Mathematics questions
18011 published questions with worked solutions.
- Let a,b,c be three non-zero real numbers such that the equation 3 a x+2b x=c, x [- 2 , 2 ], has two distinct real roots and with...
- A farmer F_1 has a land in the shape of a triangle with vertices at P(0,0), Q(1,1) and R(2,0). From this land, a neighbouring...
- For any positive integer n, define f_n:(0, ) R as f_n(x)= _ j=1 ^ n ^ -1 ( 1 1+(x+j)(x+j-1) ) for all x (0, ). (Here, the inverse...
- Let S be the set of all column matrices bmatrix b_1 b_2 b_3 bmatrix such that b_1,b_2,b_3 R and the system of equations (in real...
- Consider two straight lines, each of which is tangent to both the circle x^2+y^2= 1 2 and the parabola y^2=4x. Let these lines...
- Let f:(0, ) R be a twice differentiable function such that _ t x f(x) t-f(t) x t-x = ^2x for all x (0, ). If f ( 6 )=- 12 , then...
- The value of the integral _0^ 1 2 1+ 3 ((x+1)^2(1-x)^6 )^ 1 4 ,dx is _____.
- Let P be a matrix of order 3 3 such that all the entries in P are from the set -1,0,1 . Then, the maximum possible value of the...
- Let f: R R be a differentiable function with f(0)=0. If y=f(x) satisfies the differential equation dy dx =(2+5y)(5y-2), then the...
- Let P be a point in the first octant, whose image Q in the plane x+y=3 (that is, the line segment PQ is perpendicular to the...
- Consider the cube in the first octant with sides OP, OQ and OR of length 1, along the x-axis, y-axis and z-axis, respectively,...
- Let X= ( ^ 10 C_1 )^2+2 ( ^ 10 C_2 )^2+3 ( ^ 10 C_3 )^2+ +10 ( ^ 10 C_ 10 )^2, where ^ 10 C_r, r 1,2, ,10 denote binomial...
- Let S be the set of all complex numbers z satisfying |z-2+i| 5 . If the complex number z_0 is such that 1 |z_0-1| is the maximum...
- Let M= bmatrix ^4 & -1- ^2 1+ ^2 & ^4 bmatrix = I+ M^ -1 , where = ( ) and = ( ) are real numbers, and I is the 2 2 identity...
- A line y=mx+1 intersects the circle (x-3)^2+(y+2)^2=25 at the points P and Q. If the midpoint of the line segment PQ has...
- The area of the region (x,y):xy 8, 1 y x^2 is
- Let M= bmatrix 0 & 1 & a 1 & 2 & 3 3 & b & 1 bmatrix and adj ,M= bmatrix -1 & 1 & -1 8 & -6 & 2 -5 & 3 & -1 bmatrix where a and b...
- There are three bags B_1, B_2 and B_3. The bag B_1 contains 5 red and 5 green balls, B_2 contains 3 red and 5 green balls, and...
- In a non-right-angled triangle PQR, let p,q,r denote the lengths of the sides opposite to the angles at P,Q,R respectively. The...Not in JEE syllabus
- Define the collections E_1,E_2,E_3, of ellipses and R_1,R_2,R_3, of rectangles as follows: E_1: x^2 9 + y^2 4 =1; R_1: rectangle...