#ssc 10th
- The roots of \(x^2 - 2x - 15 = 0\) are Answer: B. 5 and -3 x² - 2x - 15 = (x - 5)(x + 3) = 0 , so x = 5 or x = -3 . 1
- If the discriminant of a quadratic equation is negative, its roots are Answer: A. not real When b² - 4ac < 0 , the quadratic equation has no real roots. 1
- The value of the discriminant of \(x^2 + 2x + 5 = 0\) is Answer: B. -16 b² - 4ac = 4 - 20 = -16 . 1
- The 10th term of the A.P. 5, 9, 13, ... is Answer: B. 41 t₁₀ = 5 + 9 × 4 = 41 . 1
- The sum of the first \(n\) odd natural numbers is Answer: A. n² S_n = n/2[2(1) + (n - 1)2] = n/2(2n) = n² . 1
- For an A.P., \(a = 6\) and \(d = 3\). Then \(S_6 = \) Answer: B. 81 S₆ = 6/2[2(6) + 5(3)] = 3(12 + 15) = 81 . 1
- The common difference of the A.P. \(\frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots\) is Answer: C. -1 d = -1/2 - 1/2 = -1 . 1
- GST stands for Answer: D. Goods and Services Tax GST is the Goods and Services Tax. 1
- The taxable value of an article is ₹ 5000 and the rate of GST is 28%. The GST charged is Answer: C. ₹ 1400 GST = 28/100 × 5000 = ₹ 1400 . 1
- Which body regulates the share market in India? Answer: B. SEBI The Securities and Exchange Board of India (SEBI) regulates the share market. 1
- The face value of a share is ₹ 100 and it is available at a premium of ₹ 20. Its market value is Answer: B. ₹ 120 MV = FV + premium = 100 + 20 = ₹ 120 . 1
- The probability of an impossible event is Answer: A. 0 An impossible event never happens, so its probability is 0. 1
- Two coins are tossed simultaneously. The probability of getting no head is Answer: B. 1/4 S = \HH, HT, TH, TT\ . Only TT has no head: P = 1/4 . 1
- For a pair of simultaneous equations, \(D = 3\), \(D_x = 9\) and \(D_y = -6\). The solution \((x, y)\) is Answer: D. (3, -2) x = D_x/D = 9/3 = 3 , y = D_y/D = -6/3 = -2 . 1
- One letter is chosen at random from the word MAHARASHTRA. The probability that it is the letter A is Answer: C. 4/11 MAHARASHTRA has 11 letters, of which 4 are A. P = 4/11 . 1
- A number is chosen at random from 1 to 50. The probability that it is a multiple of 7 is Answer: B. 7/50 Multiples of 7 up to 50: 7, 14, 21, 28, 35, 42, 49, which is 7 numbers. P = 7/50 . 1
- The upper class limit of the class 20–30 is Answer: D. 30 In the class 20–30, 20 is the lower limit and 30 is the upper limit. 1
- By the direct method, the mean of grouped data is Answer: A. X = Σ f_i x_i/Σ f_i Mean = Σ f_i x_i/Σ f_i , where x_i are class marks. 1
- In a pie diagram, the central angle of a sector is 72°. The sector represents what percentage of the total data? Answer: A. 20% 72/360 × 100 = 20% . 1
- In the step deviation method, \(A = 25\) and \(h = 10\). For the class mark \(x_i = 15\), \(u_i = \) Answer: D. -1 u_i = x_i - A/h = 15 - 25/10 = -1 . 1
- The median class of a grouped frequency distribution is Answer: D. the first class whose cumulative frequency is greater than or equal to N/2 The median class is the first class whose 'less than'... 1
- The sum of the first 15 terms of the A.P. with \(a = -3\) and \(d = 4\) is Answer: D. 375 S₁₅ = 15/2[2(-3) + 14 × 4] = 15/2(-6 + 56) = 15/2 × 50 = 375 . 1
- How many characters are there in a GSTIN (GST identification number)? Answer: C. 15 A GSTIN is a 15-character identification number. 1
- For an intra-state supply, the GST rate is 18%. The rate of CGST is Answer: D. 9% For an intra-state supply, GST is split equally into CGST and SGST: 18% ÷ 2 = 9% . 1