Mathematics questions
18011 published questions with worked solutions.
- A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a...
- Let S= x (- , ):x 0, 2 . The sum of all distinct solutions of the equation 3 x+ cosec x+2( x- x)=0 in the set S is equal toNot in JEE Main syllabus
- A computer producing factory has only two plants T_1 and T_2. Plant T_1 produces 20% and plant T_2 produces 80% of the total...
- The least value of R for which 4 x^2+ 1 x 1, for all x>0, is
- Consider a pyramid OPQRS located in the first octant (x 0,y 0,z 0) with O as origin, and OP and OR along the x-axis and the...
- Let P= bmatrix 3 & -1 & -2 2 & 0 & 3 & -5 & 0 bmatrix , where R . Suppose Q=[q_ ij ] is a matrix such that PQ=kI, where k R , k 0...
- In a triangle XYZ, let x,y,z be the lengths of sides opposite to the angles X,Y,Z, respectively, and 2s=x+y+z. If s-x 4 = s-y 3 =...Not in JEE syllabus
- A solution curve of the differential equation (x^2+xy+4x+2y+4) dy dx -y^2=0, x>0, passes through the point (1,3). Then the...
- Let f: R R , g: R R and h: R R be differentiable functions such that f(x)=x^3+3x+2, g(f(x))=x and h(g(g(x)))=x for all x R . Then
- Let RS be the diameter of the circle x^2+y^2=1, where S is the point (1,0). Let P be a variable point (other than R and S) on the...
- The total number of distinct x R for which vmatrix x & x^2 & 1+x^3 2x & 4x^2 & 1+8x^3 3x & 9x^2 & 1+27x^3 vmatrix =10 is
- Let m be the smallest positive integer such that the coefficient of x^2 in the expansion of (1+x)^2+(1+x)^3+ +(1+x)^ 49 +(1+mx)^...
- The total number of distinct x [0,1] for which _0^x t^2 1+t^4 ,dt=2x-1 is
- Let , R be such that _ x 0 x^2 ( x) x- x =1. Then 6( + ) equals
- Let z= -1+ 3 i 2 , where i= -1 , and r,s 1,2,3 . Let P= bmatrix (-z)^r & z^ 2s z^ 2s & z^r bmatrix and I be the identity matrix...
- Let P= bmatrix 1 & 0 & 0 4 & 1 & 0 16 & 4 & 1 bmatrix and I be the identity matrix of order 3. If Q=[q_ ij ] is a matrix such...
- Let b_i>1 for i=1,2, ,101. Suppose _eb_1, _eb_2, , _eb_ 101 are in Arithmetic Progression (A.P.) with the common difference _e2....
- The value of _ k=1 ^ 13 1 ( 4 + (k-1) 6 ) ( 4 + k 6 ) is equal to
- The value of _ - 2 ^ 2 x^2 x 1+e^x ,dx is equal to
- Area of the region (x,y) R ^2:y |x+3| , 5y x+9 15 is equal to