Question
51
सामान्य गणित
A chord of length 12 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the centre.
(A)
6 cm
(B)
8 cm
(C)
5 cm
(D)
10 cm
Correct Answer:
8 cm
Explanation:
The perpendicular from the centre bisects the chord. Half the chord is 6 cm, so the distance = √(10² - 6²) = 8 cm.
The perpendicular from the centre bisects the chord. Half the chord is 6 cm, so the distance = √(10² - 6²) = 8 cm.
Question
52
सामान्य गणित
Simplify: sin 47° sec 43° + cos 56° cosec 34°
(A)
2
(B)
1
(C)
(D)
1/2
Correct Answer:
2
Explanation:
Since sin 47° = cos 43° and cos 56° = sin 34°, each term equals 1. Therefore, their sum is 2.
Since sin 47° = cos 43° and cos 56° = sin 34°, each term equals 1. Therefore, their sum is 2.
Question
53
सामान्य गणित
One zero of the polynomial 2x² + 7x - 4 is:
(A)
2
(B)
1/2
(C)
-1/2
(D)
-2
Correct Answer:
1/2
Explanation:
Putting x = 1/2 gives 2(1/2)² + 7(1/2) - 4 = 0. Therefore, 1/2 is a zero of the polynomial.
Putting x = 1/2 gives 2(1/2)² + 7(1/2) - 4 = 0. Therefore, 1/2 is a zero of the polynomial.
Question
54
सामान्य गणित
The ratio of the radii of two cylinders is 2:3 and the ratio of their heights is 5:3. Find the ratio of their volumes.
(A)
10:27
(B)
17:10
(C)
20:27
(D)
17:27
Correct Answer:
20:27
Explanation:
The volume of a cylinder is πr²h. Therefore, the ratio of volumes is 2²×5 : 3²×3 = 20:27.
The volume of a cylinder is πr²h. Therefore, the ratio of volumes is 2²×5 : 3²×3 = 20:27.
Question
55
सामान्य गणित
The circumference of a circle of radius r is equal to the perimeter of a square of side x. Find r:x.
(A)
7:11
(B)
7:12
(C)
7:16
(D)
11:7
Correct Answer:
7:11
Explanation:
The circumference of the circle is 2πr and the perimeter of the square is 4x. Thus 2πr = 4x, giving r:x = 2:π ≈ 7:11.
The circumference of the circle is 2πr and the perimeter of the square is 4x. Thus 2πr = 4x, giving r:x = 2:π ≈ 7:11.
Question
56
निर्देशांक ज्यामिति
D is the midpoint of line segment AB. The coordinates of A and D are (2, 4) and (-1, 3), respectively. Find the coordinates of B.
(A)
(3, 1)
(B)
(-5, 4)
(C)
(-4, 2)
(D)
(4, -5)
Correct Answer:
(-4, 2)
Explanation:
Using the midpoint formula D = ((x₁+x₂)/2, (y₁+y₂)/2), the coordinates of B are (-4, 2).
Using the midpoint formula D = ((x₁+x₂)/2, (y₁+y₂)/2), the coordinates of B are (-4, 2).
Question
57
सामान्य गणित
Identify the geometrical figure with the greatest number of sides.
(A)
Heptagon
(B)
Triangle
(C)
Octagon
(D)
Square
Correct Answer:
Octagon
Explanation:
A heptagon has 7 sides, a triangle has 3, an octagon has 8, and a square has 4 sides. Therefore, an octagon has the most sides.
A heptagon has 7 sides, a triangle has 3, an octagon has 8, and a square has 4 sides. Therefore, an octagon has the most sides.
Question
58
सामान्य गणित
If a + b = 3 and a - b = 1, find the value of ab.
(A)
4
(B)
-4
(C)
2
(D)
-2
Correct Answer:
2
Explanation:
Adding the two equations gives 2a = 4, so a = 2 and b = 1. Therefore, ab = 2.
Adding the two equations gives 2a = 4, so a = 2 and b = 1. Therefore, ab = 2.
Question
59
सामान्य गणित
Simplify: cos²(90° - θ) - tan²θ + cos²(90° - θ) - sin²θ
(A)
1
(B)
2
(C)
(D)
-2
Correct Answer:
1
Explanation:
Using cosec(90° - θ) = sin θ, the expression becomes sin²θ - tan²θ + sin²θ - sin²θ = sin²θ - tan²θ, which is not generally 0. The question appears to contain an OCR/printing error.
Using cosec(90° - θ) = sin θ, the expression becomes sin²θ - tan²θ + sin²θ - sin²θ = sin²θ - tan²θ, which is not generally 0. The question appears to contain an OCR/printing error.
Question
60
सामान्य गणित
Simplify: sin(x+π)+sin(x−π)
(A)
-2sinx
(B)
2sinx
(C)
-sinx
(D)
Correct Answer:
-2sinx
Total Questions:
150
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