JEE Main questions
34495 published questions with worked solutions.
- 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...
- The area of the region R = (x,y) : xy≤27, 1≤y≤x² is equal to:
- The product of all possible values of α, for which _ x 0 ( 1- ( x) (( +1)x) (( +2)x) ^2(( +1)x) )=2, is:
- Let f : ℝ → ℝ be a differentiable function such that f ( x+y 3 )= f(x)+f(y) 3 for all x,y∈ℝ, and f′(0)=3. Then the minimum value...
- The value of the integral _ /6 ^ /3 ( 4- ^2x ^4x )dx is:
- Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no...
- If the sum of the coefficients of x⁷ and x¹⁴ in the expansion of ( 1 x^3 -x^4 )^n, x≠0, is zero, then the value of n is _______.
- If 4+ _ p=1 ^ 11 ^ -1 ( 2^ p-1 1+2^ 2p-1 )= , then tanα is equal to _______.