Mathematics questions
18011 published questions with worked solutions.
- Let f : R R be a function defined as f(x)= cases 3 (1- |x| 2 ), & |x| 2 0, & |x|>2 cases Let g : R be given by g(x) = f(x + 2) –...
- If the constant term, in binomial expansion of (2x^r+ 1 x^2 )^ 10 is 180, then r is equal to _____.
- Let y = y(x) be the solution of the differential equation ((x+2)e^ ( y+1 x+2 ) +(y+1) )dx=(x+2)dy, y(1) = 1. If the domain of y =...
- For the statements p and q, consider the following compound statements : (a) ( q (p q)) p (b) ((p q) p) q Then which of the...Not in JEE syllabus
- Let the mirror image of the point P(a, 6, 9) with respect to the line x-3 7 = y-2 5 = z-1 -9 is (20, b, –a –9), then |a + b| is...
- The vector equation of the plane passing through the intersection of the planes r ( i + j + k )=1 and r ( i -2 j )=-2, and the...
- If P is a point on the parabola y = x^2 + 4 which is closest to the straight line y = 4x – 1, then the co-ordinates of P are :
- The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 20 seconds at the speed of 432...Not in JEE syllabus
- If n 2 is a positive integer, then the sum of the series ^ n+1 C_2+2(^2C_2+^3C_2+^4C_2+ +^nC_2) is :
- Let f:R R be defined as, f(x)= cases -55x, & x<-5 2x^3-3x^2-120x, & -5 x 4 2x^3-3x^2-36x-336, & x>4 cases Let A = x R: f is...
- For which of the following curves, the line x+ 3 y = 2 3 is the tangent at the point ( 3 3 2 , 1 2 )?
- The value of the integral, _1^3[x^2-2x-2]dx where [x] denotes the greatest integer less than or equal to x, is :
- A possible value of ( 1 4 ^ -1 63 8 ) is :
- The negative of the statement p (p q) is :Not in JEE syllabus
- If the curve y = ax^2 + bx + c, x , passes through the point (1, 2) and the tangent line to this curve at origin is y = x, then...
- The area of the region : R= (x,y):5x^2 y 2x^2+9 is :
- Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2–x) for all x (0,2), f(0)=1 and f(2) = e^2. Then...
- Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear...
- Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be ( 10 3 , 7...
- For the system of linear equations : x – 2y = 1, x – y + kz = –2, ky + 4z = 6, k R, consider the following statements : (A) The...