Practice questions
88551 published questions with worked solutions.
- 2x + 5 7 - 6x - x^2 ,dx = A 7 - 6x - x^2 + B ^ -1 ( x + 3 4 ) + C (where C is a constant of integration), then the ordered pair...
- A plane bisects the line segment joining the points (1, 2, 3) and (–3, 4, 5) at right angles. Then this plane also passes through...
- If |z - 3 + 2i| 4 then the difference between the greatest value and the least value of |z| is -
- If the position vectors of the vertices A, B and C of a are respectively 4 i + 7 j + 8 k , 2 i + 3 j + 4 k and 2 i + 5 j + 7 k ,...
- If f(x) = ^ -1 ( 2 3^x 1 + 9^x ), then f' (- 1 2 ) equals
- Let A_n = ( 3 4 ) - ( 3 4 )^2 + ( 3 4 )^3 - + (-1)^ n-1 ( 3 4 )^n and B_n = 1 - A_n. Then, the least odd natural number p, so...
- A normal to the hyperbola, 4x^2 - 9y^2 = 36 meets the co-ordinate axes x and y at A and B, respectively. If the parallelogram...
- Let f(x) be a polynomial of degree 4 having extreme values at x = 1 and x = 2. If _ x 0 ( f(x) x^2 + 1 ) = 3 then f(–1) is equal...
- If the mean of the data : 7, 8, 9, 7, 8, 7, λ, 8 is 8, then the variance of this data is -
- An angle between the lines whose direction cosines are given by the equations, + 3m + 5n = 0 and 5 m - 2mn + 6n = 0, is -
- The tangent to the circle C_1 : x^2 + y^2 - 2x - 1 = 0 at the point (2, 1) cuts off a chord of length 4 from a circle C_2 whose...
- Suppose A is any 3 × 3 non-singular matrix and (A – 3I) (A – 5I) = O, where I = I_3 and O = O_3. If A + A^ -1 = 4I, then + is...
- The value of integral _ /4 ^ 3 /4 x 1 + x ,dx is -
- A tower T_1 of height 60 m is located exactly opposite to a tower T_2 of height 80 m on a straight road. From the top of T_1, if...Not in JEE syllabus
- If I_1 = _0^1 e^ -x ^2 x ,dx; I_2 = _0^1 e^ -x^2 ^2 x ,dx and I_3 = _0^1 e^ -x^3 ,dx; then -
- The sides of a rhombus ABCD are parallel to the lines, x - y + 2 = 0 and 7x - y + 3 = 0. If the diagonals of the rhombus...
- _ x 0 x 2x - 2x x (1 - 2x)^2 equals -
- Let f(x) = cases (x - 1)^ 1 2 - x , & x > 1, x 2 k, & x = 2 cases The value of k for which f is continuous at x = 2 is -
- If a, b, c are in A.P. and a^2, b^2, c^2 are in G.P. such that a < b < c and a + b + c = 3 4 , then the value of a is -
- Tangents drawn from the point (–8, 0) to the parabola y^2 = 8x touch the parabola at P and Q. If F is the focus of the parabola,...