Question
61
सामान्य गणित
If sin 2A = cos(A - 60°), find the value of A.
(A)
15°
(B)
50°
(C)
45°
(D)
30°
Correct Answer:
30°
Explanation:
Since cos(A - 60°) = sin(150° - A), we have sin 2A = sin(150° - A). Among the given options, A = 30° satisfies the equation.
Since cos(A - 60°) = sin(150° - A), we have sin 2A = sin(150° - A). Among the given options, A = 30° satisfies the equation.
Question
62
सामान्य गणित
If sin θ = 8/17 and θ lies in the second quadrant, find cot θ.
(A)
8/15
(B)
15/17
(C)
-15/8
(D)
-8/15
Correct Answer:
-15/8
Explanation:
In the second quadrant, cos θ is negative. From sin θ = 8/17, cos θ = -15/17. Therefore, cot θ = cosθ/sinθ = -15/8.
In the second quadrant, cos θ is negative. From sin θ = 8/17, cos θ = -15/17. Therefore, cot θ = cosθ/sinθ = -15/8.
Question
63
सामान्य गणित
What is the factorization of 4x² + 8x + 3?
(A)
(x + 1)(x + 3)
(B)
(2x + 1)(2x + 3)
(C)
(2x + 2)(2x + 5)
(D)
(2x - 1)(2x - 3)
Correct Answer:
(2x + 1)(2x + 3)
Explanation:
4x² + 8x + 3 = (2x + 1)(2x + 3).
4x² + 8x + 3 = (2x + 1)(2x + 3).
Question
64
सामान्य गणित
If the equations 6x - 5y + 11 = 0 and 15x + ky - 9 = 0 have no solution, find k.
(A)
12.5
(B)
18
(C)
-12.5
(D)
-18
Correct Answer:
-12.5
Explanation:
For two linear equations to have no solution, a₁/a₂ = b₁/b₂ ≠ c₁/c₂. Thus 6/15 = -5/k, giving k = -12.5.
For two linear equations to have no solution, a₁/a₂ = b₁/b₂ ≠ c₁/c₂. Thus 6/15 = -5/k, giving k = -12.5.
Question
65
सामान्य गणित
Find the area of an isosceles right triangle whose hypotenuse is 8 cm.
(A)
32 cm²
(B)
16 cm²
(C)
20 cm²
(D)
9 cm²
Correct Answer:
16 cm²
Explanation:
In an isosceles right triangle with hypotenuse 8 cm, each leg is 4√2 cm. Area = 1/2 × (4√2)² = 16 cm².
In an isosceles right triangle with hypotenuse 8 cm, each leg is 4√2 cm. Area = 1/2 × (4√2)² = 16 cm².
Question
66
ज्यामिति
If the sum of two angles of a triangle is equal to the third angle, what type of triangle is it?
(A)
Equilateral
(B)
Isosceles
(C)
Obtuse-angled
(D)
Right-angled
Correct Answer:
Right-angled
Explanation:
The sum of the three angles of a triangle is 180°. If the sum of two angles equals the third angle, the third angle is 90°. Hence, it is a right-angled triangle.
The sum of the three angles of a triangle is 180°. If the sum of two angles equals the third angle, the third angle is 90°. Hence, it is a right-angled triangle.
Question
67
ज्यामिति
The area of a quadrilateral is 420 m². If the perpendiculars drawn from the opposite vertices to a diagonal are 18 m and 12 m, find the length of the diagonal.
(A)
24 m
(B)
28 m
(C)
26 m
(D)
15 m
Correct Answer:
28 m
Explanation:
Area of a quadrilateral = 1/2 × diagonal × sum of the two perpendiculars. Thus 420 = 1/2 × d × 30, giving d = 28 m.
Area of a quadrilateral = 1/2 × diagonal × sum of the two perpendiculars. Thus 420 = 1/2 × d × 30, giving d = 28 m.
Question
68
सामान्य गणित
Evaluate: (x³ - 3x² + 4x - 2) / (x - 1)
(A)
x² - 2x - 2
(B)
x² + 2x + 2
(C)
x² - x + 2
(D)
x² - 2x + 2
Correct Answer:
x² - 2x + 2
Question
69
ज्यामिति
The difference between the circumference and diameter of a circle is 105 cm. Find the diameter.
(A)
44 cm
(B)
49 cm
(C)
42 cm
(D)
35 cm
Correct Answer:
49 cm
Explanation:
If the diameter is d, circumference = πd. Thus πd - d = 105. Taking π = 22/7, d(15/7) = 105, so d = 49 cm.
If the diameter is d, circumference = πd. Thus πd - d = 105. Taking π = 22/7, d(15/7) = 105, so d = 49 cm.
Question
70
ज्यामिति
The degree measures of the angles of a triangle are integers. Which of the following ratios cannot be their ratio?
(A)
2:3:4
(B)
2:5:7
(C)
3:4:5
(D)
4:5:6
Correct Answer:
2:5:7
Explanation:
For the ratio 2:5:7, the total is 14 parts. Since 180/14 is not an integer, the angle measures cannot all be integers. Hence, this ratio is not possible.
For the ratio 2:5:7, the total is 14 parts. Since 180/14 is not an integer, the angle measures cannot all be integers. Hence, this ratio is not possible.
Total Questions:
150
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