
A) \overrightarrow A \,.\,\overrightarrow A = 0
B) \overrightarrow A \times \overrightarrow A < 0
C) \overrightarrow A \times \overrightarrow A = 0
D) \overrightarrow A \times \overrightarrow A > 0
53
EasyJEE Mains2023
The initial speed of a projectile fired from ground is $\mathrm{u}. At the highest point during its motion, the speed of projectile is \frac{\sqrt{3}}{2} u$. The time of flight of the projectile is :
Options:
A) \frac{u}{g}
B) \frac{2u}{g}
C) \frac{u}{2g}
D) \frac{\sqrt3u}{g}
54
EasyJEE Mains2022
Which of the following relations is true for two unit vector $\widehat A and \widehat B making an angle \theta$ to each other?
Options:
A) |\widehat A + \widehat B| = |\widehat A - \widehat B|\tan {\theta \over 2}
B) |\widehat A - \widehat B| = |\widehat A + \widehat B|\tan {\theta \over 2}
C) |\widehat A + \widehat B| = |\widehat A - \widehat B|cos{\theta \over 2}
D) |\widehat A - \widehat B| = |\widehat A + \widehat B|\cos {\theta \over 2}
55
EasyJEE Mains2023
Two objects are projected with same velocity 'u' however at different angles $\alpha and \beta with the horizontal. If \alpha+\beta=90^\circ$, the ratio of horizontal range of the first object to the 2nd object will be :
Options:
A) 1 : 1
B) 2 : 1
C) 1 : 2
D) 4 : 1
56
MediumJEE Mains2021
Statement I :Two forces $\left( {\overrightarrow P + \overrightarrow Q } \right) and \left( {\overrightarrow P - \overrightarrow Q } \right) where \overrightarrow P \bot \overrightarrow Q , when act at an angle \theta1 to each other, the magnitude of their resultant is \sqrt {3({P^2} + {Q^2})} , when they act at an angle \theta2, the magnitude of their resultant becomes \sqrt {2({P^2} + {Q^2})} . This is possible only when {\theta _1} < {\theta _2}.Statement II :In the situation given above.\theta1 = 60^\circ and \theta2 = 90^\circ$In the light of the above statements, choose the most appropriate answer from the options given below :-
Options:
A) Statement I is false but Statement II is true
B) Both Statement I and Statement II are true
C) Statement I is true but Statement II is false
D) Both Statement I and Statement II are false.
57
EasyJEE Mains2023
The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is :
Options:
A) 136 m
B) 272 m
C) 68 m
D) 192 m
58
EasyJEE Mains2021
The resultant of these forces $\overrightarrow {OP} ,\overrightarrow {OQ} ,\overrightarrow {OR} ,\overrightarrow {OS} and \overrightarrow {OT} is approximately .......... N. [Take \sqrt 3 = 1.7, \sqrt 2 = 1.4 Given \widehat i and \widehat j$ unit vectors along x, y axis]
Options:
A) 9.25\widehat i + 5\widehat j
B) 3\widehat i + 15\widehat j
C) 2.5\widehat i - 14.5\widehat j
D) - 1.5\widehat i - 15.5\widehat j
59
EasyJEE Mains2022
At time $t=0 a particle starts travelling from a height 7 \hat{z} \mathrm{~cm} in a plane keeping z coordinate constant. At any instant of time it's position along the \hat{x} and \hat{y} directions are defined as 3 \mathrm{t} and 5 \mathrm{t}^{3}$ respectively. At t = 1s acceleration of the particle will be
Options:
A) -30 \hat{y}
B) 30 \hat{y}
C) 3 \hat{x}+15 \hat{y}
D) 3 \hat{x}+15 \hat{y}+7 \hat{z}
60
MediumJEE Mains2021
The angle between vector $\left( {\overrightarrow A } \right) and \left( {\overrightarrow A - \overrightarrow B } \right)$ is :
Options:
A) {\tan ^{ - 1}}\left( {{{ - {B \over 2}} \over {A - B{{\sqrt 3 } \over 2}}}} \right)
B) {\tan ^{ - 1}}\left( {{A \over {0.7B}}} \right)
C) {\tan ^{ - 1}}\left( {{{\sqrt 3 B} \over {2A - B}}} \right)
D) {\tan ^{ - 1}}\left( {{{B\cos \theta } \over {A - B\sin \theta }}} \right)
61
EasyJEE Mains2022
Two projectiles are thrown with same initial velocity making an angle of $45^{\circ} and 30^{\circ}$ with the horizontal respectively. The ratio of their respective ranges will be :
Options:
A) 1: \sqrt{2}
B) \sqrt{2}: 1
C) 2: \sqrt{3}
D) \sqrt{3}: 2
62
MediumJEE Mains2021
The magnitude of vectors $\overrightarrow {OA} , \overrightarrow {OB} and \overrightarrow {OC} in the given figure are equal. The direction of \overrightarrow {OA} + \overrightarrow {OB} - \overrightarrow {OC} $ with x-axis will be :
Options:
A) {\tan ^{ - 1}}{{(1 - \sqrt 3 - \sqrt 2 )} \over {(1 + \sqrt 3 + \sqrt 2 )}}
B) {\tan ^{ - 1}}{{(\sqrt 3 - 1 + \sqrt 2 )} \over {(1 + \sqrt 3 - \sqrt 2 )}}
C) {\tan ^{ - 1}}{{(\sqrt 3 - 1 + \sqrt 2 )} \over {(1 - \sqrt 3 + \sqrt 2 )}}
D) {\tan ^{ - 1}}{{(1 + \sqrt 3 - \sqrt 2 )} \over {(1 - \sqrt 3 - \sqrt 2 )}}
63
EasyJEE Mains2022
Two projectiles thrown at $30^{\circ} and 45^{\circ}$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is :
Options:
A) 1: \sqrt{2}
B) 2: 1
C) \sqrt{2}: 1
D) 1: 2
64
MediumJEE Mains2021
Assertion A : If A, B, C, D are four points on a semi-circular are with centre at 'O' such that $\left| {\overrightarrow {AB} } \right| = \left| {\overrightarrow {BC} } \right| = \left| {\overrightarrow {CD} } \right|, then \overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} = 4\overrightarrow {AO} + \overrightarrow {OB} + \overrightarrow {OC} Reason R : Polygon law of vector addition yields \overrightarrow {AB} + \overrightarrow {BC} + \overrightarrow {CD} + \overrightarrow {AD} = 2\overrightarrow {AO} $In the light of the above statements, choose the most appropriate answer from the options given below :
Options:
A) A is correct but R is not correct.
B) A is not correct but R is correct.
C) Both A and R are correct and R is the correct explanation of A.
D) Both A and R are correct but R is not the correct explanation of A.
65
MediumJEE Mains2022
A ball is projected from the ground with a speed 15 ms$-1 at an angle \theta with horizontal so that its range and maximum height are equal, then 'tan \theta$' will be equal to :
Options:
A) {1 \over 4}
B) {1 \over 2}
C) 2
D) 4
66
MediumJEE Mains2021
Two vectors $\overrightarrow X and \overrightarrow Y have equal magnitude. The magnitude of (\overrightarrow X - \overrightarrow Y ) is n times the magnitude of (\overrightarrow X + \overrightarrow Y ). The angle between \overrightarrow X and \overrightarrow Y $ is :
Options:
A) {\cos ^{ - 1}}\left( {{{ - {n^2} - 1} \over {{n^2} - 1}}} \right)
B) {\cos ^{ - 1}}\left( {{{{n^2} - 1} \over { - {n^2} - 1}}} \right)
C) {\cos ^{ - 1}}\left( {{{{n^2} + 1} \over { - {n^2} - 1}}} \right)
D) {\cos ^{ - 1}}\left( {{{{n^2} + 1} \over {{n^2} - 1}}} \right)
67
MediumJEE Mains2022
At t = 0, truck, starting from rest, moves in the positive x-direction at uniform acceleration of 5 ms$-2. At t = 20 s, a ball is released from the top of the truck. The ball strikes the ground in 1 s after the release. The velocity of the ball, when it strikes the ground, will be : (Given g = 10 ms-$2)
Options:
A) 100\widehat i - 10\widehat j
B) 10\widehat i - 100\widehat j
C) 100\widehat i
D) - 10\widehat j
68
EasyJEE Mains2021
Match List - I with List - IIChoose the correct answer from the options given below :
Options:
A) (a) $\to (iv), (b) \to (i), (c) \to (iii), (d) \to$ (ii)
B) (a) $\to (iv), (b) \to (iii), (c) \to (i), (d) \to$ (ii)
C) (a) $\to (iii), (b) \to (ii), (c) \to (iv), (d) \to$ (i)
D) (a) $\to (i), (b) \to (iv), (c) \to (ii), (d) \to$ (iii)
69
MediumJEE Mains2022
Two projectiles P1 and P2 thrown with speed in the ratio $\sqrt3 : \sqrt2, attain the same height during their motion. If P2 is thrown at an angle of 60^\circ$ with the horizontal, the angle of projection of P1 with horizontal will be :
Options:
A) 15$^\circ
B) 30$^\circ
C) 45$^\circ
D) 60$^\circ
70
EasyJEE Mains2021
What will be the projection of vector $\overrightarrow A = \widehat i + \widehat j + \widehat k on vector \overrightarrow B = \widehat i + \widehat j$ ?
Options:
A) \sqrt 2 (\widehat i + \widehat j + \widehat k)
B) (\widehat i + \widehat j)
C) \sqrt 2 (\widehat i + \widehat j)
D) 2(\widehat i + \widehat j + \widehat k)
71
EasyJEE Mains2022
A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?
Options:
A) 25 m
B) 50 m
C) 100 m
D) 200 m
72
MediumJEE Mains2021
Two vectors ${\overrightarrow P } and {\overrightarrow Q } have equal magnitudes. If the magnitude of {\overrightarrow P + \overrightarrow Q } is n times the magnitude of {\overrightarrow P - \overrightarrow Q }, then angle between {\overrightarrow P } and {\overrightarrow Q }$ is :
Options:
A) {\sin ^{ - 1}}\left( {{{n - 1} \over {n + 1}}} \right)
B) {\cos ^{ - 1}}\left( {{{n - 1} \over {n + 1}}} \right)
C) {\sin ^{ - 1}}\left( {{{{n^2} - 1} \over {{n^2} + 1}}} \right)
D) {\cos ^{ - 1}}\left( {{{{n^2} - 1} \over {{n^2} + 1}}} \right)
73
MediumJEE Mains2022
A projectile is launched at an angle '$\alpha' with the horizontal with a velocity 20 ms-1. After 10 s, its inclination with horizontal is '\beta'. The value of tan\beta will be : (g = 10 ms-$2).
Options:
A) tan$\alpha + 5sec\alpha
B) tan$\alpha - 5sec\alpha
C) 2tan$\alpha - 5sec\alpha
D) 2tan$\alpha + 5sec\alpha
74
EasyJEE Mains2021
If $\overrightarrow A and \overrightarrow B are two vectors satisfying the relation \overrightarrow A . \overrightarrow B = \left| {\overrightarrow A \times \overrightarrow B } \right|. Then the value of \left| {\overrightarrow A - \overrightarrow B } \right|$ will be :
Options:
A) \sqrt {{A^2} + {B^2} + \sqrt 2 AB}
B) \sqrt {{A^2} + {B^2}}
C) \sqrt {{A^2} + {B^2} - \sqrt 2 AB}
D) \sqrt {{A^2} + {B^2} + 2AB}
75
MediumJEE Mains2022
A girl standing on road holds her umbrella at 45$^\circ with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15\sqrt2 kmh-$1, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is :
Options:
A) 30 kmh$-$1
B) {{25} \over {\sqrt 2 }} kmh-$1
C) {{30} \over {\sqrt 2 }} kmh-$1
D) 25 kmh$-$1
76
MediumJEE Mains2021
In an octagon ABCDEFGH of equal side, what is the sum of $\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} + \overrightarrow {AF} + \overrightarrow {AG} + \overrightarrow {AH} ,if, \overrightarrow {AO} = 2\widehat i + 3\widehat j - 4\widehat k
Options:
A) - 16\widehat i - 24\widehat j + 32\widehat k
B) 16\widehat i + 24\widehat j - 32\widehat k
C) 16\widehat i + 24\widehat j + 32\widehat k
D) 16\widehat i - 24\widehat j + 32\widehat k
77
MediumJEE Mains2022
Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R. IF A and B reached the maximum height h1 and h2 respectively, then $R = 4\sqrt {{h_1}{h_2}} Reason R : Product of said heights. {h_1}{h_2} = \left( {{{{u^2}{{\sin }^2}\theta } \over {2g}}} \right)\,.\,\left( {{{{u^2}{{\cos }^2}\theta } \over {2g}}} \right)$ Choose the correct answer :
Options:
A) Both A and R are true and R is the correct explanation of A.
B) Both A and R are true but R is NOT the correct explanation of A.
C) A is true but R is false.
D) A is false but R is true.
78
MediumJEE Mains2019
Let $\left| {\mathop {{A_1}}\limits^ \to } \right| = 3, \left| {\mathop {{A_2}}\limits^ \to } \right| = 5 and \left| {\mathop {{A_1}}\limits^ \to + \mathop {{A_2}}\limits^ \to } \right| = 5. The value of \left( {2\mathop {{A_1}}\limits^ \to + 3\mathop {{A_2}}\limits^ \to } \right)\left( {3\mathop {{A_1}}\limits^ \to - \mathop {2{A_2}}\limits^ \to } \right)$ is :-
Options:
A) –118.5
B) –112.5
C) –99.5
D) –106.5
79
MediumJEE Mains2022
A projectile is projected with velocity of 25 m/s at an angle $\theta with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of \theta$ will be : [use g = 10 m/s2]
Options:
A) {1 \over 2}{\sin ^{ - 1}}\left( {{{5{t^2}} \over {4R}}} \right)
B) {1 \over 2}{\sin ^{ - 1}}\left( {{{4R} \over {5{t^2}}}} \right)
C) {\tan ^{ - 1}}\left( {{{4{t^2}} \over {5R}}} \right)
D) {\cot ^{ - 1}}\left( {{R \over {20{t^2}}}} \right)
80
MediumJEE Mains2019
Two vectors $\overrightarrow A and \overrightarrow B have equal magnitudes. The magnitude of \left( {\overrightarrow A + \overrightarrow B } \right) is 'n' times the magnitude of \left( {\overrightarrow A - \overrightarrow B } \right) . The angle between {\overrightarrow A } and {\overrightarrow B }$ is -
Options:
A) {\sin ^{ - 1}}\left[ {{{n - 1} \over {n + 1}}} \right]
B) {\sin ^{ - 1}}\left[ {{{{n^2} - 1} \over {{n^2} + 1}}} \right]
C) {\cos ^{ - 1}}\left[ {{{{n^2} - 1} \over {{n^2} + 1}}} \right]
D) {\cos ^{ - 1}}\left[ {{{n - 1} \over {n + 1}}} \right]
81
EasyJEE Mains2021
The ranges and heights for two projectiles projected with the same initial velocity at angles 42$^\circ and 48^\circ$ with the horizontal are R1, R2 and H1, H2 respectively. Choose the correct option :
Options:
A) R1 > R2 and H1 = H2
B) R1 = R2 and H1 < H2
C) R1 < R2 and H1 < H2
D) R1 = R2 and H1 = H2
82
MediumJEE Mains2019
In the cube of side ‘a’ shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be -
Options:
A) {1 \over 2}a\left( {\widehat k - \widehat i} \right)
B) {1 \over 2}a\left( {\widehat j - \widehat i} \right)
C) {1 \over 2}a\left( {\widehat j - \widehat k} \right)
D) {1 \over 2}a\left( {\widehat i - \widehat k} \right)
83
EasyJEE Mains2021
A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?
Options:
A) \sqrt {{{2gh{v^2} + 1} \over {{h^2}}}}
B) \sqrt {2gh{v^2} + {h^2}}
C) \sqrt {{{2{v^2}h} \over g} + {h^2}}
D) \sqrt {{{2gh} \over {{v^2}}} + {h^2}}
84
MediumJEE Mains2018
Let $\overrightarrow A = \left( {\widehat i + \widehat j} \right) and, \overrightarrow B = \left( {2\widehat i - \widehat j} \right). The magnitude of a coplanar vector \overrightarrow C such that \overrightarrow A .\overrightarrow C = \overrightarrow B .\overrightarrow C = \overrightarrow A .\overrightarrow B ,$ is given by :
Options:
A) \sqrt {{{10} \over 9}}
B) \sqrt {{{5} \over 9}}
C) \sqrt {{{20} \over 9}}
D) \sqrt {{{9} \over 12}}
85
EasyJEE Mains2021
A player kicks a football with an initial speed of 25 ms$-1 at an angle of 45^\circ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g = 10 ms-$2)
Options:
A) hmax = 10 mT = 2.5 s
B) hmax = 15.625 mT = 3.54 s
C) hmax = 15.625 mT = 1.77 s
D) hmax = 3.54 mT = 0.125 s
86
MediumJEE Mains2004
If $\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A $, then the angle beetween A and B is
Options:
A) {\pi \over 2}
B) {\pi \over 3}
C) \pi
D) {\pi \over 4}
87
EasyJEE Mains2021
A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :
Options:
A) hyperbola
B) parabola in the direction of motion of plane
C) straight line vertically down the plane
D) parabola in a direction opposite to the motion of plane
88
MediumMHT CET2025
Two vectors a \hat{i}+b \hat{j}+\hat{k} and 2 \hat{i}-3 \hat{j}+4 \hat{k} are perpendicular to each other. When 3 \mathrm{a}+2 \mathrm{~b}=7, the ratio of a to b is \frac{x}{2}. The value of x is
Options:
A) zero
B) 2
C) 1
D) 4
89
MediumJEE Mains2021
A butterfly is flying with a velocity $4\sqrt 2 $ m/s in North-East direction. Wind is slowly blowing at 1 m/s from North to South. The resultant displacement of the butterfly in 3 seconds is :
Options:
A) 12\sqrt 2 $ m
B) 20 m
C) 3 m
D) 15 m
90
MediumMHT CET2025
The vector sum of two forces \vec{A} and \vec{B} is perpendicular to their vector difference. Hence forces \vec{A} and \vec{B} are
Options:
A) perpendicular to each other.
B) parallel to each other.
C) unequal in magnitude.
D) equal in magnitude.
91
MediumJEE Mains2021
A mosquito is moving with a velocity $\overrightarrow v = 0.5{t^2}\widehat i + 3t\widehat j + 9\widehat k$ m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2 s?
Options:
A) {\tan ^{ - 1}}\left( {{\sqrt {85} } \over 6}\right)$ from y-axis
B) {\tan ^{ - 1}}\left( {{5 \over 2}} \right)$ from y-axis
C) {\tan ^{ - 1}}\left( {{2 \over 3}} \right)$ from x-axis
D) {\tan ^{ - 1}}\left( {{5 \over 2}} \right)$ from x-axis
92
MediumMHT CET2025
\begin{aligned} & \text { If }|\vec{a}|=\sqrt{26},|\vec{b}|=7 \\ & |\vec{a} \times \vec{b}|=35 \text {, find } \vec{a} \cdot \vec{b} \end{aligned}
Options:
A) 4
B) 5
C) 6
D) 7
93
EasyJEE Mains2021
The trajectory of a projectile in a vertical plane is y = $\alphax - \betax2, where \alpha and \beta are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection \theta$ and the maximum height attained H are respectively given by :
Options:
A) {\tan ^{ - 1}}\alpha ,{{{\alpha ^2}} \over {4\beta }}
B) {\tan ^{ - 1}}\alpha ,{{4{\alpha ^2}} \over \beta }
C) {\tan ^{ - 1}}\left( {{\beta \over \alpha }} \right),{{{\alpha ^2}} \over \beta }
D) {\tan ^{ - 1}}\beta ,{{{\alpha ^2}} \over {2\beta }}
94
MediumMHT CET2025
Vector \vec{A} of magnitude 5 \sqrt{3} units, another vector \vec{B} of magnitude of 10 units are inclined to each other at an angle of 30^{\circ}. The magnitude of vector product of the two vectors is \left[\sin 30^{\circ}=\frac{1}{2}\right]
Options:
A) 5 \sqrt{3} units
B) 10 units
C) 25 \sqrt{3} units
D) 75 units
95
MediumJEE Mains2020
When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal. On further increasing the speed of the car to (1 + $\beta )v, this angle changes to 45o. The value of \beta $ is close to :
Options:
A) 0.50
B) 0.73
C) 0.37
D) 0.41
96
MediumMHT CET2025
If \vec{P}=b \hat{i}+6 \hat{j}+\hat{k} \quad and \quad \vec{Q}=\hat{i}-a \hat{j}+4 \hat{k} \quad are perpendicular to each other, also 3 \mathrm{~b}-\mathrm{a}=5. The value of a and b is
Options:
A) \mathrm{a}=2, \mathrm{~b}=10
B) \mathrm{a}=1, \mathrm{~b}=2
C) \mathrm{a}=2, \mathrm{~b}=3
D) \mathrm{a}=4, \mathrm{~b}=3
97
MediumJEE Mains2020
A balloon is moving up in air vertically above a point A on the ground. When it is at a height h1, a girl standing at a distanced (point B) from A (see figure) sees it at an angle 45o with respect to the vertical. When the balloon climbs up a further height h2, it is seen at an angle 60o with respect to the vertical if the girl moves further by a distance 2.464 d(point C). Then the height h2 is (given tan 30o = 0.5774)
Options:
A) 0.464d
B) d
C) 0.732d
D) 1.464d
98
MediumMHT CET2025
Given \quad \vec{A}=(2 \hat{i}-3 \hat{j}+\hat{k}), \quad \vec{B}=(3 \hat{i}+\hat{j}-2 \hat{k}) and \vec{C}=(3 \hat{i}+2 \hat{j}+\hat{k}) \cdot(\vec{A}+\vec{B}) \cdot \vec{C} will be
Options:
A) 10
B) 12 c
C) 18
D) 20
99
MediumJEE Mains2020
Starting from the origin at time t = 0, with initial velocity 5$\widehat j ms-1 , a particle moves in the x-y plane with a constant acceleration of \left( {10\widehat i + 4\widehat j} \right)$ ms-2. At time t, its coordinates are (20 m, y0 m). The values of t and y0 are, respectively:
Options:
A) 5s and 25 m
B) 2s and 18 m
C) 2s and 24 m
D) 4s and 52 m
100
MediumMHT CET2025
Given \quad \vec{A}=(2 \hat{i}-3 \hat{j}+\hat{k}), \quad \vec{B}=(3 \hat{i}+\hat{j}-2 \hat{k}) and \vec{C}=(3 \hat{i}+2 \hat{j}+\hat{k}) \cdot(\vec{A}+\vec{B}) \cdot \vec{C} will be
Options:
A) 10
B) 12 c
C) 18
D) 20
101
MediumJEE Mains2020
A particle starts from the origin at t = 0 with an initial velocity of 3.0 $\widehat i m/s and moves in the x-y plane with a constant acceleration \left( {6\widehat i + 4\widehat j} \right)$ m/s2 . The x-coordinate of the particle at the instant when its y-coordinate is 32 m is D meters. The value of D is :-
Options:
A) 40
B) 32
C) 50
D) 60
102
MediumMHT CET2025
A unit vector in the direction of resultant vector of \vec{A}=-2 \hat{i}+3 \hat{j}+\hat{k} and \vec{B}=\hat{i}+2 \hat{j}-4 \hat{k} is
Options:
A) \frac{-3 \hat{\mathrm{i}}+\hat{\mathrm{j}}+5 \hat{\mathrm{k}}}{\sqrt{35}}
B) \frac{\hat{i}+2 \hat{j}-4 \hat{k}}{\sqrt{35}}
C) \frac{-2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{35}}
D) \frac{-\hat{\mathrm{i}}+5 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}}{\sqrt{35}}
103
MediumJEE Mains2020
A particle moves such that its position vector $\overrightarrow r \left( t \right) = \cos \omega t\widehat i + \sin \omega t\widehat j where \omega is a constant and t is time. Then which of the following statements is true for the velocity \overrightarrow v \left( t \right) and acceleration \overrightarrow a \left( t \right)$ of the particle :
Options:
A) \overrightarrow v and \overrightarrow a both are perpendicular to \overrightarrow r
B) \overrightarrow v and \overrightarrow a both are parallel to \overrightarrow r
C) \overrightarrow v is perpendicular to \overrightarrow r and \overrightarrow a $ is directed
towards the origin
D) \overrightarrow v is perpendicular to \overrightarrow r and \overrightarrow a $ is directed
away from the origin
104
MediumMHT CET2025
The three vector \vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}, \vec{B}=\hat{i}-3 \hat{j}+5 k and \vec{C}=2 \hat{i}-\hat{j}+4 \hat{k} will form
Options:
A) isosceles triangle.
B) equilateral triangle.
C) no triangle.
D) right angled triangle.
105
MediumJEE Mains2019
Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h1 and h2. Which of the following is correct ?
Options:
A) R2
= h1h2
B) R2
= 16 h1h2
C) R2
= 4 h1h2
D) R2 = 2h1h2
106
MediumMHT CET2025
Three vectors are expressed as \vec{a}=4 \hat{i}-\hat{j}, \vec{b}=-3 \hat{i}+2 \hat{j} and \vec{c}=-\hat{k}. The unit vector along the direction of sum of these vectors is
Options:
A) \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{3}}
B) \quad \frac{1}{3}(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})
C) \frac{1}{\sqrt{2}}(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})
D) \frac{1}{\sqrt{2}}(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})
107
MediumJEE Mains2019
The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x2 . If it were launched at an angle $\theta $0 with speed v0 then (g = 10 ms–2) :
Options:
A) {\theta _0} = {\cos ^{ - 1}}\left( {{1 \over {\sqrt 5 }}} \right) and {v_0} = {5 \over 3}$ ms-1
B) {\theta _0} = {\cos ^{ - 1}}\left( {{2 \over {\sqrt 5 }}} \right) and {v_0} = {3 \over 5}$ ms-1
C) {\theta _0} = {\sin ^{ - 1}}\left( {{2 \over {\sqrt 5 }}} \right) and {v_0} = {3 \over 5}$ ms-1
D) {\theta _0} = {\sin ^{ - 1}}\left( {{1 \over {\sqrt 5 }}} \right) and {v_0} = {5 \over 3}$ ms-1
108
MediumMHT CET2025
If \vec{A}=\hat{i}+\hat{j}+3 \hat{k}, \vec{B}=-\hat{i}+\hat{j}+4 \hat{k} and \vec{C}=2 \hat{i}-2 \hat{j}-8 \hat{k}, then the angle between the vectors \overrightarrow{\mathrm{P}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}+\overrightarrow{\mathrm{C}} and \overrightarrow{\mathrm{Q}}=(\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}) is (in degree)
Options:
A) 0^{\circ}
B) 45^{\circ}
C) 90^{\circ}
D) 60^{\circ}
109
MediumJEE Mains2019
A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product t1t2 is -
Options:
A) {{2R} \over g}
B) {R \over g}
C) {R \over {2g}}
D) {R \over {4g}}
110
MediumMHT CET2025
The resultant of two vectors \vec{A} and \vec{B} is \vec{C}. If the magnitude of \vec{B} is doubled, the new resultant vector becomes perpendicular to \vec{A}, then the magnitude of \overrightarrow{\mathrm{C}} is
Options:
A) 4 B
B) 3 B
C) B
D) 2 B
111
MediumJEE Mains2019
A plane is inclined at an angle $\alpha = 30° with respect to the horizontal. A particle is projected with a speed u = 2 ms–1 , from the base of the plane, making an angle \theta $ = 15° with respect to the plane as shown in the figure. the distance from the base, at which the particle hits the plane is close to : (Take g = 10 ms –2)
Options:
A) 14 cm
B) 18 cm
C) 20 cm
D) 26 cm
112
MediumMHT CET2020
The angle subtended by the vector A=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+12 \hat{\mathbf{k}} with the X-axis is
Options:
A) \cos ^{-1}\left(\frac{3}{13}\right)
B) \sin ^{-1}\left(\frac{3}{13}\right)
C) \sin ^{-1}\left(\frac{4}{13}\right)
D) \cos ^{-1}\left(\frac{4}{13}\right)
113
MediumJEE Mains2019
The stream of a river is flowing with a speed of 2km/h. A swimmer can swim at a speed of 4km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight ?
Options:
A) 150°
B) 120°
C) 60°
D) 90°
114
MediumMHT CET2020
What is the angle between resultant of A+B and \mathbf{A} \times \mathbf{B}.
Options:
A) \pi \mathrm{rad}
B) 0^{\circ}
C) \frac{\pi}{4} \mathrm{rad}
D) \frac{\pi}{2} \mathrm{rad}
115
MediumJEE Mains2019
Ship A is sailing towards north-east with velocity $\mathop v\limits^ \to = 30\mathop i\limits^ \wedge + 50\mathop j\limits^ \wedge km/hr where \mathop i\limits^ \wedge points east and \mathop j\limits^ \wedge $ , north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will be at minimum distance from B in :
Options:
A) 2.2 hrs
B) 4.2 hrs
C) 2.6 hrs
D) 3.2 hrs
116
MediumMHT CET2020
The $x, y components of vector \mathbf{P} have magnitudes 1 and 3 and x, y components of resultant of \mathbf{P} and \mathbf{Q} have magnitudes 5 and 6, respectively. What is the magnitude of \mathbf{Q}$ ?
Options:
A) 5
B) 4
C) 3
D) 2
117
MediumJEE Mains2019
A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60o with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is :
Options:
A) {{\sqrt 3 } \over 2}$v
B) {{2v} \over {\sqrt 3 }}
C) v
D) {v \over 2}
118
MediumMHT CET2020
The resultant of two vector $\mathbf{A} and \mathbf{B} is \mathbf{C}. If the magnitude of \mathbf{B} is doubled, the new resultant vector becomes perpendicular to A. Then, the magnitude of \mathbf{C}$ is
Options:
A) 2B
B) B
C) 3B
D) 4B
119
MediumJEE Mains2019
Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is -
Options:
A) 1 : 16
B) 1 : 8
C) 1 : 2
D) 1 : 4
120
MediumMHT CET2020
Two vectors of same magnitude have a resultant equal to either of the two vectors. The angle between two vectors is
Options:
A) \cos ^{-1}(-0.5)
B) \cos ^{-1}(-0.4)
C) \cos ^{-1}(-0.3)
D) \cos ^{-1}(-0.6)
121
MediumJEE Mains2019
The position co-ordinates of a particle moving in a 3-D coordinate system is given by x = a cos$\omega t y = a sin\omega t and z = a\omega $t The speed of the particle is :
Options:
A) \sqrt 2 \,a\omega
B) a\omega
C) \sqrt 3 \,a\omega
D) 2a$\omega
122
MediumMHT CET2019
The vectors (\mathbf{A}+\mathbf{B}) and (\mathbf{A}-\mathbf{B}) are at right. angles to each other. This is possible under the condition
Options:
A) |A|=|B|
B) A \cdot B=0
C) A \cdot B=1
D) A \times B=0
123
MediumJEE Mains2019
A particle is moving with a velocity $\overrightarrow v \, = K(y\widehat i + x\widehat j),$ where K is a constant. The general equation for its path is :
Options:
A) y = x2 + constant
B) y2 = x + constant
C) y2 = x2 + constant
D) xy = constant
124
MediumMHT CET2019
A vector P has X and Y components of magnitude 2 units and 4 units respectively. A vector Q along negative X-axis has magnitude 6 units. The vector (\mathbf{Q}-\mathbf{P}) will be
Options:
A) 4(2 \hat{i}-\hat{j})
B) -4(2 \hat{\mathbf{i}}-\hat{\mathrm{j}})
C) 4(2 \hat{i}+\hat{j})
D) -4(2 \hat{i}+\hat{j})
125
MediumJEE Mains2018
A man in a car at location Q on a straight highway is moving with speed $\upsilon $. He decides to reach a point P in a field at a distance d from the highway (point M) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance RM, so that the time taken to reach P is minimum ?
Options:
A) d
B) {d \over {\sqrt 2 }}
C) {d \over 2}
D) {d \over {\sqrt 3 }}
126
MediumMHT CET2019
\mathbf{P} and \mathbf{Q} are two non-zero vectors inclined to each other at an angle ' \theta '. ' p ' and ' q ' are unit vectors along \mathbf{P} and \mathbf{Q} respectively. The component of \mathbf{Q} in the direction of \mathbf{Q} will be
Options:
A) P \cdot Q
B) \frac{P \times Q}{P}
C) \frac{P \cdot Q}{Q}
D) p \cdot q
127
MediumJEE Mains2013
A projectile is given an initial velocity of $\left( {\widehat i + 2\widehat j} \right) m/s, where {\widehat i} is along the ground and {\widehat j}$ is along the vertical. If g = 10 m/s2, the equation of its trajectory is:
Options:
A) y = x - 5x2
B) y = 2x - 5x2
C) 4y = 2x - 5x2
D) 4y = 2x - 25x2
128
MediumMHT CET2019
The resultant \mathbf{R} of \mathbf{P} and \mathbf{Q} is perpendicular to \mathbf{P}. Also |\mathbf{P}|=|\mathbf{R}|. The angle between \mathbf{P} and \mathbf{Q} is \left[\tan 45^{\circ}=1\right]
Options:
A) \frac{5 \pi}{4}
B) \frac{7 \pi}{4}
C) \frac{\pi}{4}
D) \frac{3 \pi}{4}
129
MediumJEE Mains2012
A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be
Options:
A) 20\sqrt 2 $ m
B) 10 m
C) 10\sqrt 2 $ m
D) 20 m
130
MediumMHT CET2019
If \sqrt{A^2+B^2} represents the magnitude of resultant of two vectors (\mathbf{A}+\mathbf{B}) and (\mathbf{A}-\mathbf{B}), then the angle between two vectors is
Options:
A) \cos ^{-1}\left[-\frac{2\left(A^2-B^2\right)}{\left(A^2+B^2\right)}\right]
B) \cos ^{-1}\left[-\frac{A^2-B^2}{A^2 B^2}\right]
C) \cos ^{-1}\left[-\frac{\left(A^2+B^2\right)}{2\left(A^2-B^2\right)}\right]
D) \cos ^{-1}\left[-\frac{\left(A^2-B^2\right)}{A^2+B^2}\right]
131
MediumJEE Mains2011
A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is :
Options:
A) \pi {{{v^4}} \over {{g^2}}}
B) {\pi \over 2}{{{v^4}} \over {{g^2}}}
C) \pi {{{v^2}} \over {{g^2}}}
D) \pi {{{v^2}} \over g}
132
MediumVITEEE2024
The resultant of \mathbf{A} and \mathbf{B} is \mathbf{R}_1. On reversing the vector \mathbf{B}, the resultant becomes \mathbf{R}_2. What is the value of R_1^2+R_2^2 ?
Options:
A) A^2+B^2
B) A^2-B^2
C) 2\left(A^2+B^2\right)
D) 2\left(A^2-B^2\right)
133
MediumJEE Mains2010
A particle is moving with velocity $\overrightarrow v = k\left( {y\widehat i + x\widehat j} \right)$, where K is a constant. The general equation for its path is
Options:
A) y = x2 + constant
B) y2 = x + constant
C) xy = constant
D) y2 = x2 + constant
134
MediumJEE Mains2009
A particle has an initial velocity $3\widehat i + 4\widehat j and an acceleration of 0.4\widehat i + 0.3\widehat j$. Its speed after 10 s is:
Options:
A) 7\sqrt 2 $ units
B) 7 units
C) 8.5 units
D) 10 units
135
MediumJEE Mains2005
A particle is moving eastwards with a velocity of 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is
Options:
A) {1 \over 2}m{s^{ - 2}}$ towards north
B) {1 \over {\sqrt 2 }}m{s^{ - 2}}$ towards north-east
C) {1 \over {\sqrt 2 }}m{s^{ - 2}}$ towards north-west
D) zero
136
MediumJEE Mains2004
A projectile can have the same range 'R' for two angles of projection. If T1 and T2 be the time of flights in the two cases, then the product of the two time of flights is directly proportional to
Options:
A) R
B) {1 \over R}
C) {1 \over {{R^2}}}
D) {R^2}
137
MediumJEE Mains2004
A ball is thrown from a point with a speed ν0 at an angle of projection θ. From the same point and at the same instant person starts running with a constant speed ${{{v_0}} \over 2}$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection θ?
Options:
A) No
B) Yes, $30^\circ
C) Yes, $60^\circ
D) Yes, $45^\circ
138
MediumJEE Mains2003
A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of $30^\circ with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground? \left[ {g = 10m/{s^2},\sin 30^\circ = {1 \over 2},\cos 30^\circ = {{\sqrt 3 } \over 2}} \right]
Options:
A) 5.20 m
B) 4.33 m
C) 2.60 m
D) 8.66 m
139
MediumJEE Mains2025
The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the bank is __________ cm. (Take g=10 m/s2)
Options:
140
MediumJEE Mains2025
A particle is projected at an angle of 30^{\circ} from horizontal at a speed of 60 \mathrm{~m} / \mathrm{s}. The height traversed by the particle in the first second is \mathrm{h}_0 and height traversed in the last second, before it reaches the maximum height, is h_1. The ratio h_0: h_1 is __________. [Take, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 ]
Options:
141
MediumJEE Mains2024
A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of $100 \mathrm{~m} from the foot of the tower. A body of mass 2 \mathrm{~M} thrown at a velocity \frac{v}{2} from the top of the tower of height 4 \mathrm{H}$ will touch the ground at a distance of _______ m.
Options:
142
EasyJEE Mains2024
The maximum height reached by a projectile is $64 \mathrm{~m}. If the initial velocity is halved, the new maximum height of the projectile is ______ \mathrm{m}$.
Options:
143
MediumJEE Mains2024
A ball rolls off the top of a stairway with horizontal velocity $u. The steps are 0.1 \mathrm{~m} high and 0.1 \mathrm{~m} wide. The minimum velocity u with which that ball just hits the step 5 of the stairway will be \sqrt{x} \mathrm{~ms}^{-1} where x= __________ [use \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ].
Options:
144
MediumJEE Mains2024
A particle starts from origin at $t=0 with a velocity 5 \hat{i} \mathrm{~m} / \mathrm{s} and moves in x-y plane under action of a force which produces a constant acceleration of (3 \hat{i}+2 \hat{j}) \mathrm{m} / \mathrm{s}^2. If the x-coordinate of the particle at that instant is 84 \mathrm{~m}, then the speed of the particle at this time is \sqrt{\alpha} \mathrm{~m} / \mathrm{s}. The value of \alpha$ is _________.
Options:
145
MediumJEE Mains2023
A projectile fired at $30^{\circ} to the ground is observed to be at same height at time 3 \mathrm{~s} and 5 \mathrm{~s} after projection, during its flight. The speed of projection of the projectile is ___________ \mathrm{m} ~\mathrm{s}^{-1}. (Given g=10 \mathrm{~ms}^{-2}$ )
Options:
146
EasyJEE Mains2023
Two bodies are projected from ground with same speeds 40 \mathrm{~ms}^{-1} at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60^{\circ}, with horizontal then sum of the maximum heights, attained by the two projectiles, is \mathrm{m}. (Given \mathrm{g}=10 \mathrm{~ms}^{-2} )
Options:
147
EasyJEE Mains2023
The speed of a swimmer is $4 \mathrm{~km} \mathrm{~h}^{-1} in still water. If the swimmer makes his strokes normal to the flow of river of width 1 \mathrm{~km}, he reaches a point 750 \mathrm{~m} down the stream on the opposite bank. The speed of the river water is ___________ \mathrm{km} ~\mathrm{h}^{-1}
Options:
148
EasyJEE Mains2022
An object is projected in the air with initial velocity u at an angle $\theta$. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be _________ degree.
Options:
149
MediumJEE Mains2022
A ball of mass m is thrown vertically upward. Another ball of mass $2 \mathrm{~m} is thrown at an angle \theta with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is \frac{1}{x}$. The value of x is _____________.
Options:
150
MediumJEE Mains2022
If the initial velocity in horizontal direction of a projectile is unit vector $\hat{i} and the equation of trajectory is y=5 x(1-x). The y component vector of the initial velocity is ______________ \hat{j}. (\mathrm{Take} \left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)
Options:
151
EasyJEE Mains2022
A fighter jet is flying horizontally at a certain altitude with a speed of 200 ms$-1. When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle \theta with the horizontal, to hit the jet. If the bullet speed is 400 m/s, the value of \theta will be ___________^\circ$.
Options:
152
MediumJEE Mains2022
A body is projected from the ground at an angle of 45$^\circ with the horizontal. Its velocity after 2s is 20 ms-1. The maximum height reached by the body during its motion is __________ m. (use g = 10 ms-$2)
Options:
153
EasyJEE Mains2021
A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30$^\circ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle \theta with the line AB should be _________^\circ$, so that the swimmer reaches point B.
Options:
154
EasyJEE Mains2021
A person is swimming with a speed of 10 m/s at an angle of 120$^\circ$ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is 'x' m/s. The value of 'x' to the nearest integer is __________.
Options:
155
EasyJEE Mains2021
A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ____________$^\circ$. (Round off to the Nearest Integer) (Find the angle in degrees)
Options:
156
MediumJEE Mains2020
A particle is moving along the x-axis with its coordinate with the time 't' given be x(t) = 10 + 8t – 3t2. Another particle is moving the y-axis with its coordinate as a function of time given by y(t) = 5 – 8t3. At t = 1s, the speed of the second particle as measured in the frame of the first particle is given as $\sqrt v $. Then v (in m/s) is ______.
Options:
157
MediumNEET2024
A bob is whirled in a horizontal circle by means of a string at an initial speed of $10 \mathrm{~rpm}$. If the tension in the string is quadrupled while keeping the radius constant, the new speed is:
Options:
A) 20 rpm
B) 40 rpm
C) 5 rpm
D) 10 rpm
158
MediumNEET2024
Let $\omega_1, \omega_2 and \omega_3 be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If x_1, x_2 and x_3 are their respective angular distances in 1 minute then the factor which remains constant (k)$ is
Options:
A) \frac{\omega_1}{x_1}=\frac{\omega_2}{x_2}=\frac{\omega_3}{x_3}=k
B) \omega_1 x_1=\omega_2 x_2=\omega_3 x_3=k
C) \omega_1 x_1^2=\omega_2 x_2^2=\omega_3 x_3^2=k
D) \omega_1^2 x_1=\omega_2^2 x_2=\omega_3^2 x_3=k
159
MediumNEET2023
A ball is projected from point A with velocity $20 \mathrm{~m} \mathrm{~s}^{-1} at an angle 60^{\circ} to the horizontal direction. At the highest point \mathrm{B} of the path (as shown in figure), the velocity \mathrm{v} \mathrm{m} \mathrm{s}^{-1}$ of the ball will be:
Options:
A) 20
B) 10 \sqrt{3}
C) Zero
D) 10
160
MediumNEET2023
A particle is executing uniform circular motion with velocity $\vec{v} and acceleration \vec{a}$. Which of the following is true?
Options:
A) \vec{v} is a constant; \vec{a}$ is not a constant
B) \vec{v} is not a constant; \vec{a}$ is not a constant
C) \vec{v} is a constant; \vec{a}$ is a constant
D) \vec{v} is not a constant; \vec{a}$ is a constant
161
MediumNEET2023
A bullet is fired from a gun at the speed of $280 \mathrm{~ms}^{-1} in the direction 30^{\circ} above the horizontal. The maximum height attained by the bullet is \left(g=9.8 \mathrm{~ms}^{-2}, \sin 30^{\circ}=0.5\right)$:-
Options:
A) 2000 m
B) 1000 m
C) 3000 m
D) 2800 m
162
MediumNEET2023
A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity $4 \mathrm{~m} \mathrm{~s}^{-1}. The ball strikes the water surface after 4 \mathrm{~s}. The height of bridge above water surface is (Take g=10 \mathrm{~m} \mathrm{~s}^{-2}$ )
Options:
A) 60 m
B) 64 m
C) 68 m
D) 56 m
163
MediumNEET2022
A cricket ball is thrown by a player at a speed of 20 m/s in a direction 30$^\circ$ above the horizontal. The maximum height attained by the ball during its motion is (g = 10 m/s2)
Options:
A) 25 m
B) 5 m
C) 10 m
D) 20 m
164
MediumNEET2022
A ball is projected with a velocity, 10 ms$-1, at an angle of 60^\circ$ with the vertical direction. Its speed at the highest point of its trajectory will be
Options:
A) Zero
B) 5$\sqrt3 ms-$1
C) 5 ms$-$1
D) 10 ms$-$1
165
MediumNEET2021
A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle '$\theta' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, \theta$, is then given by :
Options:
A) \theta = {\sin ^{ - 1}}{\left( {{{2g{T^2}} \over {{\pi ^2}R}}} \right)^{1/2}}
B) \theta = {\cos ^{ - 1}}{\left( {{{g{T^2}} \over {{\pi ^2}R}}} \right)^{1/2}}
C) \theta = {\cos ^{ - 1}}{\left( {{{{\pi ^2}R} \over {g{T^2}}}} \right)^{1/2}}
D) \theta = {\sin ^{ - 1}}{\left( {{{{\pi ^2}R} \over {g{T^2}}}} \right)^{1/2}}
166
MediumNEET2021
A car starts from rest and accelerates at 5m/s2. At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s? (Take g = 10 m/s2)
Options:
A) 20$\sqrt 2 $ m/s, 10 m/s2
B) 20 m/s, 5 m/s2
C) 20 m/s, 0
D) 20$\sqrt 2 $ m/s, 0
167
MediumNEET2019
A particle moving with velocity $\overrightarrow V $ is acted by three forces shown by the vector triangle PQR. The velocity of the particle will :
Options:
A) remain constant
B) increase
C) decrease
D) change according to the smallest force $\overrightarrow {QR}
168
MediumNEET2019
When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60o with horizontal, it can travel a distance x1 along the plane. But when the inclination is decreased to 30o and the same object is shot with the same velocity, it can travel x2 distance. Then x1 : x2 will be :
Options:
A) 1 : $\sqrt 2
B) \sqrt 2 $ : 1
C) 1 : $\sqrt 3
D) 1 : 2$\sqrt 3
169
MediumNEET2017
The x and y coordinates of the particle at any time are x = 5t $-$ 2t2 and y = 10t respectively, where x and y are in metres and t in seconds. The acceleration of the particle at t = 2 s is
Options:
A) 5 m s$-$2
B) -4 m s-$2
C) -8 m s-$2
D) 0
170
MediumNEET2016
In the given figure, a = 15 m s$-$2 represents the total acceleration of particle moving in the clockwise direction in a circle of radius R = 2.5 m at a given instant of time. The speed of the particle is
Options:
A) 4.5 m s$-$1
B) 5.0 m s$-$1
C) 5.7 m s$-$1
D) 6.2 m s$-$1
171
MediumNEET2016
A particle moves so that its position vector is given by $\overrightarrow r = \cos \omega t\,\widehat x + \sin \,\omega t\,\widehat y, where \omega $ is a constant. Which of the following is true?
Options:
A) Velocity is perpendicular to $\overrightarrow r $ and acceleration is directed towards the origin.
B) Velocity is perpendicular to $\overrightarrow r $ and acceleration is directed away from the origin.
C) Velocity and acceleration both are perpendicular to $\overrightarrow r
D) Velocity and acceleration both are parallel to $\overrightarrow r
172
MediumNEET2016
If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is
Options:
A) 45o
B) 180o
C) 0o
D) 90o
173
MediumNEET2015
The positions vector of a particle $\overrightarrow R as a function of time is given by \overrightarrow R = 4sin(2\pi t)\widehat i + 4cos(2\pi t)\widehat j. Where R is in meters, t is in seconds and \widehat i and \widehat j$ denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?
Options:
A) Magnitude of the velocity of particle is 8 meter/second.
B) Path of the particle is a circle of radius 4 meter.
C) Acceleration vector is along $-\overrightarrow R $.
D) Magnitude of acceleration vector is ${{{v^2}} \over R}$ where v is the velocity of particle.
174
MediumNEET2015
If vectors $\overrightarrow A = \cos \omega t\widehat i + \sin \omega t\widehat j and \overrightarrow B = \cos {{\omega t} \over 2}\widehat i + \sin {{\omega t} \over 2}\widehat j$ are functions of time, then the value of t at which they are orthogonal to each other is
Options:
A) t = {\pi \over \omega }
B) t $=$ 0
C) t = {\pi \over {4\omega }}
D) t = {\pi \over {2\omega }}
175
MediumNEET2015
A ship A is moving Westwards with a speed of 10 km h$-1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h-$1. The time after which the distance between them becomes shortest, is
Options:
A) 5\sqrt 2 $ h
B) 10\sqrt 2 $ h
C) 0 h
D) 5 h
176
MediumNEET2014
A projectile is fired from the surface of the earth with a velocity of 5 m s$-1 and angle \theta with the horizontal. Another projectile fired from another planet with a velocity of 3 m s-1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in m s-2) is (Given g = 9.8 m s-$2)
Options:
A) 3.5
B) 5.9
C) 16.3
D) 110.8
177
MediumNEET2014
A particle is moving such that is position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m) at time t = 2 s and (13 m, 14 m) at time t = 5 s. Average velocity vector $\left( {{{\overrightarrow v }_{av}}} \right)$ from t = 0 to t = 5 s is
Options:
A) {1 \over 5}\left( {13\widehat i + 14\widehat j} \right)
B) {7 \over 3}\left( {\widehat i + \widehat j} \right)
C) 2\left( {\widehat i + \widehat j} \right)
D) {11 \over 5}\left( {\widehat i + \widehat j} \right)
178
MediumNEET2013
Vectors $\overrightarrow A ,\overrightarrow B and \overrightarrow C are such that \overrightarrow A .\overrightarrow B = 0 and \overrightarrow A .\overrightarrow C = 0. Then the vector parallel to \overrightarrow A $ is
Options:
A) \overrightarrow A \times \overrightarrow B
B) \overrightarrow B + \overrightarrow C
C) \overrightarrow B \times \overrightarrow C
D) \overrightarrow B and \overrightarrow C
179
MediumNEET2013
The velocity of a projectile at the initial point A is $\left( {2\widehat i + 3\widehat j} \right)$ m/s. It's velocity (in m/s) at point B is
Options:
A) 2\widehat i - 3\widehat j
B) 2\widehat i + 3\widehat j
C) -2\widehat i - 3\widehat j
D) -2\widehat i + 3\widehat j
180
MediumNEET2012
A particle has initial velocity $\left( {2\overrightarrow i + 3\overrightarrow j } \right) and acceleration \left( {0.3\overrightarrow i + 0.2\overrightarrow j } \right)$. The magnitude of velocity after 10 seconds will be
Options:
A) 9\sqrt 2
B) 5\sqrt 2
C) 5 units
D) 9 units
181
MediumNEET2012
The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is
Options:
A) \theta = tan-1\left( {{1 \over 4}} \right)
B) \theta = tan-$1(4)
C) \theta = tan-$1(2)
D) \theta $ = 45o
182
MediumNEET2011
A projectile is fired at an angle of 45o with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection, is
Options:
A) 45o
B) 60o
C) tan$-1 \left( {{1 \over 2}} \right)
D) tan$-1 \left( {{{\sqrt 3 } \over 2}} \right)
183
MediumNEET2011
A body is moving with velocity 30 m/s towards east . After 10 seconds its velocity becomes 40 m/s towards north. The average acceleration of the body is
Options:
A) 1 m/s2
B) 7 m/s2
C) \sqrt 7 $ m/s2
D) 5 m/s2
184
MediumNEET2011
A missile is fired for maximum range with an initial velocity of 20 m/s. If g = 10 m/s2, the range of the missile is
Options:
A) 40 m
B) 50 m
C) 60 m
D) 20 m
185
MediumNEET2011
A particle moves in a circle of radius 5 cm with constant speed and time period 0.2$\pi $ s. The acceleration of the particle is
Options:
A) 15 m/s2
B) 25 m/s2
C) 36 m/s2
D) 5 m/s2
186
MediumNEET2010
The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is
Options:
A) 60o
B) 15o
C) 30o
D) 45o
187
MediumNEET2010
A particle moves in x-y plane according to rule x = asin$\omega t and y = acos\omega $t. The particle follows
Options:
A) an elliptical path
B) a circular path
C) a parabolic path
D) a straight line path inclined equally to x and y-axes
188
MediumNEET2010
A particle has initial velocity $\left( {3\widehat i + 4\widehat j} \right) and has acceleration \left( {0.4\widehat j + 0.3\widehat j} \right).$ Its speed after 10 s is
Options:
A) 7 units
B) 7\sqrt 2 $ units
C) 8.5 units
D) 10 units
189
MediumNEET2010
Six vectors, $\overrightarrow a through \overrightarrow f $ have the magnitudes and directions indicated in the figure. Which of the following statements is true ?
Options:
A) \overrightarrow b + \overrightarrow c = \overrightarrow f
B) \overrightarrow d + \overrightarrow c = \overrightarrow f
C) \overrightarrow d + \overrightarrow e = \overrightarrow f
D) \overrightarrow b + \overrightarrow e = \overrightarrow f
190
MediumNEET2008
A particle shows distance - time curve as given in this figure. The maximum instaneous velocity of the particle is around the point
Options:
A) D
B) A
C) B
D) C
191
MediumNEET2007
A particle starting from the origin (0, 0) moves in a straight line in the (x, y) planes. Its coordinates at a later time are $\left( {\sqrt 3 ,3} \right)$. The path of the particle makes with the x-axes an angle of
Options:
A) 45o
B) 60o
C) 0o
D) 30o.
192
MediumNEET2007
\overrightarrow A and \overrightarrow B are two vectors and \theta is the angle between them, if \left| {\overrightarrow A \times \overrightarrow B } \right| = \sqrt 3 \left( {\overrightarrow A .\overrightarrow B } \right), the value of \theta $ is
Options:
A) 45o
B) 30o
C) 90o
D) 60o
193
MediumNEET2006
For angles of projection of a projectile at angle (45o $- \theta ) and (45o + \theta $), the horizontal range described by the projectile are in the ratio of
Options:
A) 2 : 1
B) 1 : 1
C) 2 : 3
D) 1 : 2.
194
MediumNEET2006
The vectors $\overrightarrow A and \overrightarrow B are such that \left| {\overrightarrow A + \overrightarrow B } \right| = \left| {\overrightarrow A - \overrightarrow B } \right|.$ The angle between the two vectors is
Options:
A) 45o
B) 90o
C) 60o
D) 75o
195
MediumNEET2005
If a vector $2\widehat i + 3\widehat j + 8\widehat k is perpendicular to the vector 4\widehat j - 4\widehat i + \alpha \widehat k, then the value of \alpha $ is
Options:
A) 1/2
B) -$ 1/2
C) 1
D) -$ 1.
196
MediumNEET2005
If the angle between the vectors $\overrightarrow A and \overrightarrow B is \theta , the value of the product \left( {\overrightarrow B \times \overrightarrow A } \right).\overrightarrow A $ is equal to
Options:
A) BA2sin$\theta
B) BA2cos$\theta
C) BA2sin$\theta cos\theta
D) zero.
197
MediumNEET2005
Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other in a time t, where t is
Options:
A) {a \over {\sqrt {{v^2} + {v_1}^2} }}
B) {a \over {v + {v_1}}}
C) {a \over {v - {v_1}}}
D) \sqrt {{a \over {{v^2} - {v_1}^2}}}
198
MediumNEET2004
If $\left| {\overrightarrow A \times \overrightarrow B } \right| = \sqrt 3 \overrightarrow A .\overrightarrow B then the value of \left| {\overrightarrow A + \overrightarrow B } \right|$ is
Options:
A) (A2 + b2 + AB)1/2
B) {\left( {{A^2} + {B^2} + {{AB} \over {\sqrt 3 }}} \right)^{1/2}}
C) A + B
D) (A2 + B2 + ${\sqrt 3 }$AB)1/2.
199
MediumNEET2003
The vector sum of two forces is perpendicular to their vector differences. In that case, the forces
Options:
A) are equal to each other
B) are equal to each other in magnitude
C) are not equal to each other in magnitude
D) cannot be predicted.
200
MediumNEET2002
A particle A is dropped from a height and another particle B is projected in horizontal direction with speed of 5/sec from the same height then correct statement is
Options:
A) particle A will reach at ground first with respect to particle B
B) particle B will reach at ground first with respect to particle A
C) both particles will reach at ground simultaneously
D) both particles will reach at ground with same speed.
201
MediumNEET2001
If $\left| {\overrightarrow A + \overrightarrow B } \right| = \left| {\overrightarrow A } \right| + \left| {\overrightarrow B } \right|$ then angle between A and B will be
Options:
A) 90o
B) 120o
C) 0o
D) 60o.
202
MediumNEET2001
Two particles having mass M and m are moving in a circular path having radius R and r. If their time period are same then the ratio of angular velocity will be
Options:
A) {r \over R}
B) {R \over r}
C) 1
D) \sqrt {{R \over r}}
203
MediumNEET2000
The width of river is 1 km. The velocity of boat is 5 km/hr. The boat covered the width of river in shortest time 15 min. Then the velocity of river stream is
Options:
A) 3 km/hr
B) 4 km/hr
C) \sqrt {29} $ km/hr
D) \sqrt {41} $ km/hr.
204
MediumNEET2000
A man is slipping on a frictionless inclined plane and a bag falls down from the same height. Then the velocity of both is related as
Options:
A) {v_B} > {v_m}
B) {v_B} < {v_m}
C) {v_B} = {v_m}
D) {v_B} and {v_m}$ can't be related.
205
MediumNEET2000
Two projectiles of same mass and with same velocity are thrown at an angle 60o and 30o with the horizontal, then which will remain same
Options:
A) time of flight
B) range of projectile
C) maximum height acquired
D) all of them.
206
MediumNEET2005
A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revoluations in 44 seconds, what is the magnitude and direction of acceleration of the stone ?
Options:
A) {\pi ^2}\, m s-$2 and direction along the radius towards the centre
B) {\pi ^2}\, m s-$2 and direction along the radius away from the centre
C) {\pi ^2}\, m s-$2 and direction along the tangent to the circle
D) {\pi ^2}\,/4 ms-$2 and direction along the radius towards the centre.
206
Total Questions
53
Easy
152
Medium
1
Hard
Study Tips
Before You Start
- • Review the chapter concepts thoroughly
- • Keep a notebook for important formulas
- • Practice similar problems from your textbook
- • Time yourself to improve speed
After Practice
- • Review all incorrect answers carefully
- • Watch video solutions for difficult questions
- • Make notes of common mistakes
- • Practice similar questions again later