Which of the following figures represents uniform motion of a moving object correctly?
Question: Which of the following figures represents uniform motion of a moving object correctly? Solution: (a) Explanation: For uniform motion, distance $^{\infty}$ time....
Read More →Four cars A, B, C and D are moving on a levelled road.
Question: Four cars $A, B, C$ and $D$ are moving on a levelled road. Their distance versus time graphs are shown in Fig. 2 Choose the correct statement $Q$ (a) Car A is faster than car D (b) Car B is the slowest (c) Car $D$ is faster than car $C$ (d) Car $\mathrm{C}$ is the slowest. Solution: (b) Explanation: Slope of distance - time graph = speed of object....
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Question: $\left\{\frac{\cos 65^{\circ}}{\sin 25^{\circ}}+\frac{\operatorname{cosec} 34^{\circ}}{\sec 56^{\circ}}-\frac{2 \cos 43^{\circ} \operatorname{cosec} 47^{\circ}}{\tan 10^{\circ} \tan 40^{\circ} \tan 50^{\circ} \tan 80^{\circ}}\right\}$ Solution: $\left\{\frac{\cos 65^{\circ}}{\sin 25^{\circ}}+\frac{\operatorname{cosec} 34^{\circ}}{\sec 56^{\circ}}-\frac{2 \cos 43^{\circ} \operatorname{cosec} 47^{\circ}}{\tan 10^{\circ} \tan 40^{\circ} \tan 50^{\circ} \tan 80^{\circ}}\right\}$ $=\left\{\...
Read More →Find x, y, a and b if
Question: Findx,y,aandbif (i) $\left[\begin{array}{ccc}2 x-3 y a-b 3 \\ 1 x+4 y 3 a+4 b\end{array}\right]=\left[\begin{array}{ccc}1 -2 3 \\ 1 6 29\end{array}\right]$ Solution: Since the corresponding elements of two equal matrices are equal, $\left[\begin{array}{ccc}2 x-3 y a-b 3 \\ 1 x+4 y 3 a+4 b\end{array}\right]=\left[\begin{array}{ccc}1 -2 3 \\ 1 6 29\end{array}\right]$ $\Rightarrow 2 x-3 y=1$ ....(1) $x+4 y=6$ $\Rightarrow x=6-4 y$ .....(2) Putting the value of $x$ in eq. (1), we get $2(6-...
Read More →Area under a v-t graph represents
Question: Area under a $v-t$ graph represents a physical quantity which has the unit (a) $m^{2}$ (b) $m$ (c) $m^{3}$ (d) $m s^{-1}$ Solution: (b) Explanation: Area $=v \times t=(m / s) \times s=m$....
Read More →Suppose a boy is enjoying a ride on a merry-go-round
Question: Suppose a boy is enjoying a ride on a merry-go-round which is moving with a constant speed of $10 \mathrm{~m} \mathrm{~s}^{-1}$. It implies that the boy is (a) at rest (b) moving with no acceleration (c) in accelerated motion (d) moving with uniform velocity. Solution: (c) Explanation: Velocity of the boy changes continuously due to the change in direction of motion in circular path,...
Read More →From the given u -t graph (Fig. 1), it can be inferred that the object is
Question: From the given u -t graph (Fig. 1), it can be inferred that the object is (a) in uniform motion (b) at rest (c) in non-uniform motion (d) moving with uniform acceleration. Solution: (a) Explanation: Velocity of object is constant....
Read More →If the displacement of an object is proportional to square of time,
Question: If the displacement of an object is proportional to square of time, then the object moves with (a) uniform velocity (b) uniform acceleration (c) increasing acceleration (d) decreasing acceleration. Solution:...
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Question: $\left\{\frac{\sin ^{2} 22^{\circ}+\sin ^{2} 68^{\circ}}{\cos ^{2} 22^{\circ}+\cos ^{2} 68^{\circ}}+\sin ^{2} 63^{\circ}+\cos 63^{\circ} \sin 27^{\circ}\right\}$ Solution: $\left\{\frac{\sin ^{2} 22^{\circ}+\sin ^{2} 68^{\circ}}{\cos ^{2} 22^{\circ}+\cos ^{2} 68^{\circ}}+\sin ^{2} 63^{\circ}+\cos 63^{\circ} \sin 27^{\circ}\right\}$ $=\left\{\frac{\left(\sin \left(90^{\circ}-68^{\circ}\right)\right)^{2}+\sin ^{2} 68^{\circ}}{\cos ^{2} 22^{\circ}+\cos ^{2} 68^{\circ}}+\sin ^{2} 63^{\circ...
Read More →The numerical ratio of displacement to distance for a moving object is
Question: The numerical ratio of displacement to distance for a moving object is (a) always less than 1 (b) always equal to 1 (c) always more than 1 (d) equal or less than 1 Solution: (d) Explanation : Displacement $\leq$ distance....
Read More →A body is thrown vertically upward with velocity u,
Question: A body is thrown vertically upward with velocity u, the greatest height $h$ to which it will rise is, Solution: (b) Explanation: $u^{2}-v^{2}=-2 g h$ or $0-u^{2}=-2 g h$ ( $\therefore u=0$ at highest point). $\therefore h=u^{2} / 2 g$....
Read More →Solve the following Question
Question: Find $x, y, a$ and $b$ if $\left[\begin{array}{ccc}3 x+4 y 2 x-2 y \\ a+b 2 a-b -1\end{array}\right]=\left[\begin{array}{rrr}2 2 4 \\ 5 -5 -1\end{array}\right]$ Solution: Since the corresponding elements of two equal matrices are equal, $\left[\begin{array}{ccc}3 x+4 y 2 x-2 y \\ a+b 2 a-b -1\end{array}\right]=\left[\begin{array}{ccc}2 2 4 \\ 5 -5 -1\end{array}\right]$ $\Rightarrow 3 x+4 y=2$ ....(1) $\Rightarrow x-2 y=4$ $\Rightarrow x=4+2 y$ .....(2) Putting the value of $x$ in eq. $...
Read More →A particle is moving in a circular path of radius r.
Question: A particle is moving in a circular path of radius $r$. The displacement after half a circle would be : (a) Zero (b) $\pi r$ (c) $2 r$ (d) $2 \pi r .$ Solution: (c) Explanation : Particle is just opposite to the initial position on the circle....
Read More →Write true (T) or false (F) for the following statements.
Question: Write true (T) or false (F) for the following statements. (i) The number of digits in a square number is even. (ii) The square of a prime number is prime. (iii) The sum of two square numbers is a square number. (iv) The difference of two square numbers is a square number. (v) The product of two square numbers is a square number. (vi) No square number is negative. (vii) There is no square number between 50 and 60. (viii) There are fourteen square number upto 200. Solution: (i) False Exa...
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Question: $\left\{\frac{\cos 70^{\circ}}{\sin 20^{\circ}}+\frac{\cos 55^{\circ} \operatorname{cosec} 35^{\circ}}{\tan 5^{\circ} \tan 25^{\circ} \tan 45^{\circ} \tan 65^{\circ} \tan 85^{\circ}}\right\}$ Solution: $\left\{\frac{\cos 70^{\circ}}{\sin 20^{\circ}}+\frac{\cos 55^{\circ} \operatorname{cosec} 35^{\circ}}{\tan 5^{\circ} \tan 25^{\circ} \tan 45^{\circ} \tan 65^{\circ} \tan 85^{\circ}}\right\}$ $=\left\{\frac{\cos \left(90^{\circ}-20^{\circ}\right)}{\sin 20^{\circ}}+\frac{\cos \left(90^{\c...
Read More →Write five numbers which you cannot decide whether they are square just by
Question: Write five numbers which you cannot decide whether they are square just by looking at the unit's digit. Solution: A number whose unit digit is 2, 3, 7 or 8 cannot be a perfect square. On the other hand, a number whose unit digit is 1, 4, 5, 6, 9 or 0 might be a perfect square although we have to verify that. Applying these two conditions, we cannot determine whether the following numbers are squares just by looking at their unit digits: 1111, 1001, 1555, 1666 and 1999...
Read More →Write five numbers for which you cannot decide whether they are squares.
Question: Write five numbers for which you cannot decide whether they are squares. Solution: A number whose unit digit is 2, 3, 7 or 8 cannot be a perfect square. On the other hand, a number whose unit digit is 1, 4, 5, 6, 9 or 0 might be a perfect square (although we will have to verify whether it is a perfect square or not). Applying the above two conditions, we cannot quickly decide whether the following numbers are squares of any numbers: 1111, 1444, 1555, 1666, 1999...
Read More →Why do we keep both snake and turtle
Question: Why do we keep both snake and turtle in the same class? (CCE 2012) Solution: Both Snake and Turtle have been placed in class reptilia because of the common characteristics: 1. Skin without glands 2. Three chambered (incompletely four chambered) heart 3. Respiration through lungs 4. Cold blooded 5. Hard shelled eggs 6. Embryo protected by extra embryonal membranes....
Read More →Construct a 4 × 3 matrix whose elements are
Question: Construct a $4 \times 3$ matrix whose elements are (i) $a_{i j}=2 i+\frac{i}{j}$ (ii) $a_{i j}=\frac{i-j}{i+j}$ (iii) $a_{i j}=i$ Solution: (i) $a_{i j}=2 i+\frac{i}{j}$ Here, $a_{11}=2(1)+\frac{1}{1}=\frac{2+1}{1}=\frac{3}{1}=3, a_{12}=2(1)+\frac{1}{2}=\frac{4+1}{2}=\frac{5}{2}, a_{13}=2(1)+\frac{1}{3}=\frac{6+1}{3}=\frac{7}{3}$ $a_{21}=2(2)+\frac{2}{1}=\frac{4+2}{1}=\frac{6}{1}=6, a_{22}=2(2)+\frac{2}{2}=\frac{8+2}{2}=\frac{10}{2}=5, a_{23}=2(2)+\frac{2}{3}=\frac{12+2}{3}=\frac{14}{3...
Read More →By just examining the units digits, can you tell which of the following cannot be whole squares?
Question: By just examining the units digits, can you tell which of the following cannot be whole squares? (i) 1026 (ii) 1028 (iii) 1024 (iv) 1022 (v) 1023 (vi) 1027 Solution: If the units digit of a number is 2, 3, 7 or 8, the number cannot be a whole square. (i) 1026 has 6 as the units digit, so it is possibly a perfect square. (ii) 1028 has 8 as the units digit, so it cannot be a perfect square. (iii) 1024 has 4 as the units digit, so it is possibly a perfect square. (iv) 1022 has 2 as the un...
Read More →List out some common features in Cat,
Question: List out some common features in Cat, Rat and Bat. (CCE2012, 2013) Solution: Cat, Rat and Bat belong to same class of mammalia. The common features are 1. Hair 2. Mammary glands 3. Integumentary glands 4. Seven cervical vertebrae 5. Diaphragm 6. 4-Chambered heart 7. External pinnae 8. Vivipary....
Read More →Which of the following numbers are squares of even numbers?
Question: Which of the following numbers are squares of even numbers? 121, 225, 256, 324, 1296, 6561, 5476, 4489, 373758 Solution: The numbers whose last digit is odd can never be the square of even numbers. So, we have to leave out 121, 225, 6561 and 4489, leaving only 256, 324, 1296, 5476 and 373758. For each number, use prime factorisation method and make pairs of equal factors. (i) 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = (2 x 2) x (2 x 2) x (2 x 2) x (2 x 2) There are no factors that are not p...
Read More →Differentiate between flying Lizard and Bird.
Question: Differentiate between flying Lizard and Bird. Draw the diagram. Solution:...
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Question: $2\left(\frac{\cos 58^{\circ}}{\sin 32^{\circ}}\right)-\sqrt{3}\left(\frac{\cos 38^{\circ} \operatorname{cosec} 52^{\circ}}{\tan 15^{\circ} \tan 60^{\circ} \tan 75^{\circ}}\right)$ Solution: $2\left(\frac{\cos 58^{\circ}}{\sin 32^{\circ}}\right)-\sqrt{3}\left(\frac{\cos 38^{\circ} \operatorname{cosec} 52^{\circ}}{\tan 15^{\circ} \tan 60^{\circ} \tan 75^{\circ}}\right)$ $=2\left(\frac{\cos \left(90^{\circ}-32^{\circ}\right)}{\sin 32^{\circ}}\right)-\sqrt{3}\left(\frac{\cos \left(90^{\ci...
Read More →Observe the following pattern
Question: Observe the following pattern $1^{2}=\frac{1}{6}[1 \times(1+1) \times(2 \times 1+1)]$ $1^{2}+2^{2}=\frac{1}{6}[2 \times(2+1) \times(2 \times 2+1)]$ $1^{2}+2^{2}+3^{2}=\frac{1}{6}[3 \times(3+1) \times(2 \times 3+1)]$ $1^{2}+2^{2}+3^{2}+4^{2}=\frac{1}{6}[4 \times(4+1) \times(2 \times 4+1)]$ and find the values of each of the following: (i) 12+ 22+ 32+ 42+ ... + 102 (ii) 52+ 62+ 72+ 82+ 92+ 102+ 112+ 122 Solution: Observing the six numbers on the RHS of the equalities: The first equality,...
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