The area of a square playground is 256.6404 square metres.
Question: The area of a square playground is 256.6404 square metres. Find the length of one side of the playground. Solution: The length of one side of the playground is the square root of its area.So, the length of one side of the playground is 16.02 metres....
Read More →Compare the power at which each of the following
Question: Compare the power at which each of the following is moving upwards against the force of gravity? (given $g$ $=10 \mathrm{~ms}^{-2}$ ) 1. a butterfly of mass $1.0 \mathrm{~g}$ that flies upward at a rate of $0.5 \mathrm{~m} \mathrm{~s}^{-1}$. 2. a $250 \mathrm{~g}$ squirrel climbing up on a tree at a rate of $0.5 \mathrm{~m} \mathrm{~s}^{-1}$. Solution: 1. $P=F v=m g v=1 \times 10^{-3} \times 10 \times 0.5=5 \times 10^{-3} \mathrm{~W}$ 2. $P=F v=m g=250 \times 10^{-3} \times 10 \times 0...
Read More →What is that fraction which when multiplied by itself gives
Question: What is that fraction which when multiplied by itself gives 227.798649? Solution: We have to find the square root of the given number.Hence, the fraction, which when multiplied by itself, gives 227.798649 is 15.093....
Read More →If A is a square matrix
Question: If $A$ is a square matrix such that $A^{2}=A$, then write the value of $7 A-(l+A)^{3}$, where $/$ is the identity matrix. Solution: $7 A-(I+A)^{3}=7 A-\left(I^{3}+A^{3}+3 A^{2} I+3 A I^{2}\right)$ $=7 A-\left(I+A \cdot A^{2}+3 A^{2}+3 A\right)$ $=7 A-(I+A \cdot A+3 A+3 A) \quad\left(\because A^{2}=A\right)$ $=7 A-\left(I+A^{2}+6 A\right)$ $=7 A-(I+A+6 A) \quad\left(\because A^{2}=A\right)$ $=7 A-(I+7 A)$ $=7 A-I-7 A$ $=-I$ Hence, the value of $7 A-(I+A)^{3}$ is $-I$....
Read More →Define watt. Express kilowatt in terms of joule per second.
Question: Define watt. Express kilowatt in terms of joule per second. A $150 \mathrm{~kg}$ car engine develops $500 \mathrm{~W}$ for each $\mathrm{kg}$. What force does it exert in moving the car at a speed of $20 \mathrm{~m} \mathrm{~s}^{-1}$ ? Solution: $\mathrm{kW}=1000 \mathrm{~W}=10^{3} \mathrm{Js}^{-1}$ Power, $\mathrm{P}=150 \times 500=75000 \mathrm{~W}, \mathrm{u}=20 \mathrm{~m} \mathrm{~s}^{-1}$ $\therefore \mathrm{F}=\frac{\mathrm{P}}{v}=\frac{75000}{20}=3750 \mathrm{~N}$...
Read More →Find the square root in decimal form:
Question: Find the square root in decimal form:0.00038809 Solution: Hence, the square root of 0.00038809 is 0.0197....
Read More →Find the square root in decimal form:
Question: Find the square root in decimal form:9998.0001 Solution: Hence, the square root of 9998.0001 is 99.99....
Read More →How is the power related to the speed
Question: How is the power related to the speed at which a body can be lifted? How many kilograms will a man working at the power of $100 \mathrm{~W}$, be able to lift at constant speed of $1 \mathrm{~ms}^{-1}$ vertically ? $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$ Solution: $\mathrm{P}=\mathrm{Fu}=m g u$ $\therefore m=\frac{P}{g v}=\frac{100}{10 \times 1}=10 \mathrm{~kg} .$...
Read More →Find the square root in decimal form:
Question: Find the square root in decimal form:176.252176 Solution: Hence, the square root of 176.252176 is 13.276....
Read More →(a) W = F x S = mgS= 250 x 10 x 1 =25.0 J.
Question: (a) $W=F \times S=m g S=250 \times 10 \times 1=25.0 \mathrm{~J}$. (b) Zero. This is because displacement of box is zero. (c) They get tired because muscular force applied by them is needed to balance the weight of the box. Solution: The Jog Falls in Karnataka State are nearly $200 \mathrm{~m}$ high. 2000 tonnes of water falls from it in a minute. Calculate the equivalent power if all this energy can be utilized ? $\left(g=10 \mathrm{~ms}^{-2}\right)$ Here, $b=200 m, m=2000 \times 1000=...
Read More →Solve the following equations
Question: If matrix $A=\left[\begin{array}{cc}2 -2 \\ -2 2\end{array}\right]$ and $A^{2}=p A$, then write the value of $p$. Solution: Given: $A=\left[\begin{array}{cc}2 -2 \\ -2 2\end{array}\right]$ $A^{2}=\left[\begin{array}{cc}2 -2 \\ -2 2\end{array}\right]\left[\begin{array}{cc}2 -2 \\ -2 2\end{array}\right]$ $=\left[\begin{array}{cc}4+4 -4-4 \\ -4-4 4+4\end{array}\right]$ $=\left[\begin{array}{cc}8 -8 \\ -8 8\end{array}\right]$ $=4\left[\begin{array}{cc}2 -2 \\ -2 2\end{array}\right]$ $=4 A$...
Read More →Find the square root in decimal form:
Question: Find the square root in decimal form:0.00059049 Solution: Hence, the square root of 0.00059049 is 0.0243....
Read More →Find the square root in decimal form:
Question: Find the square root in decimal form:236.144689 Solution: Hence, the square root of 236.144689 is 15.367....
Read More →Find the square root in decimal form:
Question: Find the square root in decimal form: 3600.720036 Solution: Hence, the square root of 3600.720036 is 60.006....
Read More →For what value of x,
Question: For what value of $x$, is the matrix $A=\left[\begin{array}{ccc}0 1 -2 \\ -1 0 3 \\ x -3 0\end{array}\right]$ a skew-symmetric matrix? Solution: Since,Ais a skew symmetric matrix. $\therefore A^{\top}=-A$ $\left[\begin{array}{ccc}0 1 -2 \\ -1 0 3 \\ x -3 0\end{array}\right]^{T}=-\left[\begin{array}{ccc}0 1 -2 \\ -1 0 3 \\ x -3 0\end{array}\right]$ $\Rightarrow\left[\begin{array}{ccc}0 -1 x \\ 1 0 -3 \\ -2 3 0\end{array}\right]=\left[\begin{array}{ccc}0 -1 2 \\ 1 0 -3 \\ -x 3 0\end{arra...
Read More →A girl having mass of
Question: A girl having mass of $35 \mathrm{~kg}$ sits on a trolley of mass $5 \mathrm{~kg}$. The trolley is given an initial velocity of $4 \mathrm{~ms}^{-1}$ by applying a force. The trolley comes to rest after travelling a distance of $16 \mathrm{~m}$. (a) How much work is done on the trolley? (b) How much work is done by the girl? Solution: Here, $u=4 \mathrm{~ms}^{-1}, v=0, \mathrm{~S}=16 \mathrm{~m}$ Using, $\quad v^{2}-u^{2}=2 a S$, we get $a=\frac{v^{2}-u^{2}}{2 S}=\frac{0-16}{2 \times 1...
Read More →For what value of x,
Question: For what value of $x$, is the matrix $A=\left[\begin{array}{ccc}0 1 -2 \\ -1 0 3 \\ x -3 0\end{array}\right]$ a skew-symmetric matrix? Solution: Since,Ais a skew symmetric matrix. $\therefore A^{\top}=-A$ $\left[\begin{array}{ccc}0 1 -2 \\ -1 0 3 \\ x -3 0\end{array}\right]^{T}=-\left[\begin{array}{ccc}0 1 -2 \\ -1 0 3 \\ x -3 0\end{array}\right]$ $\Rightarrow\left[\begin{array}{ccc}0 -1 x \\ 1 0 -3 \\ -2 3 0\end{array}\right]=\left[\begin{array}{ccc}0 -1 2 \\ 1 0 -3 \\ -x 3 0\end{arra...
Read More →Find the square root in decimal form:
Question: Find the square root in decimal form:225.6004 Solution: Hence, the square root of 225.6004 is 15.02...
Read More →Find the square root in decimal form:
Question: Find the square root in decimal form: 150.0625 Solution: Hence, the square root of 150.0625 is 12.25....
Read More →Find the square root in decimal form:
Question: Find the square root in decimal form: 0.00002025 Solution: Hence, the square root of 0.00002025 is 0.0045....
Read More →Find the square root in decimal form:
Question: Find the square root in decimal form: 0.813604 Solution: Hence, the square root of 0.813604 is 0.902....
Read More →Solve the following equations
Question: If $\left[\begin{array}{cc}a-b 2 a+c \\ 2 a-b 3 c+d\end{array}\right]=\left[\begin{array}{cc}-1 5 \\ 0 13\end{array}\right]$, find the value of $b$ Solution: $\left[\begin{array}{cc}a-b 2 a+c \\ 2 a-b 3 c+d\end{array}\right]=\left[\begin{array}{cc}-1 5 \\ 0 13\end{array}\right]$ Corresponding elements of equal matrices are equal. $\Rightarrow a-b=-1 \quad$ and $\quad 2 a-b=0$ $\Rightarrow a-b=-1 \quad$ and $\quad 2 a=b$ $\Rightarrow a-2 a=-1 \quad$ and $\quad 2 a=b$ $\Rightarrow a=1 \q...
Read More →An automobile engine propels a
Question: An automobile engine propels a $1000 \mathrm{~kg}$ car $(A)$ along a levelled road at a speed of $36 \mathrm{~km} \mathrm{~h}^{-1}$. Find power if the opposing frictional force is $100 \mathrm{~N}$. Now, suppose after travelling a distance of $200 \mathrm{~m}$, this car collides with another stationary car (B) of same mass and comes to rest. Let its engine also stops at the same time. Now car (B) starts moving on the same level road without getting its engine started. Find the speed of...
Read More →Find the square root in decimal form:
Question: Find the square root in decimal form: 0.7225 Solution: Hence, the square root of 0.7225 is 0.85....
Read More →Find the square root in decimal form:
Question: Find the square root in decimal form: 84.8241 Solution: Hence, the square root of 84.8241 is 9.21....
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