21 - 30 of 49 Questions
# | Question | Ans |
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21. |
A binary operation on the real set of numbers excluding -1 is such that for all m, n ∈ R, mΔn = m+n+mn. Find the identity element of the operation. A. 1 B. zero C. -1/2 D. -1 |
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22. |
A. 100o B. 80o C. 50o D. 30o Detailed SolutionExterior angle = sum of two interior opposite anglesy = 50° (vert. opp ∠s are equal) X = y + 30 X = 50 + 30 X = 80° There is an explanation video available below. |
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23. |
Find the exterior angle of a 12 sided regular polygon A. 12o B. 24o C. 25o D. 30o Detailed SolutionExterior angle = 360 / n= 360 / 12 = 30o There is an explanation video available below. |
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24. |
In the diagram above ∠OPQ is? A. 90o B. 53o C. 36o D. 26o Detailed Solutiona = a(base ∠s of Iss Δ)∴ a+a+74 = 180 2a + 74 = 180 2a = 180-74 2a = 106 a = 53 ∴∠OPQ = 53o There is an explanation video available below. |
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25. |
Find the area of the figure above A. 12.5 cm2 B. 75.0 cm2 C. 78.5 cm2 D. 84.8 cm2 Detailed SolutionArea of the figure = Area of rect + area of semi circle\(=L \times h + \frac{1}{2}\pi r^2\\ 5 \times 15 + \frac{1}{2} \times \frac{22}{7} \times \left(\frac{5}{2}\right)^2\\ =75+\frac{(22\times 25)}{2\times7}\\ =75 + 9\frac{23}{28}\\ =84.8cm\) There is an explanation video available below. |
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26. |
Find the angle subtended at the center of a circle by a chord which is equal in length to the radius of the circle. A. 30o B. 45o C. 60o D. 90o Detailed SolutionIf a length of a chord is equal to the length of a radius in the same circle, the triangle formed y the chord and the radii is an equilateral triangle∴each angle = 60o There is an explanation video available below. |
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27. |
Find the capacity in liters of a cylindrical well of radius 1 meter and depth 14 meters A. 44,000 liters B. 4,400 liters C. 440 liters D. 44 liters Detailed SolutionV = πr2h1m = 100cm 14cm = 1400cm \(∴V = \frac{22}{7} \times \frac{100x100x1400}{1000}\\ = 44, 000 liters\) There is an explanation video available below. |
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28. |
The locus of a point equidistant from two points p(6,2) and R(4,2) is a perpendicular bisector of PR passing through? A. (2,5) B. (5,2) C. (1,0) D. (0,1) Detailed Solution\(X = \frac{6+2}{2}=\frac{10}{2}=5\\Y = \frac{2+2}{2}=\frac{4}{2}=2\\ ∴X,Y = (5,2)\) There is an explanation video available below. |
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29. |
Find the gradient of a line which is perpendicular to the line with the equation 3x + 2y + 1 = 0 A. 3/2 B. 2/3 C. -2/3 D. -3/2 Detailed Solution3X + 2Y + 1 = 02Y = -3X - 1 \(\frac{-3}{2}X - \frac{1}{2}\) Gradient of 3X + 2Y +1 = 0 is -3/2 Gradient of a line perpendicular to 3X + 2Y + 1 = 0 \(=-1 \div \frac{3}{2}\\ =-1 \times \frac{-2}{3}=\frac{2}{3}\) There is an explanation video available below. |
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30. |
If sinθ = 3/5. Find Tanθ A. 3/4 B. 3/5 C. 2/5 D. 1/4 |
21. |
A binary operation on the real set of numbers excluding -1 is such that for all m, n ∈ R, mΔn = m+n+mn. Find the identity element of the operation. A. 1 B. zero C. -1/2 D. -1 |
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22. |
A. 100o B. 80o C. 50o D. 30o Detailed SolutionExterior angle = sum of two interior opposite anglesy = 50° (vert. opp ∠s are equal) X = y + 30 X = 50 + 30 X = 80° There is an explanation video available below. |
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23. |
Find the exterior angle of a 12 sided regular polygon A. 12o B. 24o C. 25o D. 30o Detailed SolutionExterior angle = 360 / n= 360 / 12 = 30o There is an explanation video available below. |
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24. |
In the diagram above ∠OPQ is? A. 90o B. 53o C. 36o D. 26o Detailed Solutiona = a(base ∠s of Iss Δ)∴ a+a+74 = 180 2a + 74 = 180 2a = 180-74 2a = 106 a = 53 ∴∠OPQ = 53o There is an explanation video available below. |
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25. |
Find the area of the figure above A. 12.5 cm2 B. 75.0 cm2 C. 78.5 cm2 D. 84.8 cm2 Detailed SolutionArea of the figure = Area of rect + area of semi circle\(=L \times h + \frac{1}{2}\pi r^2\\ 5 \times 15 + \frac{1}{2} \times \frac{22}{7} \times \left(\frac{5}{2}\right)^2\\ =75+\frac{(22\times 25)}{2\times7}\\ =75 + 9\frac{23}{28}\\ =84.8cm\) There is an explanation video available below. |
26. |
Find the angle subtended at the center of a circle by a chord which is equal in length to the radius of the circle. A. 30o B. 45o C. 60o D. 90o Detailed SolutionIf a length of a chord is equal to the length of a radius in the same circle, the triangle formed y the chord and the radii is an equilateral triangle∴each angle = 60o There is an explanation video available below. |
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27. |
Find the capacity in liters of a cylindrical well of radius 1 meter and depth 14 meters A. 44,000 liters B. 4,400 liters C. 440 liters D. 44 liters Detailed SolutionV = πr2h1m = 100cm 14cm = 1400cm \(∴V = \frac{22}{7} \times \frac{100x100x1400}{1000}\\ = 44, 000 liters\) There is an explanation video available below. |
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28. |
The locus of a point equidistant from two points p(6,2) and R(4,2) is a perpendicular bisector of PR passing through? A. (2,5) B. (5,2) C. (1,0) D. (0,1) Detailed Solution\(X = \frac{6+2}{2}=\frac{10}{2}=5\\Y = \frac{2+2}{2}=\frac{4}{2}=2\\ ∴X,Y = (5,2)\) There is an explanation video available below. |
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29. |
Find the gradient of a line which is perpendicular to the line with the equation 3x + 2y + 1 = 0 A. 3/2 B. 2/3 C. -2/3 D. -3/2 Detailed Solution3X + 2Y + 1 = 02Y = -3X - 1 \(\frac{-3}{2}X - \frac{1}{2}\) Gradient of 3X + 2Y +1 = 0 is -3/2 Gradient of a line perpendicular to 3X + 2Y + 1 = 0 \(=-1 \div \frac{3}{2}\\ =-1 \times \frac{-2}{3}=\frac{2}{3}\) There is an explanation video available below. |
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30. |
If sinθ = 3/5. Find Tanθ A. 3/4 B. 3/5 C. 2/5 D. 1/4 |