10th Class Math Quiz

Section A

• Question 1: The product of zeroes of the polynomial kx² - 4x - 7 is 2. Find k. The answer is -7/2.

• Question 2: In an arithmetic progression (A.P.), given a = 8 and a₁₁ = -19, calculate the common difference (d). The answer is -3.

• Question 3: The midpoint of the line segment joining points (-1, 3) and (8, 3) is (7/2, 3).

• Question 4: If sin θ = 1/√3, calculate the value of sec θ. The answer is 2√2/3.

• Question 5: The highest common factor (HCF) of 132 and 77 is 11.

• Question 6: In a quadratic equation 4x² - 5x + k = 0, if the roots are real and equal, the value of k is 25/16.

• Question 7: If the probability of winning a game is p, the probability of losing the game is 1 - p.

• Question 8: The distance between points (2, -3) and (-2, 3) is 2√13 units.

• Question 9: Find the value of θ for which sin²θ + sinθcosθ + cos²θ = 2. The answer is 90°.

• Question 10: The probability of drawing a red queen from a standard deck of 52 playing cards is 2/26 = 1/13.

• Question 11: In statistics, if a variable divides a data set into two equal parts, it's called the median.

Section B

• Question 12: A sphere with radius 7 cm has a volume of 539/3 cubic cm.

• Question 13: In a statistical data set, if the mean and median are 21 and 23 respectively, then the mode is 27.

• Question 14: The slant height of a right circular cone with a height of 24 cm and a radius of 7 cm is 25 cm.

• Question 15: If one of the roots of the quadratic polynomial (a - 1)x² + ax + 1 = 0 is -3, then the value of 'a' is 4/3.

• Question 16: If one end of a diameter of a circle is (-4, 0), and the diameter has a length of 6 cm, the other end of the diameter on the x-axis is (2, 0).

• Question 17: The value of k for which the pair of linear equations 5x + 2y - 7 = 0 and 2x + ky + 1 = 0 do not have a solution is 4/5.

• Question 18: The probability of getting a doublet when rolling two dice is 1/6.

• Question 19: Assertion (A) : If PA and PB are tangents from an external point P to a circle with center O, then quadrilateral OAPB is a cyclic quadrilateral. Reason (R): Opposite angles in a cyclic quadrilateral are equal. The correct answer is (c) The assertion is true but the reason is false.

• Question 20: Assertion (A): The zeroes of the polynomial p(x) = x² - 2x - 3 are -1 and 3. Reason (R): The graph of p(x) intersects the x-axis at (-1, 0) and (3, 0). The correct answer is (a) Both Assertion (A) and Reason (R) are true and Reason (R) explains Assertion (A) completely.

• Question 21: Given D is a point on BC of triangle ABC such that angle ADC = angle BAC, prove AC² = BC * DC. (This is a geometry proof problem.)