Mathematics questions
18011 published questions with worked solutions.
- The function f(x)= cases 4 + ^ -1 x, & |x| 1 1 2 (|x|-1), & |x|>1 cases is
- Let a_1, a_2, ….., a_n be a given A.P. whose common difference is an integer and S_n=a_1+a_2+ +a_n. If a_1=1, a_n=300 and 15 n...
- The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line x 2 = y 3 = z -6 is :
- The minimum value of 2^ x +2^ x is :
- If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of (1+x)^ n+5 are in the...
- Contrapositive of the statement : 'If a function f is differentiable at a, then it is also continuous at a', is :Not in JEE syllabus
- Suppose the vectors x_1, x_2 and x_3 are the solutions of the system of linear equations, Ax = b when the vector b on the right...
- The circle passing through the intersection of the circles, x^2+y^2-6x=0 and x^2+y^2-4y=0, having its centre on the line. 2x – 3y...
- The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30°. If the angle of depression of the image of C...Not in JEE syllabus
- The integral _ /6 ^ /3 x ^23x(2 x 3x+3 x 6x)dx is equal to :
- Let f:(0, ) (0, ) be a differentiable function such that f(1) = e and _ t x t^2f^2(x)-x^2f^2(t) t-x =0. If f(x) = 1, then x is...
- If the variance of the following frequency distribution : Class : 10-20, 20-30, 30-40 Frequency : 2, x, 2 is 50, then x is equal...
- Let x and [x] denote the fractional part of x and the greatest integer x respectively of a real number x. If _0^n x dx, _0^n[x]dx...
- Let PQ be a diameter of the circle x^2+y^2=9. If and are the lengths of the perpendiculars from P and Q on the straight line, x +...
- If a =2 i + j +2 k , then the value of | i ( a i ) |^2+ | j ( a j ) |^2+ | k ( a k ) |^2 is equal to _________.
- A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of...
- If 3^ 2 2 -1 , 14 and 3^ 4-2 are the first three terms of an A.P. for some , then sixth term of this A.P. is :
- If the function f(x)= cases k_1(x- )^2-1, & x _2 x, & x> cases is twice differentiable, then the ordered pair (k_1,k_2) is equal...
- If the common tangent to the parabolas y^2=4x and x^2=4y also touches the circle, x^2+y^2=c^2, then c is equal to :
- If the volume of a parallelopiped, whose coterminus edges are given by the vectors a = i + j +n k , b =2 i +4 j -n k and c = i +n...