Which of the above two graphs (a) and (b) (Fig. 3)
Question: Which of the above two graphs (a) and (b) (Fig. 3) representing the human voice is likely to be the male voice ? Give reason for your answer. Solution: Frequency of male voice is lesser than that of female voice. So, graph (a) represents the human voice....
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Question: If $\left[\begin{array}{l}x+y \\ x-y\end{array}\right]=\left[\begin{array}{ll}2 1 \\ 4 3\end{array}\right]\left[\begin{array}{c}1 \\ -2\end{array}\right]$, then write the value of $(x, y)$. Solution: $\left[\begin{array}{l}x+y \\ x-y\end{array}\right]=\left[\begin{array}{ll}2 1 \\ 4 3\end{array}\right]\left[\begin{array}{c}1 \\ -2\end{array}\right]$ $\Rightarrow\left[\begin{array}{l}x+y \\ x-y\end{array}\right]=\left[\begin{array}{c}2-2 \\ 4-6\end{array}\right]$ $\Rightarrow\left[\begi...
Read More →The given graph (Fig. 2) shows the displacement versus time
Question: The given graph (Fig. 2) shows the displacement versus time relation for a disturbance travelling with velocity of 1500 the wavelength of the disturbance. Solution: Here $v=1500 \mathrm{~m} \mathrm{~s}^{-1}$ $T=2 \mu s=2 \times 10^{-6} \mathrm{~s}$ $\therefore$ Frequency, $v=\frac{1}{T}=\frac{1}{2 \times 10^{-6}}=5 \times 10^{5} \mathrm{~Hz}$ Using $v=v \hat{\lambda}$, we get $\lambda=\frac{v}{v}=\frac{1500}{5 \times 10^{5}}=3 \times 10^{-3} \mathrm{~m}=3 \mathrm{~mm}$...
Read More →Find the square root of 11 correct to five decimal places.
Question: Find the square root of 11 correct to five decimal places. Solution: Using the long division method: $\therefore \sqrt{11}=3.31662$...
Read More →Find the square root of 12.0068 correct to four decimal places.
Question: Find the square root of 12.0068 correct to four decimal places. Solution: $\therefore \sqrt{12.0068}=3.46508$ We can round it off to four decimal places, i.e. 3.4651....
Read More →Find the square root of each of the following correct to three places of decimal.
Question: Find the square root of each of the following correct to three places of decimal. (i) 5 (ii) 7 (iii) 17 (iv) 20 (v) 66 (vi) 427 (vii) 1.7 (viii) 23.1 (ix) 2.5 (x) 237.615 (xi) 15.3215 (xii) 0.9 (xiii) 0.1 (xiv) 0.016 (xv) 0.00064 (xvi) 0.019 (XVii) $\frac{7}{8}$ (XViii) $\frac{5}{12}$ (xix) $2 \frac{1}{2}$ (XX) $287 \frac{5}{8}$ Solution: (i) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three deci...
Read More →Construct a 2 × 2 matrix A = [aij] whose elements aij are given by
Question: Construct a $2 \times 2$ matrix $A=\left[a_{i j}\right]$ whose elements $a_{i j}$ are given by $a_{i j}= \begin{cases}\frac{|-3 i+j|}{2} , \text { if } i \neq j \\ (i+j)^{2} , \text { if } i=j\end{cases}$ Solution: Given: $a_{i j}= \begin{cases}\frac{|-3 i+j|}{2}, \text { if } i \neq j \\ (i+j)^{2}, \text { if } i=j\end{cases}$ $a_{11}=(1+1)^{2}=4$ $a_{12}=\frac{|-3 \times 1+2|}{2}=\frac{1}{2}$ $a_{21}=\frac{|-3 \times 2+1|}{2}=\frac{5}{2}$ $a_{22}=(2+2)^{2}=16$ Hence, the matrix $A=\l...
Read More →Before playing the orchestra in a musical concert,
Question: Before playing the orchestra in a musical concert, a sitarist tries to adjust the tension and pluck the string suitably. By doing so, he is adjusting (a) intensity of sound only (b) amplitude of sound only (c) frequency of the sitar string with the frequency of other musical instruments (d) loudness of sound. Solution: (c) frequency of the sitar string with the frequency of other musical instruments...
Read More →Infrasound can be heard by
Question: Infrasound can be heard by (a) dog (b) bat (c) rhinoceros (d) human beings. Solution: (c) rhinoceros...
Read More →Earthquake produces which kind of sound before the main shock wave begins
Question: Earthquake produces which kind of sound before the main shock wave begins (a) ultrasound (b) infrasound (c) audible sound (d) none of the above Solution: (b) infrasound...
Read More →In the curve (Fig. 1) half the wavelength is
Question: In the curve (Fig. 1) half the wavelength is (a) $A B$ (b) $B D$ (c) DE (d) $A E$ Solution: (b) B D...
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Question: If $\left[\begin{array}{cc}x y 4 \\ z+6 x+y\end{array}\right]=\left[\begin{array}{ll}8 w \\ 0 6\end{array}\right]$, write the value of $(x+y+z)$ Solution: $\left[\begin{array}{cc}x y 4 \\ z+6 x+y\end{array}\right]=\left[\begin{array}{ll}8 w \\ 0 6\end{array}\right]$ Corresponding elements of equal matrices are equal. $\therefore z+6=0 \quad$ and $\quad x+y=6$ $\Rightarrow z=-6 \quad$ and $\quad x+y=6$ Therefore, $x+y+z=6-6=0$....
Read More →When we change feeble sound to loud sound we increase its
Question: When we change feeble sound to loud sound we increase its (a) frequency (b) amplitude (c) velocity (d) wavelength Solution: (b). Loudness depends on the amplitude of vibration....
Read More →Find the value of
Question: Find the value of $\sqrt{103.0225}$ and hence find the value of Solution: The value of $103.0225$ is: Hence, the square root of 103.0225 is 10.15. Now, we can solve the following questions as shown below: (i) $\sqrt{10302.25}=\sqrt{103.0225 \times 100}=\sqrt{103.0225} \times \sqrt{100}=10.15 \times 10=101.5$ (ii) $\sqrt{1.030225}=\sqrt{\frac{103.0225}{100}}=\frac{\sqrt{103.0225}}{\sqrt{100}}=\frac{10.15}{10}=1.015$...
Read More →Write a 2 × 2 matrix which is both symmetric and skew-symmetric.
Question: Write a $2 \times 2$ matrix which is both symmetric and skew-symmetric. Solution: A matrix which is both symmetric and skew-symmetric is a : matrix. Hence, the required matrix is $\left[\begin{array}{ll}0 0 \\ 0 0\end{array}\right]$....
Read More →Sound travels in air if
Question: Sound travels in air if (a) particles of medium travel from one place to another (b) there is no moisture in the atmosphere (c) disturbance moves (d) both particles as well as disturbance travel from one place to another. Solution: (c) disturbance moves...
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Question: If $\left[\begin{array}{cc}a+4 3 b \\ 8 -6\end{array}\right]=\left[\begin{array}{cc}2 a+2 b+2 \\ 8 a-8 b\end{array}\right]$, write the value of $a-2 b$. Solution: $\left[\begin{array}{cc}a+4 3 b \\ 8 -6\end{array}\right]=\left[\begin{array}{cc}2 a+2 b+2 \\ 8 a-8 b\end{array}\right]$ Corresponding elements of equal matrices are equal. $\therefore a+4=2 a+2 \quad$ and $\quad 3 b=b+2$ $\Rightarrow 4-2=2 a-a \quad$ and $\quad 3 b-b=2$ $\Rightarrow a=2 \quad$ and $\quad 2 b=2$ $\Rightarrow ...
Read More →Solve the following
Question: Evaluate $\sqrt{50625}$ and hence find the value of $\sqrt{506.25}+\sqrt{5.0625}$ Solution: We have: $\sqrt{50625}=\sqrt{3 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5 \times 5}=3 \times 3 \times 5 \times 5=225$ Next, we will calculate $\sqrt{506.25}$ and $\sqrt{5.0625}$ $\sqrt{506.25}=\sqrt{\frac{50625}{100}}=\frac{\sqrt{50625}}{\sqrt{100}}=\frac{225}{10}=22.5$ $\sqrt{5.0625}=\sqrt{\frac{50625}{10000}}=\frac{\sqrt{50625}}{\sqrt{10000}}=\frac{225}{100}=2.25$ $\sqrt{506.25}+\sq...
Read More →In SONAR, we use
Question: In SONAR, we use (a) ultrasonic waves (b) infrasonic waves (c) radio waves (d) audible sound waves Solution: (a) ultrasonic waves...
Read More →Simplify:
Question: Simplify:' (i) $\frac{\sqrt{59.29}-\sqrt{5.29}}{\sqrt{59.29}+\sqrt{5.29}}$ (ii) $\frac{\sqrt{0.2304}+\sqrt{0.1764}}{\sqrt{0.2304}-\sqrt{0.1764}}$ Solution: (i) We have:; $\sqrt{59.29}=\sqrt{\frac{5929}{100}}=\frac{\sqrt{7 \times 7 \times 11 \times 11}}{10}=\frac{7 \times 11}{10}=7.7$ $\sqrt{5.29}=\sqrt{\frac{529}{100}}=\frac{\sqrt{529}}{\sqrt{100}}=\frac{23}{10}=2.3$ $\frac{\sqrt{59.29}-\sqrt{5.29}}{\sqrt{59.29}+\sqrt{5.29}}=\frac{7.7-2.3}{7.7+2.3}=\frac{5.4}{10}=0.54$ (ii) We have: $\...
Read More →A key of a mechanical piano struck gently and then struck again but much harder this time. In the second case
Question: A key of a mechanical piano struck gently and then struck again but much harder this time. In the second case (a) sound will be louder but pitch will not be different (b) sound will be louder and pitch (c) sound will be louder but pitch will be lower (d) both loudness and pitch will remain unaffected Solution: (a). Loudness depends on the amplitude of vibration....
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Question: If $\left[\begin{array}{ll}x 1\end{array}\right]\left[\begin{array}{cc}1 0 \\ -2 0\end{array}\right]=O$, find $x .$ Solution: $\left[\begin{array}{ll}x 1\end{array}\right]\left[\begin{array}{cc}1 0 \\ -2 0\end{array}\right]=O$ $\Rightarrow\left[\begin{array}{ll}x-2 0+0\end{array}\right]=\left[\begin{array}{ll}0 0\end{array}\right]$ $\Rightarrow\left[\begin{array}{ll}x-2 0\end{array}\right]=\left[\begin{array}{ll}0 0\end{array}\right]$ $\Rightarrow x-2=0$ $\Rightarrow x=2$ $\therefore x...
Read More →Note is a sound
Question: Note is a sound (a) of mixture of several frequencies (b) of mixture of two frequencies only (c) of a single frequency (d) always unpleasant to listen Solution: (a) of mixture of several frequencies...
Read More →Solve the following equations
Question: If $2\left[\begin{array}{ll}3 4 \\ 5 x\end{array}\right]+\left[\begin{array}{ll}1 y \\ 0 1\end{array}\right]=\left[\begin{array}{cc}7 0 \\ 10 5\end{array}\right]$, find $x-y$ Solution: $2\left[\begin{array}{ll}3 4 \\ 5 x\end{array}\right]+\left[\begin{array}{ll}1 y \\ 0 1\end{array}\right]=\left[\begin{array}{cc}7 0 \\ 10 5\end{array}\right]$ $\Rightarrow\left[\begin{array}{cc}6+1 8+y \\ 10+0 2 x+1\end{array}\right]=\left[\begin{array}{cc}7 0 \\ 10 5\end{array}\right]$ $\Rightarrow\lef...
Read More →What is the fraction which when multiplied by itself gives
Question: What is the fraction which when multiplied by itself gives 0.00053361? Solution: We have to find the square root of the given number.Hence, the fraction, which when multiplied by itself, gives 0.00053361 is 0.0231....
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