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- If f(x) = ∫t(sinx - sint)dt for t ∈ [0, x] then (A) f'''(x) + f''(x) Answer: (C) f'''(x) + f'(x) = cos x - 2xsin x Write f(x) = sin x∫₀^x t dt - ∫₀^x tsin t dt = dfracx²2sin x - (sin x - xcos x) . Differentiat... 1
- evaluate int x-1/(x+1)^3 e^x dx {integration question } The correct answer is e^xover (x+1)²+c Explaination: 1
- l,m,n are the pth and rth term of G.P all positive then Correct option is 4) 0 Let x and y are first term and common ratio of GP respectively. first and second row are identical =0 1
- find the value of α for which A2 = B, is The correct answer is option d) no real value Explanation:: 1
- A ^−1 = 1/6(A^ 2 +cA+dI) where c, d ∈ R, then pair of values (c, d) are _________ Correct answer is -6,11 Explanation::: 1
- The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is The correct answer is option C) 77 solution:: there can be two cases numbers can be case 1 :: 1, 1, 1, 1, 2, 2, 2 possible 7 digits number b... 1
- If a, b, c are odd positive integers, then number of integral solutions of a + b + c = 13, is The correct answer is option b) 21 explaination :: Let a = 2k + 1, b = 2l + 1, c = 2m + 1 where k, l, m are whole number a + b + c = 13 2k +... 1
- The total number of positive integral solution for x, y, z such that xyz = 24, is The correct answer is option a)30 solution::: xyz = 24 xyz = 2³ × 3¹ The number of ways of distributing 'n' identical balls into 'r' differe... 1
- Two numbers are chosen from 1, 3, 5, 7,… 147, 149 and 151 and multiplied together in all possible ways. The correct answer is d) 1020 In the given numbers 1, 3,5,7,…, 147, 148, 151the numbers which are multiple of 5 are 5, 15, 25, 35,…, 145 whi... 1
- The integral int (2x^12+5x^9 /(x^5+x^3+x)^3) dx is equal to The correct answer is x¹⁰over 2(x⁵+x³+1)²+C Explanation :: 1
- Which of the following is a tautology ? A) (∼p)∧(p∨q)→q option 1) is correct ∼p∧(p∨q)→q (∼p∧p)∨(∼p∧q)→q C∨(∼p∧q)→q (∼p∧q)→q ∼(∼p∧q)∨q =(p∨∼q)∨q=p∨t=t 1
- If sec 4θ − sec 2θ = 2, then find the general value of θ Answer is θ=nπ+π/2 or nπ/5+π/2 Explanation:: Video Solution:: https://youtu.be/pWg7L988Dt8 1
- The greatest coefficient in the expansion of (1+x) 2n+2 is correct option is B) (2n+2)!over [(n+1)!]² 1
- If z is a complex number, then the minimum value of |z| + |z − 1| is ______. First, note that |-z|=|z| and |z1 + z2| ≤ |z1| + |z2| Now |z| + |z-1| = |z| + |1 - z| ≤ |z + (1 - z)| = |1| = 1 Hence, minimum value of |z|... 2
- If (1 + i) (1 + 2i) (1 + 3i) ….. (1 + ni) = x + iy, then what is 2 * 5 * 10….(1 + n2) is equal to? option C) is the correct detailed solution :: We have (1 + i) (1 + 2i) (1 + 3i) ….. (1 + ni) = x + iy …..(i) (1 − i) (1 − 2i) (1 − 3i) ….. (... 1
- For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = 1/4 The correct answer is option B)7/16 P(A) + P(B) – 2P (A ∩ B) = 1/4 P(B) + P(C) – 2P(B ∩C) = 1/4 P(A) + P(C) – 2P(A ∩ C) = 1/4 P (A ∩ B ∩ C)... 1
- If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls, is The correct answer is A)55/3(2/3)¹1 Explanation:: There are 12 balls and they are identical . And 3 identical boxes . That hspace0.2cmmeans... 1
- The number of solution of the equation x+2tanx=π/2 in interval [0,2π] is The correct answer is 3 interval For more information and video solution visit Link not available 1
- The general solution of sin x − 3 sin2x + sin3x = cos x − 3 cos2x + cos3x is _________. Below answer is correct 2
- A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45° 20sqrt3-1 is the correct answer 2
- If x = √3/2 + i/2(i = √-1), then (1 + iz + z5 + iz8)9 is equal to - The correct answer is A) -1 Detailed solution:: 1
- If (z - α)/(z + α) (α ∈ R) is a purely imaginary number and |z| = 2, then a value of α is : The correct answer is B) 2 Explanation :: dfrac z -α z +α +dfrac overline z -α overline z +α =0 z z + z α - α z - α ^ 2 + z z - z α + z α -... 1
- Let A={θϵ(-π/2π):3+2isinθ/1-2isinθ is purely imaginary} then the sum of elements in A is The correct answer is D)2π/3 Detailed answer 1
- Cos190.cos10+sin190.sin10= a)2 b)0 c)-1 d)1 The correct answer is c)-1 Detailed solution 1