Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: The solution set of the equation $\left|\begin{array}{ccc}x-2 2 x-3 3 x-4 \\ x-4 2 x-9 3 x-16 \\ x-8 2 x-27 2 x-64\end{array}\right|=0$ is A. $\{4\}$ B. $\{2,4\}$ C. $\{2,8\}$ D. $\{4,8\}$ Solution: To find: Value of $x$...
Read More →Six particles situated at the corners of a regular hexagon
Question: Six particles situated at the corners of a regular hexagon of side a move at a constant speed v. Each particle maintains a direction towards the particle at the next corner. Calculate the time the particle will take to meet each other. Solution: Relative velocity $=\mathrm{v}-\mathrm{v} \cos \theta$...
Read More →Suppose A and B in the previous problem
Question: Suppose A and B in the previous problem change their positions in such a way that the line joining them becomes perpendicular to the direction of wind while maintaining the separation $x$. What will be the time lad $B$ finds between seeing and hearing the drum beating by $A$ ? Solution: Let $v$ be the velocity of sound along direction $\mathrm{AC}$ so it can reach $\mathrm{B}$ with resultant velocity $\mathrm{AD}$ Velocity along $A B=\sqrt{V^{2}-U^{2}}$ Time $=\frac{\text { distance }}...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: The solution set of the equation $\left|\begin{array}{ccc}\mathrm{x} 3 7 \\ 2 \mathrm{x} 2 \\ 7 6 \mathrm{x}\end{array}\right|=0$ is A. $\{2,-3.7\}$ B. $\{2,7,-9\}$ C. $[-2,3,-7\}$ D. none of these Solution:...
Read More →Two friends A and B are standing a distance x
Question: Two friends $A$ and $B$ are standing a distance $x$ apart in an open field and wind is blowing from $A$ to $B$. A beats a drum and $B$ hears the sound $t_{1}$ time after he sees the event. $A$ and $B$ interchange their positions and the experiment is repeated. This time $B$ hears the drum $\mathrm{t}_{2}$ time after he sees the event. Calculate the velocity of sound in still air $v$ and the velocity of win $u$. Neglect the time light takes in travelling between the friends. Solution: I...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: If $\left|\begin{array}{ccc}5 3 -1 \\ -7 x 2 \\ 9 6 -2\end{array}\right|=0$ then $x=?$ A. 0 B. 6 C. $-6$ D. 9 Solution: To find: Value of $x$...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{ccc}x+1 x+2 x+4 \\ x+3 x+5 x+8 \\ x+7 x+10 x+14\end{array}\right|=?$ A. $-2$ B. 2 C. $x^{2}-2$ D. $x^{2}+2$ Solution:...
Read More →An aero plane has to go from point A
Question: An aero plane has to go from point $A$ to another point $B, 500 \mathrm{~km}$ away due to $30^{\circ}$ east of north. A wind is blowing due north at a seed of $20 \mathrm{~m} / \mathrm{s}$. The air speed of the plane is $150 \mathrm{~m} / \mathrm{s}$. (a) Find the direction in which the pilot should head the plane to reach the point $B$. (b) Find the time taken by the plane to gr from $A$ to $B$. Solution: (a)...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{lll}a 1 b+c \\ b 1 c+a \\ c 1 a+b\end{array}\right|=?$ A. $a+b+c$ B. $2(a+b+c)$ C. $4 a b c$ D. $a^{2} b^{2} c^{2}$ Solution:...
Read More →Consider the situation of the previous problem.
Question: Consider the situation of the previous problem. The man has to reach the other shore at the point directly opposite to his starting point. If he reaches the other shore somewhere else, he has to walk down to this point, Find the minimum distance that he has to walk. Solution:...
Read More →A swimmer wishes to cross
Question: A swimmer wishes to cross $500 \mathrm{~m}$ wide river flowing at $5 \mathrm{~km} / \mathrm{h}$. His speed with respect to water is 3 $\mathrm{km} / \mathrm{h}$. (a) If he heads in a direction making an angle $\theta$ with the flow, find the time he takes to cross the river. (b) Find the shortest possible time to cross the river. Solution: (a) Velocity responsible for crossing $=3 \sin \theta \mathrm{kmph}$ $=3 \times \frac{5}{18} \sin \theta$ Time to cross= distance/speed $=\frac{500 ...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{ccc}\mathrm{b}+\mathrm{c} \mathrm{a} \mathrm{a} \\ \mathrm{b} \mathrm{c}+\mathrm{a} \mathrm{b} \\ \mathrm{c} \mathrm{c} \mathrm{a}+\mathrm{b}\end{array}\right|=?$ A. $4 a b c$ B. $2(a+b+c)$ C. $(a b+b c+c a)$ D. none of these Solution:...
Read More →A river 400 wide is flower at a rate of
Question: A river $400 \mathrm{~m}$ wide is flowing at a rate of $2.0 \mathrm{~m} / \mathrm{s}$. A boat is sailing at a velocity of $10 \mathrm{~m} / \mathrm{s}$ with respect to the water, in a direction perpendicular to the river. (a) Find the time taken by the boat to reach the opposite bank. (b) How far from the point directly opposite to the starting point does the boat reach the opposite bank? Solution:...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{lll}b c b+c 1 \\ c a c+a 1 \\ a b a+b 1\end{array}\right|=?$ A. $(a-b)(b-c)(c-a)$ B. $-(a-b)(b-c)(c-a)$ C. $(a+b)(b+c)(c+a)$ D. None of these Solution:...
Read More →One man is sitting on the shores of a river.
Question: One man is sitting on the shores of a river. He is in the line of $1.0 \mathrm{~m}$ long boat and is $5.5 \mathrm{~m}$ away from the center of the boat. If he can throw the apply only with a speed of $10 \mathrm{~m} / \mathrm{s}$. find the minimum and maximum angles of projection for successful shot. Assume that the point of projection and the edge pf the boat are in the same horizontal level. Solution: For near point of boat $\mathrm{R}=5 \mathrm{~m}=\frac{\mathrm{u}^{\mathrm{m}} \sin...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{ccc}1 1 1 \\ 1 1+x 1 \\ 1 1 1+y\end{array}\right|=?$ A. $(x+y)$ B. $(x-y)$ C. $x y$ D. none of these Solution:...
Read More →The benches of a gallery in a cricket stadium
Question: The benches of a gallery in a cricket stadium are $1 \mathrm{~m}$ wide and $1 \mathrm{~m}$ high. A batsman strikes the ball at a level one metre above the ground and hits a mammoth sixer. The ball starts at $35 \mathrm{~m} / \mathrm{s}$ at an angle of $53^{\circ}$ with the horizontal. The benches are perpendicular to the place of motion and the first bench is $110 \mathrm{~m}$ from the batsman on which bench hwill the ball hit? Solution:...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{lll}b+c a b \\ c+a c a \\ a+b b c\end{array}\right|=?$ A. $(a+b+c)(a-c)$ B. $(a+b+c)(b-c)$ C. $(a+b+c)(a-c)^{2}$ D. $(a+b+c)(b-c)^{2}$ Solution:...
Read More →A person is standing on a truck moving with a constant velocity
Question: A person is standing on a truck moving with a constant velocity of $14.7 \mathrm{~m} / \mathrm{s}$ on a horizontal road. The man throws a ball in such a way that it returns to the truck after the truck has moved $58.8 \mathrm{~m}$. Find the speed and the angle of projection (a) as seen from the truck, (b) as seen from the road. Solution: Time taken by ball=Time taken by truck to cover $58.8 \mathrm{~m}$ Time $=\frac{\text { distance }}{\text { speed }}=\frac{58.8}{14.7}=4 \mathrm{sec}$...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{ccc}a a+2 b a+2 b+3 c \\ 3 a 4 a+6 b 5 a+7 b+9 c \\ 6 a 9 a+12 b 11 a+15 b+18 c\end{array}\right|=?$ A. $a^{3}$ B. $-a^{3}$ C. 0 D. none of these Solution:...
Read More →A staircase contains three steps each
Question: A staircase contains three steps each $10 \mathrm{~cm}$ high and $20 \mathrm{~cm}$ wide as shown in figure. What should be the minimum horizontal velocity of a hall rolling off the uppermost plane so as to hit directly the lowest plane? Solution: For minimum velocity ball will just be touching point B If $A$ is origin then coordinates of $B(40,-20)$ $Y=x \tan \theta-\frac{1}{2} \frac{x^{\mathrm{a}}}{g^{u^{2} \cos ^{2} \theta}}$ $-20=40 \tan 0^{\circ}-\frac{1}{2} \frac{\mathrm{g}(40)^{2...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{ccc}a^{2}+2 a 2 a+1 1 \\ 2 a+1 a+2 1 \\ 3 3 1\end{array}\right|=?$ A. $(a-1)$ B. $(a-1)^{2}$ C. $(a-1)^{3}$ D. none of these Solution: $\Rightarrow(\mathrm{a}-1)^{3}$...
Read More →A boy is standing on a long railroad car throws a ball straight upwards.
Question: A boy is standing on a long railroad car throws a ball straight upwards. The car is moving on the horizontal road with an acceleration of $1 \mathrm{~m} / \mathrm{s}^{2}$ and the projection velocity in the vertical direction is $9.8$ $\mathrm{m} / \mathrm{s}$. How far behind the boy will the ball fall on the car? Solution: $=\frac{2 \mathrm{usin} \theta}{\mathrm{g}}$ $=\frac{2(9.8) \sin 90^{\prime}}{\mathrm{g}}$ $t=2 s e c$ For ball-car, along horizontal direction $u_{\text {rel }}=0$ ...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{ccc}x+y x x \\ 5 x+4 y 4 x 2 x \\ 10 x+8 y 8 x 3 x\end{array}\right|=?$ A. 0 B. $x^{3}$ C. $\mathrm{y}^{3}$ D. none of these Solution:...
Read More →A bomb is dropped from a plane flying horizontally
Question: A bomb is dropped from a plane flying horizontally with uniform speed, Show that the bomb will explode vertically below the plane. Is the statement true if the plane flies with uniform speed but not horizontally? Solution:...
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