Mathematics — MCQ Practice Questions & Answers

Question 1

If x, y, z are in arithmetic progression and x + y + z = 15, then the middle term is:

Accepted Answer

Correct answer: B. 5 — When three numbers are in arithmetic progression, they can be written as (a-d), a, (a+d) where a is the middle term. Their sum is (a-d) + a + (a+d) = 3a = 15, giving a = 5. Therefore, the middle term y = 5.

Answer

A. 3

Answer

C. 7

Answer

D. 9

Question 2

If p and q are roots of x² - 5x + 6 = 0, then the value of (1/p + 1/q) is:

Accepted Answer

Correct answer: A. 5/6 — Using Vieta's formulas: p + q = 5 and pq = 6. We need 1/p + 1/q = (p+q)/pq = 5/6. This approach avoids finding individual roots and uses the relationship between roots directly.

Answer

B. 6/5

Answer

C. 1/2

Answer

D. 2

Question 3

In a right-angled triangle, the altitude drawn to the hypotenuse divides it into segments of lengths 9 cm and 16 cm. What is the length of the altitude?

Accepted Answer

Correct answer: A. 12 cm — By the geometric mean altitude theorem, when an altitude is drawn to the hypotenuse of a right triangle, the altitude is the geometric mean of the two segments of the hypotenuse. Therefore, altitude = √(9 × 16) = √144 = 12 cm. This is a fundamental property used frequently in competitive exams.

Answer

B. 15 cm

Answer

C. 18 cm

Answer

D. 20 cm

Question 4

In triangle ABC, point D lies on BC such that AD is the angle bisector. If AB = 6 cm, AC = 9 cm, and BD = 4 cm, what is the length of DC?

Accepted Answer

Correct answer: B. 6 cm — By the Angle Bisector Theorem, the angle bisector divides the opposite side in the ratio of the adjacent sides. Therefore, BD/DC = AB/AC, which gives 4/DC = 6/9. Solving: DC = (4 × 9)/6 = 36/6 = 6 cm. This theorem is essential for solving numerous geometry problems in competitive exams.

Answer

A. 5 cm

Answer

C. 7 cm

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D. 8 cm

Question 5

sin 30° = ?

Accepted Answer

Correct answer: B. 0.5 — This question tests your knowledge of standard trigonometric ratios for common angles. Step 1: Recall the standard trigonometric ratios table for common angles (0°, 30°, 45°, 60°, 90°). Step 2: Locate the value of sin 30° from the standard table: \sin 30° = \frac{1}{2} = 0.5 Step 3: Verify using the unit circle or right triangle approach — in a 30-60-90 triangle, the side opposite to 30° is half the hypotenuse, giving us \sin 30° = \frac{1}{2} . Step 4: Convert the fraction to decimal form: \frac{1}{2} = 0.5 Therefore, sin 30° = 0.5 Answer: B) 0.5

Answer

A. 1

Answer

C. √3/2

Answer

D. 1/√2

Question 6

Solve: 2x + 5 = 15

Accepted Answer

Correct answer: B. x=5 — This is a linear equation problem where we need to isolate the variable x on one side. Step 1: Start with the equation 2x + 5 = 15 Step 2: Subtract 5 from both sides to remove the constant term 2x + 5 - 5 = 15 - 5 2x = 10 Step 3: Divide both sides by 2 to isolate x \frac{2x}{2} = \frac{10}{2} x = 5 Step 4: Verify by substituting x = 5 back into the original equation 2(5) + 5 = 10 + 5 = 15 ✓ Therefore, x = 5 The answer is B) x = 5

Answer

A. x=4

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C. x=6

Answer

D. x=3

Question 7

Area of circle with radius 7cm (π=22/7)?

Accepted Answer

Correct answer: A. 154 sq cm — To find the area of a circle, we use the formula Area = πr², where r is the radius. Step 1: Write the formula for area of a circle. A = \pi r^2 Step 2: Substitute the given values. - Radius r = 7 cm - π = 22/7 A = \frac{22}{7} 	imes 7^2 Step 3: Calculate 7². A = \frac{22}{7} 	imes 49 Step 4: Simplify by canceling 7. A = 22 	imes 7 = 154 	ext{ sq cm} Therefore, the area of the circle is 154 sq cm. The answer is (A) 154 sq cm.

Answer

B. 144 sq cm

Answer

C. 164 sq cm

Answer

D. 174 sq cm

Question 8

Sum of angles in a triangle?

Accepted Answer

Correct answer: B. 180° — The sum of all three interior angles of any triangle is always constant, regardless of the triangle's shape or size. Step 1: Understand the fundamental property Every triangle has exactly 3 interior angles. These angles are formed where two sides of the triangle meet. Step 2: Apply the angle sum theorem The angle sum property of a triangle states: 	ext{Angle 1} + 	ext{Angle 2} + 	ext{Angle 3} = 180° Step 3: Verify with examples - Equilateral triangle: 60° + 60° + 60° = 180° - Right triangle: 90° + 45° + 45° = 180° - Isosceles triangle: 70° + 70° + 40° = 180° This property holds for all triangles without exception. It's a basic axiom in Euclidean geometry. Therefore, the sum of angles in a triangle = 180° Answer: B) 180°

Answer

A. 90°

Answer

C. 270°

Answer

D. 360°

Mathematics - MCQ Practice Questions