Practice questions
90156 published questions with worked solutions.
- Let α, β be the roots of the equation x²−x+p=0 and γ, δ be the roots of the equation x²−4x+q=0; p,q∈ℤ. If α, β, γ, δ are in G.P.,...
- Let z₁,z₂∈ℂ be the distinct solutions of the equation z²+4z−(1+12i)=0. Then |z₁|²+|z₂|² is equal to:
- If f : ℕ → ℤ is defined by f(n)= vmatrix n & -1 & -5 -2n^2 & 3(2k+1) & 2k+1 -3n^3 & 3k(2k+1) & 3k(k+2)+1 vmatrix , k∈ℕ, and _ n=1...
- Let M be a 3×3 matrix such that M pmatrix 1 0 0 pmatrix = pmatrix 1 2 3 pmatrix , M pmatrix 0 1 0 pmatrix = pmatrix 0 1 2 pmatrix...
- Let A₁,A₂,A₃,…,A₃₉ be 39 arithmetic means between the numbers 59 and 159. Then the mean of A₂₅, A₂₈, A₃₁ and A₃₆ is equal to:
- The coefficient of x² in the expansion of (2x^2+ 1x )^ 10 , x≠0, is:
- The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4, respectively....
- A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each...
- Let the point P be the vertex of the parabola y=x²−6x+12. If a line passing through the point P intersects the circle...
- Let the directrix of the parabola P : y²=8x, cut the x-axis at the point A. Let B(α,β), α>1, be a point on P such that the slope...
- Let the eccentricity e of a hyperbola satisfy the equation 6e²−11e+3=0. If the foci of the hyperbola are (3,5) and (3,−4), then...
- Let a triangle PQR be such that P and Q lie on the line x+3 8= y-4 2= z+1 2 and are at a distance of 6 units from R(1,2,3). If...
- If the distance of the point (a,2,5) from the image of the point (1,2,7) in the line x1= y-1 1= z-2 2 is 4, then the sum of all...
- Let O be the origin, OP = a and OQ = b. If R is the point on OP such that OP =5 OR , and M is the point such that OQ =5 RM , then...
- Let f(x)= _ y 0 (1- (xy)) (xy) y^3 . Then the number of solutions of the equation f(x)=sinx, x∈ℝ is:
- Let (2^(1−a)+2^(1+a)), f(a), (3^a+3^(−a)) be in A.P. and α be the minimum value of f(a). Then the value of the integral _ _e( -1)...
- 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