Mathematics questions
18011 published questions with worked solutions.
- Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of 16((sec–1x)² +...
- Let a1, a2, a3..... be a G.P. of increasing positive terms. If a1a5 = 28 and a2 + a4 = 29, then a6 is equal to
- Let L1 : x-1 2 = y-2 3 = z-3 4 and L2 : x-2 3 = y-4 4 = z-5 5 be two lines. Then which of the following points lies on the line...
- The product of all solutions of the equation e^ 5( _e x)^2+3 = x^8 , x > 0, is :
- If _ r=1 ^ n T_r = (2n-1)(2n+1)(2n+3)(2n+5) 64 , then _ n _ r=1 ^ n ( 1 T_r ) is equal to :
- From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in...
- Let for ƒ(x) = 7tan⁸x + 7tan⁶x – 3tan⁴x – 3tan²x, I_1 = _0^ /4 f(x)dx and I_2 = _0^ /4 xf(x)dx. Then 7I1 + 12I2 is equal to :
- Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the...
- Let the function f(x) = cases -3ax^2-2, & x<1 a^2+bx & x 1 cases Be differentiable for all x ∈ R, where a > 1, b ∈R. If the area...
- If _ r=0 ^ 5 ^ 11 C_ 2r+1 2r+2 = m n , gcd (m, n) = 1, then m – n is equal to _______.
- Let A be a square matrix of order 3 such that det(A) = –2 and det(3adj(–6adj(3A))) = 2^ m+n .3^ mn , m > n. Then 4m + 2n is equal...
- Let L1 : x-1 3 = y-1 -1 = z+1 0 and L2 : x-2 2 = y 0 = z+4 , α ∈R, be two lines, which intersect at the point B. If P is the foot...
- Let c be the projection vector of b = i +4 k , λ > 0, on the vector a = i +2 j +2 k . If | a + c | = 7, then the area of the...
- In a group of 3 girls and 4 boys, there are two boys B_1 and B_2. The number of ways, in which these girls and boys can stand in...
- Let P(4, 4 3 ) be a point on the parabola y^2 = 4ax and PQ be a focal chord of the parabola. If M and N are the foot of...
- For a 3 3 matrix M, let trace (M) denote the sum of all the diagonal elements of M. Let A be a 3 3 matrix such that |A| = 1 2 and...
- Suppose that the number of terms in an A.P is 2k, k N. If the sum of all odd terms of the A.P. is 40, the sum of all even terms...
- If _ x ( ( e 1-e ) ( 1 e - x 1+x ) )^x = , then the value of _e 1+ _e equals :
- Let f(x) = _0^ x^2 t^2-8t+15 e^t ,dt, x R . Then the number of local maximum and local minimum points of f, respectively, are :
- If x = f(y) is the solution of the differential equation (1+y^2) + (x - 2e^ ^ -1 y ) dy dx = 0, y (- 2 , 2 ) With f(0) = 1, then...