Mathematics questions
18011 published questions with worked solutions.
- Let f : [1,∞) → ℝ be a differentiable function defined as f(x)= _1^x f(t)dt+(1-x)( _ex-1)+e. Then the value of f(f(1)) is:
- Let A= 1,4,7 and B= 2,3,8 . Then the number of elements, in the relation R= ((a₁,b₁),(a₂,b₂))∈((A×B)×(A×B)) : a₁+b₂ divides a₂+b₁...
- From the point (−1,−1), two rays are sent making angles of 45° with the line x+y=0. These rays get reflected from the mirror...
- If S= [- , ] : 5 2= 7 7 2 , then n(S) is equal to _______.Not in JEE Main syllabus
- Let f : ℝ → ℝ be a function such that f(x)+3f(π/2−x)=sinx, x∈ℝ. Let the maximum value of f on ℝ be α. If the area of the region...
- Let y=y(x) be the solution of the differential equation ( x)^ 1/2 dy=( ^3x-( x)^ 3/2 y)dx, 0<x< 2, y ( 4 )= 6 2 5. If y ( 3 )= 45...
- Let a, b ∈ ℂ. Let α, β be the roots of the equation x² + ax + b = 0. If β − α = √11 and β² − α² = 3i√11, then (β³ − α³)² is equal...
- Let the sum of the first n terms of an A.P. be 3n²+5n. Then the sum of squares of the first 10 terms of the A.P. is:
- Let A be a 3×3 matrix such that A^T bmatrix 1 0 1 bmatrix = bmatrix 5 2 2 bmatrix , A^T bmatrix 0 0 1 bmatrix = bmatrix 3 1 1...
- Consider the system of linear equations in x,y,z: x+2y+tz=0, 6x+y+5tz=0, 3x+t²y+f(t)z=0, where f : ℝ → ℝ is a differentiable...
- _ n=1 ^ 10 ( 528 n(n+1)(n+2) ) is equal to:
- Let tanA, tanB, where A,B∈(−π/2,π/2), be the roots of the quadratic equation x²−2x−5=0. Then 20 ^2 ( A+B 2 ) is equal to:
- A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN...
- The mean deviation about the mean for the data | xᵢ | 5 | 7 | 9 | 10 | 12 | 15 | |---|---|---|---|---|---|---| | fᵢ | 8 | 6 | 2 |...
- Let a focus of the ellipse E : x²/a²+y²/b²=1 be S(4,0) and its eccentricity be 4/5. If the point P(3,α) lies on E and O is the...
- In an equilateral triangle PQR, let the vertex P be at (3,5) and the side QR be along the line x+y=4. If the orthocentre of the...
- The sum of all the integral values of p such that the equation 3sin²x+12cosx−3=p, x∈ℝ, has at least one solution, is:
- The square of the distance of the point P(5,6,7) from the line x-2 2= y-5 3= z-2 4 is equal to:
- Let a= 7 i+ j- k and b= j+2 k. If r is a vector such that r a+ a b= 0 and r a=0, then |3r|² is equal to:
- The square of the distance of the point of intersection of the lines r=( i+ j- k)+ (a i- j), a≠0 and r=(4 i- k)+ (2 i+a k) from...