21 - 30 of 46 Questions
# | Question | Ans |
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21. |
An arc of a circle subtends an angle of 60o at the centre. If the radius of the circle is 3cm, find , in terms of \(\pi\), the length of the arc A. \(\pi\)cm B. 2\(\pi\)cm C. 3\(\pi\)cm D. 6\(\pi\)cm Detailed SolutionLength of arc = \(\frac{\theta}{360} \times 2\pi r\)= \(\frac{60}{360} \times 2\pi \times 3cm\) = \(\pi\)cm |
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22. |
Solve \(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0 A. 1 B. \(\frac{1}{5}\) C. -\(\frac{1}{5}\) D. -1 Detailed Solution\(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0\(\frac{4(2n + 1) - 6(3x - 1)}{24}\) = 0 -10x + 10 = 0 -10x = -10 x = \(\frac{-10}{-10}\) x = 1 |
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23. |
If a positive integer, list the values of x which satisfy the equation 3x - 4 < 6 and x - 1 > 0 A. {1, 2, 3} B. {2, 3} C. {2, 3, 4} D. {2, 3, 4, 5} Detailed Solution3x - 4 < 6 = 3x < 6 = 43x < 10 x < \(\frac{10}{3}\) x < 3.33 and x - 1 = 0 n > 1 = 1< x; since x is an integer, and 1 < x3.33 x = {2, 3} |
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24. |
If c and k are the roots of 6 - x - x2 = 0, find c + k A. 2 B. 1 C. -1 D. -3 Detailed Solution6 - x - x2 = 0a = -1; b = -1; c = 6 Sum of roots = c + k = -\(\frac{-b}{a}\) = \(\frac{-(-1)}{-1}\) = -1 |
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25. |
Each of the interior angles of a regular polygon is 140o. Calculate the sum of all the interior angles of the polygon A. 1080o B. 1260o C. 1800o D. 2160o Detailed SolutionEach interior angle = 140\(\frac{(n - 2) \times 180}{n} = 140\) (n - 2) x 180 = 140n 150 - 360 = 140n 180m - 140n = 360 40n - 360 n = \(\frac{360}{40}\) n = 9 Sum of all interior angles = (n - 2) x 180 = (9 - 2) x 180 = 7 x 180 = 1260 |
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26. |
A bucket holds 10 litres of water. How many buckets of water will fill a reservoir of size 8m x 7m x 5m.(1 litre = 1000cm3)` A. 28 B. 280 C. 2800 D. 28000 Detailed SolutionNo. of buckets of water = \(\frac{\text{Capacity of reservoir}}{\text{Capacity of buckets}}\)= \(\frac{800 \times 700 \times 500}{10 \times 1000}\) = \(\frac{28000 0000}{10000}\) = 28000 |
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27. |
A box contains black, white and red identical balls. The probability of picking a black ball at random from the box is \(\frac{3}{10}\) and the probability of picking a white ball at random is \(\frac{2}{5}\). If there are 30 balls in the box, how many of them are red? A. 3 B. 7 C. 9 D. 12 Detailed SolutionTotal no of balls = 30Let x = no. of red balls Pr(red) = \(\frac{x}{30}\) Pr(black) = \(\frac{3}{10} = \frac{9}{30}\) Pr(white) = \(\frac{2}{5} = \frac{12}{30}\) No. of black balls = 9 No. of white balls = 12 9 = 12 + x = 30 x = 30 - 21 x = 9 No. of red balls = 9 |
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28. |
Simplify; \(\frac{1}{2}\sqrt{32} - \sqrt{18} \sqrt{2}\) A. zero B. \(\sqrt{2}\) C. 2\(\sqrt{2}\) D. 4\(\sqrt{2}\0 Detailed Solution\(\frac{1}{2}\sqrt{32} - \sqrt{18} \sqrt{2}\) = \(\frac{1}{2} (4\sqrt{2}) - 3\sqrt{2} + \sqrt{2}\)= 2\(\sqrt{2} - 3\sqrt{2} + \sqrt{2}\) = 3\(\sqrt{2} - 3\sqrt{2} - 3\sqrt{2}\) = 0 |
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29. |
The angles of triangle are (x + 10)o, (2x - 40)o and (3x - 90)o. Which of the following accurately describes the triangle? A. it is a scalene triangle B. it is right angled isosceles triangle C. t is an equilateral triangle D. It is an isosceles triangle but not right angled Detailed Solution(x + 10)o + (2x - 40)o + (3x - 90)o = 1806x - 120 = 180 6x = 180 + 120 6x = 300 x = \(\frac{300}{6}\) x = 50 x + 10o = 50o + 10o = 60o 2x - 40 = 2(50o) - 40 = 60o 3x - 90 = 3(50o) - 90o = 60o Hence, it is an equilateral triangle |
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30. |
Simplify (x - 3y)2 - (x + 3y)2 A. 2(x + 3y) B. (2x - 3y) C. -12xy D. 6xy Detailed Solution(x - 3y)2 - (x + 3y)2 = [(x - 3y) - (x + 3y)][(x + 3y + x + 3y)] = [-6y] [2x] = -12xy |
21. |
An arc of a circle subtends an angle of 60o at the centre. If the radius of the circle is 3cm, find , in terms of \(\pi\), the length of the arc A. \(\pi\)cm B. 2\(\pi\)cm C. 3\(\pi\)cm D. 6\(\pi\)cm Detailed SolutionLength of arc = \(\frac{\theta}{360} \times 2\pi r\)= \(\frac{60}{360} \times 2\pi \times 3cm\) = \(\pi\)cm |
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22. |
Solve \(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0 A. 1 B. \(\frac{1}{5}\) C. -\(\frac{1}{5}\) D. -1 Detailed Solution\(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0\(\frac{4(2n + 1) - 6(3x - 1)}{24}\) = 0 -10x + 10 = 0 -10x = -10 x = \(\frac{-10}{-10}\) x = 1 |
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23. |
If a positive integer, list the values of x which satisfy the equation 3x - 4 < 6 and x - 1 > 0 A. {1, 2, 3} B. {2, 3} C. {2, 3, 4} D. {2, 3, 4, 5} Detailed Solution3x - 4 < 6 = 3x < 6 = 43x < 10 x < \(\frac{10}{3}\) x < 3.33 and x - 1 = 0 n > 1 = 1< x; since x is an integer, and 1 < x3.33 x = {2, 3} |
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24. |
If c and k are the roots of 6 - x - x2 = 0, find c + k A. 2 B. 1 C. -1 D. -3 Detailed Solution6 - x - x2 = 0a = -1; b = -1; c = 6 Sum of roots = c + k = -\(\frac{-b}{a}\) = \(\frac{-(-1)}{-1}\) = -1 |
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25. |
Each of the interior angles of a regular polygon is 140o. Calculate the sum of all the interior angles of the polygon A. 1080o B. 1260o C. 1800o D. 2160o Detailed SolutionEach interior angle = 140\(\frac{(n - 2) \times 180}{n} = 140\) (n - 2) x 180 = 140n 150 - 360 = 140n 180m - 140n = 360 40n - 360 n = \(\frac{360}{40}\) n = 9 Sum of all interior angles = (n - 2) x 180 = (9 - 2) x 180 = 7 x 180 = 1260 |
26. |
A bucket holds 10 litres of water. How many buckets of water will fill a reservoir of size 8m x 7m x 5m.(1 litre = 1000cm3)` A. 28 B. 280 C. 2800 D. 28000 Detailed SolutionNo. of buckets of water = \(\frac{\text{Capacity of reservoir}}{\text{Capacity of buckets}}\)= \(\frac{800 \times 700 \times 500}{10 \times 1000}\) = \(\frac{28000 0000}{10000}\) = 28000 |
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27. |
A box contains black, white and red identical balls. The probability of picking a black ball at random from the box is \(\frac{3}{10}\) and the probability of picking a white ball at random is \(\frac{2}{5}\). If there are 30 balls in the box, how many of them are red? A. 3 B. 7 C. 9 D. 12 Detailed SolutionTotal no of balls = 30Let x = no. of red balls Pr(red) = \(\frac{x}{30}\) Pr(black) = \(\frac{3}{10} = \frac{9}{30}\) Pr(white) = \(\frac{2}{5} = \frac{12}{30}\) No. of black balls = 9 No. of white balls = 12 9 = 12 + x = 30 x = 30 - 21 x = 9 No. of red balls = 9 |
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28. |
Simplify; \(\frac{1}{2}\sqrt{32} - \sqrt{18} \sqrt{2}\) A. zero B. \(\sqrt{2}\) C. 2\(\sqrt{2}\) D. 4\(\sqrt{2}\0 Detailed Solution\(\frac{1}{2}\sqrt{32} - \sqrt{18} \sqrt{2}\) = \(\frac{1}{2} (4\sqrt{2}) - 3\sqrt{2} + \sqrt{2}\)= 2\(\sqrt{2} - 3\sqrt{2} + \sqrt{2}\) = 3\(\sqrt{2} - 3\sqrt{2} - 3\sqrt{2}\) = 0 |
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29. |
The angles of triangle are (x + 10)o, (2x - 40)o and (3x - 90)o. Which of the following accurately describes the triangle? A. it is a scalene triangle B. it is right angled isosceles triangle C. t is an equilateral triangle D. It is an isosceles triangle but not right angled Detailed Solution(x + 10)o + (2x - 40)o + (3x - 90)o = 1806x - 120 = 180 6x = 180 + 120 6x = 300 x = \(\frac{300}{6}\) x = 50 x + 10o = 50o + 10o = 60o 2x - 40 = 2(50o) - 40 = 60o 3x - 90 = 3(50o) - 90o = 60o Hence, it is an equilateral triangle |
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30. |
Simplify (x - 3y)2 - (x + 3y)2 A. 2(x + 3y) B. (2x - 3y) C. -12xy D. 6xy Detailed Solution(x - 3y)2 - (x + 3y)2 = [(x - 3y) - (x + 3y)][(x + 3y + x + 3y)] = [-6y] [2x] = -12xy |