#ssc 10th
- The Y-axis divides the segment joining \((-3, 4)\) and \((6, 1)\) in the ratio Answer: C. 1 : 2 Let the ratio be m : n . On the Y-axis x = 0 : 6m - 3n/m + n = 0 ⇒ 6m = 3n ⇒ m : n = 1 : 2 . 1
- The total of the central angles of all the sectors in a pie diagram is Answer: D. 360° The whole circle represents the total data, so the central angles add up to 360°. 1
- In the assumed mean method, the mean of grouped data is given by Answer: C. X = A + d With d_i = x_i - A and d = Σ f_i d_i/Σ f_i , the mean is X = A + d . 1
- The class mark of the class 10–20 is Answer: B. 15 Class mark = 10 + 20/2 = 15 . 1
- A family's total monthly expenditure is ₹ 12,000, of which ₹ 3000 is spent on food. In a pie diagram, the central angle for food is Answer: C. 90° Central angle = 3000/12000 × 360° = 90° . 1
- In the formula for the median of grouped data, \(\text{Median} = L + \left[\frac{\frac{N}{2} - cf}{f}\right] \times h\), \(cf\) denotes Answer: C. the cumulative frequency of the class preceding the median class cf is the 'less than' cumulative frequency of the class just bef... 1
- The formula for the mode of grouped data is Answer: A. L + [f₁ - f₀/2f₁ - f₀ - f₂] × h Mode = L + [f₁ - f₀/2f₁ - f₀ - f₂] × h , where f₁ is the frequency of the modal class and f₀, f₂... 1
- For a frequency distribution, \(\sum f_i x_i = 1860\) and \(\sum f_i = 60\). The mean is Answer: A. 31 X = Σ f_i x_i/Σ f_i = 1860/60 = 31 . 1
- How many tangents can be drawn to a circle at a point on the circle? Answer: B. 1 By the tangent theorem, exactly one tangent can be drawn at a point on a circle. 1
- The angle between a tangent to a circle and the radius at the point of contact is Answer: A. 90° A tangent is perpendicular to the radius at the point of contact. 1
- The measure of an inscribed angle is 50°. The measure of its intercepted arc is Answer: B. 100° An inscribed angle is half its intercepted arc, so the arc is 2 × 50° = 100° . 1
- For the distribution with classes 0–10, 10–20, 20–30, 30–40, 40–50 and frequencies 5, 8, 12, 10, 5 respectively, the median is (approximately) Answer: D. 25.83 N = 40 , N/2 = 20 . Cumulative frequencies are 5, 13, 25, ..., so the median class is 20–30 with L = 20, cf = 13, f = 12, h... 1
- For the distribution with classes 0–10, 10–20, 20–30, 30–40, 40–50 and frequencies 3, 7, 15, 9, 6 respectively, the mode is (approximately) Answer: A. 25.71 The modal class is 20–30: L = 20, f₁ = 15, f₀ = 7, f₂ = 9, h = 10 . Mode = 20 + 15 - 7/30 - 7 - 9 × 10 = 20 + 80/14 ≈ 25.71... 1
- In the step deviation method, \(A = 25\), \(h = 10\), \(\sum f_i u_i = 20\) and \(\sum f_i = 50\). The mean is Answer: A. 29 X = A + Σ f_i u_i/Σ f_i × h = 25 + 20/50 × 10 = 25 + 4 = 29 . 1
- Which of the following cannot be the probability of an event? Answer: C. 1.5 For any event A , 0 ≤ P(A) ≤ 1 . 1.5 is greater than 1. 1
- A card is drawn from a well-shuffled pack of 52 playing cards. The probability that it is a king is Answer: A. 1/13 There are 4 kings: P = 4/52 = 1/13 . 1
- Two dice are thrown simultaneously. The probability that the sum of the numbers on the upper faces is 7 is Answer: C. 1/6 n(S) = 36 . Favourable: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), so P = 6/36 = 1/6 . 1
- If \(P(A) = 0.35\), then \(P(A') = \) Answer: D. 0.65 P(A') = 1 - P(A) = 1 - 0.35 = 0.65 . 1
- Which of the following is a quadratic equation? Answer: B. x² + 2x + 11 = 0 A quadratic equation has degree 2. (x+2)² = x² + 5 simplifies to 4x - 1 = 0 , which is linear; x³ - x² + 3 = 0 h... 1
- Which of the following is a root of \(x^2 - 5x + 6 = 0\)? Answer: B. 2 x² - 5x + 6 = (x - 2)(x - 3) , so the roots are 2 and 3. Only 2 is among the options. 1
- A card is drawn from 25 cards numbered 1 to 25. The probability that the number is prime is Answer: A. 9/25 Primes up to 25: 2, 3, 5, 7, 11, 13, 17, 19, 23, which is 9 numbers. P = 9/25 . 1
- Three coins are tossed simultaneously. The probability of getting at least two heads is Answer: A. 1/2 n(S) = 8 . At least two heads: HHT, HTH, THH, HHH, which is 4 outcomes. P = 4/8 = 1/2 . 1
- A two-digit number is formed using the digits 2, 3 and 5 without repetition. The probability that the number is divisible by 5 is Answer: B. 1/3 S = \23, 25, 32, 35, 52, 53\ , n(S) = 6 . Divisible by 5: 25 and 35. P = 2/6 = 1/3 . 1
- The value of the discriminant of \(2x^2 - 5x + 1 = 0\) is Answer: D. 17 b² - 4ac = (-5)² - 4(2)(1) = 25 - 8 = 17 . 1