Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: If $a, b, c$ be distinct positive real numbers then the value of $\left|\begin{array}{lll}a b c \\ b c a \\ c a b\end{array}\right|$ is A. positive B. negative C. a perfect square D. 0 Solution:...
Read More →Find the average velocity of a projectile between
Question: Find the average velocity of a projectile between the instants it crosses half the maximum height. It is projected with a speed $u$ at an angle $\theta$ with the horizontal Solution:...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{ccc}\sin \alpha \cos \alpha \sin (\alpha+\delta) \\ \sin \beta \cos \beta \sin (\beta+\delta) \\ \sin \gamma \cos \gamma \sin (\gamma+\delta)\end{array}\right|=?$ A. 0 B. 1 C. $\sin (\alpha+\delta)+\sin (\beta+\delta)+\sin (\gamma+\delta)$ D. none of these Solution:...
Read More →A ball is projected from a point on the floor with
Question: A ball is projected from a point on the floor with a speed of $12 \mathrm{~m} / \mathrm{s}$ at an angle 60 with the horizontal, Will it hit a vertical wall $5 \mathrm{~m}$ away from the point of projection and perpendicular to the plane of projection without hitting the floor? Will the answer differ if the wall is $22 \mathrm{~m}$ away? Solution: $\mathrm{R}=\frac{\mathrm{u}^{2} \sin 2 \theta}{\mathrm{g}}$ $=\frac{(15)^{2} \sin (2 x 60)}{9.8}$ $R=19.88 \mathrm{~m}$ Ball will hit $5 \ma...
Read More →A person standing on top of a cliff
Question: A person standing on top of a cliff $171 \mathrm{ft}$ high has to throw a packet to his friend standing on the ground $228 \mathrm{ft}$ horizontally away. If he throws the packet directly aiming at the friend with a speed of $15.0 \mathrm{ft} / \mathrm{s}$, how short will the packet fall? Solution: $\operatorname{Tan}_{\theta=53^{\circ}} \theta=228 / 171=4 / 3$ $x$-axis $y$-axis $u_{x}=15 \sin 53 u_{y}=15 \cos 53$ $u_{x}=12 \mathrm{ft} /$ sec $u_{y}=9 \mathrm{ft} / \mathrm{sec}$ $\math...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{ccc}1 1 1 \\ a b c \\ a^{3} b^{3} c^{3}\end{array}\right|=?$ A. $(a-b)(b-c)(c-a)$ B. $-(a-b)(b-c)(c-a)$ C. $(a-b)(b-c)(c-a)(a+b+c)$ D. $a b c(a-b)(b-c)(c-a)$ Solution:...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{ccc}1 1+p 1+p+q \\ 2 3+2 p 1+3 p+2 q \\ 3 6+3 p 1+6 p+3 q\end{array}\right|=?$ A. 0 B. 1 C. $-1$ D. none of these Solution:...
Read More →The given figure shows a 11.7 ft wide ditch with
Question: The given figure shows a $11.7 \mathrm{ft}$ wide ditch with the approach roads at tan angle of $15^{\circ}$ with the horizontal. With what minimum speed should a motorbike be moving on the roads so that it safely crosses the ditch? Assume that the length of the bike is $5 \mathrm{ft}$ and it leaves the road when the front part runs out of the approach road. Solution: Range to be covered by bike $=11.7+5=16.7 \mathrm{ft}$ $\mathrm{R}=\frac{\frac{\mathrm{u}}{\sin 2 \theta}}{2 \mathrm{~g}...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{lll}a-b b-c c-a \\ b-c c-a a-b \\ c-a a-b b-c\end{array}\right|=?$ A. $(a+b+c)$ B. $3(a+b+c)$ C. $3 a b c$ D. 0 Solution: If every element of a row is 0 then the value of the determinant will be 0...
Read More →A popular game in Indian villages is goli which is played with
Question: A popular game in Indian villages is goli which is played with small glass balls called golis. The goli of one player is situated at a distance of $2.0 \mathrm{~m}$ from the goli of the second player. The second player has to project his goli by keeping the thumb of the left hand at the place of his goli, holding the goli between his two middle fingers and making the throw. If the projected goli hits the goli of the first player, the second player wins. If the height from which the gol...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{lll}1 ! 2 ! 3 ! \\ 2 ! 3 ! 4 ! \\ 3 ! 4 ! 5 !\end{array}\right|=?$ A. 2 B. 6 C. 24 D. 120 Solution: . $\Rightarrow 24$...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{ccc}1^{2} 2^{2} 3^{2} \\ 2^{2} 3^{2} 4^{2} \\ 3^{2} 4^{2} 5^{2}\end{array}\right|=?$ A. 8 B. $-8$ C. 16 D. 142 Solution:...
Read More →In a soccer practice session the football is kept
Question: In a soccer practice session the football is kept at the center of the field 40 yards from the $10 \mathrm{ft}$ goalposts. A goal is attempted by kicking the football at a speed of $64 \mathrm{ft} / \mathrm{s}$ at an angle of $45^{\circ}$ to the horizontal. Will the ball reach the goal post? Solution: $\mathrm{y}=\mathrm{x} \tan \theta-\frac{1}{2} \mathrm{~g} \frac{\mathrm{x}^{\mathrm{2}}}{\mathrm{u}^{2} \cos ^{2} \mathrm{e}}$ $=(40 \times 3) \tan 45^{-\frac{1}{2}} \frac{(32)(40 \times...
Read More →A ball is thrown at a speed of
Question: A ball is thrown at a speed of $40 \mathrm{~m} / \mathrm{s}$ at an angle of $60^{\circ}$ with the horizontal. Find (a) The maximum height reached (b) The range of the ball Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ Solution: (a) $a x=\frac{\mathrm{u}^{2} \sin 2 \theta}{2 \mathrm{~g}}=\frac{40^{2}\left(\sin ^{2} 60\right)}{2 \mathrm{~g}}$ $\mathrm{H}_{\max }=60 \mathrm{~m}$ (b) $R=\frac{\mathrm{u}^{2} \sin 2 \theta}{\mathrm{g}}=\frac{40^{\mathrm{a}} \sin (2 \mathrm{x} 60)}{\mathr...
Read More →A ball is thrown horizontally from a point
Question: A ball is thrown horizontally from a point $100 \mathrm{~m}$ above the ground with a speed of $20 \mathrm{~m} / \mathrm{s}$ Find (a) The time it takes to reach the ground (b) The horizontal distance it travels before reaching the ground (c) The velocity (direction and magnitude) with which it strikes the ground. Solution: $x$-axis $y$-axis $u_{x}=20 \mathrm{~m} / \mathrm{s} u_{y}=0 \mathrm{~m} / \mathrm{s}$ $a_{x}=0 \mathrm{~m} / \mathrm{s}^{2} a_{y}=\mathrm{gm} / \mathrm{s}^{2}$ $\mat...
Read More →An elevator is descending with uniform acceleration.
Question: An elevator is descending with uniform acceleration. To measure the acceleration a person in the elevator drops a coin at the moment the elevator starts. The coin is $6 \mathrm{ft}$ above the floor of the elevator at the time it is dropped, The person observes that the coin strikes the floor in 1 second. Calculate from these data the acceleration of the elevator. Solution: For coin-lift $u_{\text {rel }}=0 \mathrm{~m} / \mathrm{s}$ $t_{\text {rel }}=1 \mathrm{sec}$ $\mathrm{S}_{\mathrm...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: If $\omega$ is a complex cube root of unity then the value of $\left|\begin{array}{ccc}1 \omega 1+\omega \\ 1+\omega 1 \omega \\ \omega 1+\omega 1\end{array}\right|$ is A. 2 B. 4 C. 0 D. $-3$ Solution:...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: If $\omega$ is a complex root of unity then $\left|\begin{array}{ccc}1 \omega \omega^{2} \\ \omega \omega^{2} 1 \\ \omega^{2} 1 \omega\end{array}\right|=?$ A. 1 B. $-1$ C. 0 D. none of these Solution:...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{cc}a+i b c+i d \\ -c+i d a-i d\end{array}\right|=?$ A. $\left(a^{2}+b^{2}-c^{2}-d^{2}\right)$ B. $\left(a^{2}-b^{2}+c^{2}-d^{2}\right)$ C. $\left(a^{2}+b^{2}+c^{2}+d^{2}\right)$ D. none of these Solution:...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{cc}\sin 23^{\circ} -\sin 7^{\circ} \\ \cos 23^{\circ} \cos 7^{\circ}\end{array}\right|=?$ A. $\frac{\sqrt{3}}{2}$ B. $\frac{1}{2}$ C. $\sin 16^{\circ}$ D. $\cos 16^{\circ}$ Solution:...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{cc}\cos 15^{\circ} \sin 15^{\circ} \\ \sin 15^{\circ} \cos 15^{\circ}\end{array}\right|=?$ A. 1 B. $\frac{1}{2}$ C. $\frac{\sqrt{3}}{2}$ D. none of these Solution:...
Read More →Mark the tick against the correct answer in the following:
Question: Mark the tick against the correct answer in the following: $\left|\begin{array}{cc}\cos 70^{\circ} \sin 20^{\circ} \\ \sin 70^{\circ} \cos 20^{\circ}\end{array}\right|=?$ A. 1 B. 0 C. $\cos 50^{\circ}$ D. $\sin 50^{\circ}$ Solution:...
Read More →A ball is dropped from a height of
Question: A ball is dropped from a height of $5 \mathrm{~m}$ onto a sandy floor and penetrates the sand up to $10 \mathrm{~cm}$ before coming to rest. Find the retardation of the ball in sand assuming it to be uniform. Solution:...
Read More →A ball is dropped from a height.
Question: A ball is dropped from a height. If it takes $0.200 \mathrm{~s}$ to cross the last $6.00 \mathrm{~m}$ before hitting the ground, find the height from which it was dropped. Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ Solution:...
Read More →Solve this following
Question: If the points $\mathrm{A}(\mathrm{a}, 0), \mathrm{B}(0, \mathrm{~b})$ and $\mathrm{C}(1,1)$ are collinear, prove that $\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{~b}}=1$. Solution:...
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