Question 1 :
A jet airplane travelling at the speed of $500\ kmh^{-1}$ ejects the burnt gases at the speed of $1400\ kmh^{-1}$ relative to the jet airplane. The speed of burnt gases relative to stationary observer on the earth is
Question 2 :
Assertion: The trajectory of projectile is linear in $y$ and quadratic in $x$
Reason: $y$ component of trajectory is independent of $x$-component
Question 3 :
Find a vector in thedirection of $5\widehat{i}- \widehat{j}+2\widehat{k}$ which has magnitude 8 units.<br>
Question 4 :
Two boats A and B having same speed relative to river are moving ina river. Boat A moves normal to the river current as observed by an observer moving with velocity of river current.Boat B moves normal to the river as observed by the observer on the ground.
Question 5 :
The vector in the direction of the vector $\hat i-2\hat j +2\hat k$ that has magnitude $9$ is
Question 6 :
If $|a|=5.|\vec{b}|=4$, and $|c|=3$. then what will be the value of $\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}$ given that $\vec{a}+\vec{b}+\vec{c}=0$
Question 7 :
Unit vector parallel to the resultant of vectors $\displaystyle \vec{A}= 4\hat{i}-3\hat{j}\:and\:\vec{B}= 8\hat{i}+8\hat{j}$ will be
Question 8 :
What is the torque of the force $\vec F=(2\hat i -3\hat j+4\hat k)N$, acting at the point $\vec r=(3\hat i+2\hat j+3\hat k)m$ about the origin (in $N-m$):
Question 10 :
Find the unit vectors perpendicular to each of the following pairs of vectors:<div>$2i +k$,<div>$i+j+k$<br/></div></div>
Question 11 :
If $\overline {A} \times\overline {B} =\overline {C}$ which of the following statement is not correct?
Question 12 :
A particle has an initial velocity of $3\hat i + 4\hat j$ and an acceleration of $0.4\hat i + 0.3\hat j$. The magnitude of its velocity after $10\ s$ is
Question 13 :
If the position vectors of three points $A, B, C$ are $\hat{i}+\hat{j}+\hat{k},\ 2\hat{i}+3\hat{j}-4\hat{k}$ and $3\hat{i}+2\hat{j}+\hat{k}$ respectively, then the unit vector perpendicular to the plane of the triangle $ABC$ is<br/>
Question 14 :
A unit vector perpendicular to the lines $\cfrac{x+1}{3}=\cfrac{y+2}{1}=\cfrac{z+1}{2}$ and $\cfrac{x-2}{1}=\cfrac{y+2}{2}=\cfrac{z-3}{3}$ is
Question 15 :
An aeroplane flying at a constant speed releases a bomb. As the bomb moves away from the aeroplane, it will
Question 16 :
The unit vector in the direction of the vector $\vec {a} + 2\vec {b} - \vec {c}$ is equal to
Question 17 :
A car A is going north east at 80 kmh-1 and another car B is going south east with a velocity of ${ 60kmh }^{ -1 }$. the velocity of A relative to B makes an angle with the north equal to:
Question 18 :
lf $\vec{\mathrm{A}},\vec{\mathrm{B}}$ and $\vec{\mathrm{C}}$ are non-zero vectors, and if $\vec{\mathrm{A}}\times\vec{\mathrm{B}}= 0$ and $\vec{\mathrm{B}}\times\vec{\mathrm{C}}= 0$, then the value of $\vec{\mathrm{A}}\times\vec{\mathrm{C}}$ is:<br/>
Question 19 :
A unit vector perpendicular to the plane of $\overrightarrow { a } =2\hat { i } -6\hat { j } -3\hat { k }$, $ \overrightarrow { b } =4\hat { i } +3\hat { j } -\hat { k } $ is
Question 20 :
<p> A circular platform is mounted on a frictionless vertical axle. Its radius R=2m and its moment of inertia about the axle is $200kg{m^2}$. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of $1m{s^{ - 1}}$ relative to the ground. Time taken by the man to compete one revolution with respect to disc is:</p>
Question 21 :
Two particles are moving with velocities $v_1$ and $v_2$.Their relative velocity is the maximum, when the angle between their velocities is:
Question 22 :
A particle is dropped from height 100 m and another particle is projected vertically up with velocity 50 m/s from the ground along the same line. Find out the height where two particle will meet? (take g = 10 $m/s^2$)
Question 23 :
A body is projected vertically upwards with a velocity of $19.6 \ m/s$. The total time for which the body will remain in the air is (Take $g = 9.8 m/s^2$)
Question 24 :
Two vectors $ \overrightarrow P $ and $ \overrightarrow Q $ are inclined to each other at angle $ \theta $ . Which of the following is the unit vector perpendicular to $ \overrightarrow P $ and $ \overrightarrow Q. $<br>
Question 25 :
If a, b, c are position vectors of the vertices of a $\displaystyle \Delta ABC,$ then $ \displaystyle \overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}=$
Question 26 :
If $\displaystyle \vec{a}$ and $\vec{b}$ are two vectors then the value of $\displaystyle \left ( \vec{a}+\vec{b} \right )\times \left ( \vec{a}-\vec{b} \right )$ is:
Question 27 :
What is the equation of parabolic trajectory of a projectile? ($\theta=$ angle between the projectile motion and the horizontal)
Question 28 :
Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes with same speed. A man cycling with speed of 20km/h in the direction A to B, notices that a bus goes past him every ${ t }_{ 1 }$=18 minutes in the direction of motion, and every ${ t }_{ 2 }$=6 minutes in the opposite direction. What is the period T of the bus service? Assume that velocity of cyclist is less than velocity of bus.
Question 29 :
A person is at a distance $x$ from a bus when the bus begins to move with a constant acceleration $a$ .What is the minimum velocity with which the person should run towards the bus so as to catch it ?
Question 30 :
Let the position vectors of the points $P$ and $Q$ be $4 \hat i + \hat j + \lambda \hat k$ and $2 \hat i - \hat j + \lambda \hat k$, respectively. Vector $\hat i - \hat j + 6 \hat k$ is perpendicular to the plane containing the origin and the points $P$ and $Q$. Then $\lambda$ equals
Question 31 :
Assertion: Statement-I : The angle between vectors $\vec{A}\times\vec{B}$ and $\vec{B}\times\vec{A}$ is $\pi$ radian. <br> Because
Reason: Statement-II : $\vec{B}\times\vec{A}=-\vec{A}\times\vec{B}$
Question 32 :
<div>Given $ \overrightarrow{F}=(4\widehat{i}+10\widehat{j})$ and $\overrightarrow{r}=(5\widehat{i}-3\widehat{j}).$ Then torque $\tau $ is :<br/></div>
Question 33 :
lf a body starts with a velocity $2\hat{i}-3\hat{j}+11\hat{k}\;m\mathrm{s}^{-1}$ and moves with an acceleration of $10\hat{i}+10\hat{j}+10\hat{k}\; ms^{-2}$ then its velocity after $0.25$ s will be:<br>
Question 34 :
A vector has co-ordinates $(1,1,2)$ for initial point and $(2,1,3)$ as the terminal point. The length of the vector is
Question 35 :
Two bodies are projected simultaneously from the same point, in the same vertical plane, one towards east and other towards west with velocities $8ms^{-1}$and $2ms^{-1}$ respectively. The time at which their velocities are perpendicular to each other is
Question 36 :
A vector $\bar{F}_{1}$ is along the positive x- axis. If its cross product with another vector $\bar{F}_{2}$ is zero, then $\bar{F}_{2}$ could be:
Question 37 :
What are the speeds of two objects if they move uniformly towards each other, they get 4m closer in each second and if they move uniformly in the same direction with the original speeds they get 4m closer in each 10 sec ?
Question 38 :
The unit vector perpendicular to the plane determined by $P(1, -1, 2)$, $Q(2, 0, -1)$, $R(0, 2, 1)$ is
Question 39 :
A boat is sailing at a velocity $3\hat{i}+4\hat{j}$ with respect to ground and water in river is flowing with a velocity $-3\hat{i}-4\hat{j}$. Relative velocity of the boat with respect to water is :-
Question 40 :
A steamer is moving due east with $10 km/h$. To a man in the steamer the wind appears to blow at $5 km/h$ due north. Find the velocity of the wind.
Question 41 :
Ramu and Somu are running towards north with 3 m/s and 4 m/s. Their friend Srinu is running towards south with 2 m/s. Then the magnitude of relative velocity of Somu w.r.t Ramu
Question 42 :
The plane which can be formed with the vectors $\overline{a}=3\overline{i}-4\overline{j}+2\overline{k},\ \overline{b}=2\overline{i}-\overline{j}-6\overline{k}$,$\overline{c}=5\overline{i}-5\overline{j}-4\overline{k}$ is<br/>
Question 43 :
Two trains, each 50m long are travelling in opposite direction with velocity 10 m/s and 15 m/s The time of crossing is:-
Question 44 :
The vector $\overset{-}{A}=0.4 \hat {i}+0.8 \hat {j}+c \hat {k}$ represents a unit vector, then $c$ must be:
Question 45 :
A mosquito flies from the hole in a mosquito net top corner diametrically opposite. If the net is $3 \times 2 \times 2 \: m$ then the displacement of the mosquito is:<p></p>
Question 46 :
A unit vector along the direction $\hat i + \hat j + \hat k$ has a magnitude:
Question 47 :
If a vector has an x-component of -25 units and a y-component of 40 units, then the magnitude and direction of this vector are:
Question 48 :
If two vectors $2\hat{i}+3\hat{j}-\hat{k}$ and $-4\hat{i}-6\hat{j}-\lambda \hat{k}$ are parallel to each other then value of $\lambda$ be
Question 49 :
Which of the following algebraic operations with scalar and vector physical quantities are meaningful.<div><br/>(i) adding any two vectors<br/>(ii) adding a scalar to a vector of the same dimensions<br/>(iii) multiplying any vector by any scalar<br/>(iv) multiplying any two scalars<br/>(v) adding any two scalars<br/>(vi) adding a component of a vector to the same vector.</div>
Question 50 :
Study the following<div><br/> List - I List - II<br/> <table class="wysiwyg-table"><tbody><tr><td>a) Horizontal motion of a projectile<br/></td><td>e) zero velocity</td></tr><tr><td>b) Freely falling body <br/></td><td>f) retarded motion from <br/>a small height<br/></td></tr><tr><td>c) Parachutist<br/></td><td>g) uniform descending down<br/> acceleration.<br/></td></tr><tr><td>d) Maximum height of a body thrown<br/>vertically up<br/></td><td>h) uniform velocity<br/><br/></td></tr></tbody></table><br/></div><div>The correct match is<br/></div>