Mathematics — MCQ Practice Questions & Answers

Question 1

If the sum of the roots of the quadratic equation 2x² + (k-3)x + (k-5) = 0 is equal to half of their product, then the value of k is:

Accepted Answer

Correct answer: A. 11 — For a quadratic equation ax² + bx + c = 0, sum of roots = -b/a and product of roots = c/a. Here, sum = -(k-3)/2 and product = (k-5)/2. Given that sum = (1/2) × product, we have -(k-3)/2 = (1/2) × (k-5)/2. Solving: -(k-3)/2 = (k-5)/4, which gives -2(k-3) = k-5, leading to -2k+6 = k-5, thus k = 11.

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B. 9

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C. 7

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D. 5

Question 2

A circle is inscribed in a square of side 8 cm. If a smaller square is inscribed in the circle, what is the area of the smaller square?

Accepted Answer

Correct answer: A. 32 cm² — The inscribed circle in the square has diameter 8 cm, so radius = 4 cm. When a square is inscribed in this circle, its diagonal equals the diameter (8 cm). If the diagonal of the smaller square is 8 cm, then using diagonal = side√2, we get side = 8/√2 = 4√2 cm. Therefore, area = (4√2)² = 32 cm².

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B. 64 cm²

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C. 16 cm²

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D. 48 cm²

Question 3

Two concentric circles have radii r and R (where r < R). The area of the ring formed between them is equal to the area of the inner circle. What is the ratio R:r?

Accepted Answer

Correct answer: A. √2:1 — The area of the ring = π(R² - r²). Given that this equals the area of the inner circle = πr², we have R² - r² = r², which gives R² = 2r², so R = r√2. Therefore, the ratio R:r = √2:1.

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B. 2:1

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C. √3:1

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D. 3:1

Question 4

A regular hexagon is inscribed in a circle of radius 6 cm. What is the difference between the perimeter of the hexagon and the circumference of the circle?

Accepted Answer

Correct answer: B. 12π - 36 cm — For a regular hexagon inscribed in a circle of radius R, the side length equals R. Here, side = 6 cm, so perimeter = 6 × 6 = 36 cm. The circumference of the circle = 2πR = 12π cm. Since 12π ≈ 37.7 > 36, the difference is 12π - 36 cm (circumference is greater).

Answer

A. 36 - 12π cm

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C. 36 - 6π cm

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D. 6π - 36 cm

Question 5

Median of: 5,8,3,9,1,7,6?

Accepted Answer

Correct answer: A. 6 — To find the median, we must first arrange all numbers in ascending order, then locate the middle value. Step 1: Count the total numbers We have 7 numbers: 5, 8, 3, 9, 1, 7, 6 Step 2: Arrange in ascending order 1, 3, 5, 6, 7, 8, 9 Step 3: Find the position of median Since n = 7 (odd number), median position = \frac{n+1}{2} = \frac{7+1}{2} = 4 Step 4: Identify the 4th element Counting from left: 1st is 1, 2nd is 3, 3rd is 5, 4th is 6 Therefore, the median is 6. The answer is (A) 6

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B. 5

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C. 7

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D. 8

Question 6

Differentiate y = 3x²

Accepted Answer

Correct answer: A. 6x — Differentiation is finding the rate of change of a function with respect to a variable. Step 1: Identify the function and the rule to apply. We have y = 3x² and we need to use the Power Rule of differentiation. Step 2: Recall the Power Rule. The Power Rule states: If y = ax^n, then \frac{dy}{dx} = n \cdot a \cdot x^{n-1} Step 3: Apply the Power Rule to our function. Here, a = 3 and n = 2 \frac{dy}{dx} = 2 \cdot 3 \cdot x^{2-1} Step 4: Simplify. \frac{dy}{dx} = 6 \cdot x^1 = 6x Therefore, the derivative of y = 3x² is 6x Answer: A) 6x

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B. 3x

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C. 6x²

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D. 3x²

Question 7

Solve: x² - 5x + 6 = 0

Accepted Answer

Correct answer: A. x=2,3 — This question asks you to find the roots of a quadratic equation using factorization. Step 1: Write the equation in standard form. x^2 - 5x + 6 = 0 Step 2: Find two numbers that multiply to give 6 (constant term) and add to give -5 (coefficient of x). The numbers are -2 and -3, because: (-2) × (-3) = 6 (-2) + (-3) = -5 Step 3: Factorize the quadratic. (x - 2)(x - 3) = 0 Step 4: Solve for x by setting each factor equal to zero. x - 2 = 0 → x = 2 x - 3 = 0 → x = 3 Step 5: Verify by substituting back. For x = 2: (2)² - 5(2) + 6 = 4 - 10 + 6 = 0 ✓ For x = 3: (3)² - 5(3) + 6 = 9 - 15 + 6 = 0 ✓ Therefore, x = 2, 3 The answer is (A).

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B. x=1,6

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C. x=3,4

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D. x=2,4

Question 8

7! (7 factorial) = ?

Accepted Answer

Correct answer: B. 5040 — Factorial is the product of all positive integers from 1 up to a given number. Step 1: Understand factorial notation 7! means 7 × 6 × 5 × 4 × 3 × 2 × 1 Step 2: Multiply step by step 7! = 7 	imes 6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1 Step 3: Calculate from left to right 7 × 6 = 42 42 × 5 = 210 210 × 4 = 840 840 × 3 = 2520 2520 × 2 = 5040 5040 × 1 = 5040 Therefore, 7! = 5040 The answer is (B) 5040

Answer

A. 2520

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C. 720

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D. 1260

Mathematics - MCQ Practice Questions