Draw a histogram for the following data:
Question: Draw a histogram for the following data: Hint.Take 1 small division = 3. Solution:...
Read More →There are________perfect squares
Question: There are________perfect squares between 1 and 100. Solution: 8 There are 8 perfect squares between 1 and 100, i.e. 4, 9,16, 25, 36, 49, 64 and 81....
Read More →Draw a histogram for the following data:
Question: Draw a histogram for the following data:/spanbr data-mce-bogus="1"/ppimg src="https://www.esaral.com/qdb/uploads/2022/02/07/image51044.png" alt="" width="423" height="67" Hint.Take 1 small division = 3. Solution:...
Read More →Given that,
Question: Given that, $\sqrt{4096}=64$, the value of $\sqrt{4096}+\sqrt{40.96}$ is (a) 74 (b) $60.4$ (c) $64.4$ (d) $70.4$ Solution: (d) Given, $\sqrt{4096}=64$ So, $\sqrt{4096}+\sqrt{40.96}$ $=64+\sqrt{4096 \times 10^{-2}}$ $=64+\sqrt{4096} \sqrt{10^{-2}}$ $=64+64 \times 10^{-1}$ $=64+6.4=70.4$...
Read More →Draw a histogram for the frequency distribution of the following data:
Question: Draw a histogram for the frequency distribution of the following data: Solution:...
Read More →Draw a histogram for the frequency distribution of the following data:
Question: Draw a histogram for the frequency distribution of the following data:/spanbr data-mce-bogus="1"/ppimg src="https://www.esaral.com/qdb/uploads/2022/02/07/image86547.png" alt="" width="468" height="83" Solution:...
Read More →The value of
Question: The value of $\sqrt{248+\sqrt{52+\sqrt{144}}}$ is (a) 14 (b) 12 (c) 16 (d) 13 Solution: (c) We have, $\sqrt{248+\sqrt{52+\sqrt{144}}}$ $=\sqrt{248+\sqrt{52+12}}$ $[\because$ square root of $144=12]$ $=\sqrt{248+\sqrt{64}}$ $=\sqrt{248+8}$ $[\because$ square root of $64=8]$ $=\sqrt{256}=16$ $[\because$ square root of $256=16]$...
Read More →Draw a histogram for the frequency distribution of following data:
Question: Draw a histogram for the frequency distribution of following data: Hint.Take 1 small division = 10. Solution:...
Read More →Draw a histogram for the frequency distribution of following data:
Question: Draw a histogram for the frequency distribution of following data:/spanbr data-mce-bogus="1"/ppimg src="https://www.esaral.com/qdb/uploads/2022/02/07/image17612.png" alt="" width="519" height="91" Hint.Take 1 small division = 10. Solution:...
Read More →The ages (in years) of 360 patients treated in a hospital on a particular day are given below:
Question: The ages (in years) of 360 patients treated in a hospital on a particular day are given below: Draw a histogram for the given data. Hint.Take 10 small divisions = 10 patients. Solution:...
Read More →If m is the cube root of
Question: If $m$ is the cube root of $n$, then $n$ is (a) $m^{3}$ (b) $\sqrt{m}$ (c) $\frac{m}{3}$ (d) $\sqrt[3]{m}$ Solution: (a) Given, $m$ is the cube root of $n$, i.e. $m=\sqrt[3]{n}$ $\Rightarrow \quad m=(n)^{1 / 3}$ $\Rightarrow \quad m^{3}=(n)^{3 / 3}$ [taking cube on both sides] $\therefore \quad m^{3}=n$...
Read More →The top speeds of 30 different land animals have been organised into a frequency table given below:
Question: The top speeds of 30 different land animals have been organised into a frequency table given below: Draw a histogram for the given data. Solution:...
Read More →A perfect square number having n digits,
Question: A perfect square number having n digits, where n is even, will have square root with (a) $(n+1)$ digit (b) $\frac{n}{2}$ digit (c) $\frac{n}{3}$ digit (d) $\left(\frac{n+1}{2}\right)$ digit Solution: (b) A perfect square number having n digits, where n is even, will have square root with n/2 digit....
Read More →If m is the square of a natural number
Question: If $m$ is the square of a natural number $n$, then $n$ is (a) the square of $m$ (b) greater than $m$ (c) equal to $m$ (d) $\sqrt{m}$ Solution: (d) Given, $m$ is the square of $n, \mathrm{i}_{4} e . m=n^{2}$ Taking square root both sides, we get $n=\sqrt{m}$...
Read More →The heights (in cm) of 22 students were recorded as under:
Question: The heights (in cm) of 22 students were recorded as under: 125, 132, 138, 144, 142, 136, 134, 125, 135, 130, 126, 132, 135, 142, 143, 128, 126, 136, 135, 130, 130, 133. Prepare a frequency distribution table, taking equal class intervals and starting from 125130, where 130 is not included. Solution: Arranging the given observations in increasing order, we get 125, 125, 126, 126, 128, 130, 130, 130, 132, 132, 133, 134, 135, 135, 135, 136, 136, 138, 142, 142, 143 and 144.Thus, the freque...
Read More →prove that
Question: $\sqrt[3]{1000}$ is equal to (a) 10 (b) 100 (c) 1 (d) None of these Solution: (a) We have, $\sqrt[3]{1000}=\sqrt[3]{10 \times 10 \times 10}=\sqrt[3]{(10)^{3}}=(10)^{3 / 3}=10$...
Read More →The daily earnings (in rupees) of 24 stores in a market was recorded as under:
Question: The daily earnings (in rupees) of 24 stores in a market was recorded as under: 715, 650, 685, 550, 573, 530, 610, 525, 742, 680, 736, 524, 500, 585, 723, 545, 532, 560, 580, 545, 625, 630, 645, 700. Prepare a frequency table taking equal class sizes. One such class is 500550, where 550 is not included. Solution: Arranging the given observations in increasing order, we get: 500, 524, 525, 530, 532, 545, 545, 550, 560, 573, 580, 585, 610, 625, 630, 645, 650, 680, 685, 700, 715, 723, 736,...
Read More →Which of the following numbers
Question: Which of the following numbers is not a perfect cube? (a) 216 (b) 567 (c) 125 (d) 343 Solution: (b) 216=6 x 6 x 6, 567 = 3 x 3 x 3 x 3 x 7 125 = 5 x 5 x 5, 343 = 7 x 7 x 7 Clearly, 567 is not a perfect cube, because in grouping, the factors in triplets of equal factors, we are left with two factors 3 x 7....
Read More →The weekly pocket expenses (in rupees) of 30 students of a class are given below:
Question: The weekly pocket expenses (in rupees) of 30 students of a class are given below: 62, 80, 110, 75, 84, 73, 60, 62, 100, 87, 78, 94, 117, 86, 65, 68, 90, 80, 118, 72, 95, 72, 103, 96, 64, 94, 87, 85, 105, 115. Construct a frequency table with class intervals 6070 (where 70 is not included), 7080, 8090, etc. Solution: Arranging the given observations in increasing order, we get: 60, 62, 62, 64, 65, 68, 72, 72, 73, 75, 78, 80, 80, 84, 85, 86, 87, 87, 90, 94, 94, 95, 96, 100, 103, 105, 110...
Read More →A perfect square can never have
Question: A perfect square can never have the following digit in its ones place. (a) 1 (b) 8 (c) 0 (d) 6 Solution: (b) We know that, a number ending with digits 2, 3, 7 or 8 can never be a perfect square. Clearly, a perfect square can never have the digit 8 in its ones place....
Read More →The weekly wages (in rupees) of 28 workers of a factory are given below:
Question: The weekly wages (in rupees) of 28 workers of a factory are given below: 668, 610, 642, 658, 668, 620, 719, 720, 700, 690, 710, 642, 672, 654, 692, 706, 718, 702, 704, 678, 615, 640, 680, 716, 705, 615, 636, 656. Construct a frequency table with equal class intervals, taking the first of the class intervals as 610630, where 630 is not included. Solution: Arranging the given observations in ascending order, we get: 610, 615, 615, 620, 636, 640, 642, 642, 654, 656, 658, 668, 668, 672, 67...
Read More →Which among
Question: Which among 432 , 672, 522, 592would end with digit 1? (a) 432 (b)672 (c)522 (d)592 Solution: (d) We know that, the unit's digit of the square of a natural number is the unit's digit of the square of the digit at unit's place of the given natural number. $\therefore$ Unit's digit of $43^{2}=9 \quad\left[\because 3^{2}=9\right]$ Unit's digit of $67^{2}=9$$\left[\because\right.$ unit's digit of $7^{2}$ is 9$]$ Unit's digit of $52^{2}=4$ $\left[\because 2^{2}=4\right]$ Unit's digit of $59...
Read More →The electricity bills (in rupees) of 25 houses of a certain locality for a month are given below:
Question: The electricity bills (in rupees) of 25 houses of a certain locality for a month are given below: 324, 700, 617, 400, 356, 365, 435, 506, 548, 736, 780, 378, 570, 685, 312, 630, 584, 674, 754, 776, 596, 745, 565, 763, 472. Arrange the above data in increasing order and form a frequency table using equal class intervals, starting from 300400, where 400 is not included. Solution: Arranging the given observations in increasing order, we get: 312, 324, 356, 365, 378, 400, 435, 472, 506, 54...
Read More →The marks obtained by 40 students of a class in an examination are given below:
Question: The marks obtained by 40 students of a class in an examination are given below: 8, 47, 22, 31, 17, 13, 38, 26, 3, 34, 29, 11, 22, 7, 15, 24, 38, 31, 21, 35, 42, 24, 45, 23, 21, 27, 29, 49, 25, 48, 21, 15, 18, 27, 19, 45, 14, 34, 37, 34. Prepare a frequency distribution table with equal class intervals, starting from 010 (where 10 not included). Solution: Arranging the given observations in ascending order, we get:3, 7, 8, 11, 13, 14, 15, 15, 17, 18, 19, 21, 21, 21, 22, 22, 23, 24, 24, ...
Read More →Solve this
Question: $3 x^{2}+7 i x+6=0$ Solution: Given: $3 x^{2}+7 i x+6=0$ $\Rightarrow 3 x^{2}+9 i x-2 i x+6=0$ $\Rightarrow 3 x(x+3 i)-2 i\left(x-\frac{6}{2 i}\right)=0$ $\Rightarrow \quad 3 x(x+3 i)-2 i\left(x-\frac{3 \times i}{i \times i}\right)=0 \quad \ldots\left(i^{2}=-1\right)$ $\Rightarrow 3 x(x+3 i)-2 i\left(x-\frac{3 \times i}{-1}\right)=0$ $\Rightarrow 3 x(x+3 i)-2 i(x+3 i)=0$ $\Rightarrow(x+3 i)(3 x-2 i)=0$ $\Rightarrow x+3 i=0 \ 3 x-2 i=0$ $\Rightarrow \mathrm{x}=3 \mathrm{i} \^{x}=\frac{2...
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