Mathematics questions
18011 published questions with worked solutions.
- If a_r= 2r 9 +i 2r 9 , r = 1, 2, 3 …. i= -1 , then the determinant vmatrix a_1&a_2&a_3 _4&a_5&a_6 _7&a_8&a_9 vmatrix is equal to :
- The line 12x cos + 5y sin = 60 is tangent to which of the following curves ?
- Let [t] denote the greatest integer . Then the value of 8. _ 1/2 ^1([2x]+|x|dx) is _______
- A point z moves in the complex plane such that ( z-2 z+2 )= 4 , then the minimum value of |z-9 2-2i|^2 is equal to _______.
- The square of the distance of the point of intersection of the line x-1 2 = y-2 3 = z+1 6 and the plane 2x – y + z = 6 from the...
- If 'R' is the least value of 'a' such that the function f(x) = x^2 + ax + 1 is increasing on [1, 2] and 'S' is the greatest value...
- The mean of 10 numbers 7 8, 10 10, 13 12, 16 14, ….. is _______
- Let two circles of radius r_1 = 1 at centre (1, 1) and r_2 = 2 at centre (9, 1) with equation (x-9)^2+(y-1)^2=4. A common tangent...
- The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the...
- If x (x) = _5^x(3t^2-2 '(t))dt, x > –2, and (0) = 4, then (2) is_____.
- If ( 3^6 4^4 )k is the term, independent of x, in the binomial expansion of ( x 4 - 12 x^2 )^ 12 then k is equal to_____.
- An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The...
- Let A be a 3 × 3 matrix with det(A) = 4. Let R_i denote the i^ th row of A. If a matrix B is obtained by performing the operation...
- The integral e^ 3 _e2x +5e^ 2 _e2x e^ 4 _ex +5e^ 3 _ex -7e^ 2 _ex dx, x > 0, is equal to : (where c is a constant of integration)
- The shortest distance between the line x – y = 1 and the curve x^2=2y is :
- If , R are such that 1-2i (here i^2=–1) is a root of z^2+ z+ =0, then ( - ) is equal to :
- A hyperbola passes through the foci of the ellipse x^2 25 + y^2 16 =1 and its transverse and conjugate axes coincide with major...
- If 0 < x, y < and cosx + cosy – cos(x+y) = 3 2 , then sinx + cosy is equal to :
- A plane passes through the points A(1, 2, 3), B(2, 3, 1) and C(2, 4, 2). If O is the origin and P is (2, –1, 1), then the...
- In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are...