Practice questions
88551 published questions with worked solutions.
- Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R : Assertion A : FSH acts...
- Given below are two statements: Statement I : Mitochondria and chloroplasts both double membranes bound organelles. Statement II...
- Given below are two statements: Statement I : The cerebral hemispheres are connected by nerve tract known as corpus callosum....
- Let α, β be the roots of the equation x² − 3x + r = 0 and 2, 2β be the roots of the equation x² + 3x + r = 0. If the roots of the...
- Let the circles C₁ : |z| = r and C₂ : |z − 3 − 4i| = 5, z ∈ ℂ, be such that C₂ lies within C₁. If z₁ moves on C₁, z₂ moves on C₂...
- If the system of equations x + 5y + 6z = 4, 2x + 3y + 4z = 7, x + 6y + az = b has infinitely many solutions, then the point (a,...
- Let a₁, a₂, a₃, … be an A.P. and g₁ = a₁, g₂, g₃, … be an increasing G.P. If a₁ = a₂ + g₂ = 1 and a₃ + g₃ = 4, then a₁₀ + g₅ is...
- The sum 1^3 1 + 1^3+2^3 1+3 + 1^3+2^3+3^3 1+3+5 + up to 8 terms, is:
- If for 3 ≤ r ≤ 30, 30 30-r + 3 30 31-r + 3 30 32-r + 30 33-r = mr, then m equals:
- The mean and variance of n observations are 8 and 16, respectively. If the sum of the first (n − 1) observations is 48 and the...
- Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines x + (k − 1)y...
- Let O be the origin, and P and Q be two points on the rectangular hyperbola xy = 12 such that the mid point of the line segment...
- Let the parabola y = x² + px + q passing through the point (1, −1) be such that the distance between its vertex and the x-axis is...
- Let P = θ ∈ [0, 4π] : tan²θ ≠ 1 and S = a ∈ ℤ : 2(cos⁸θ − sin⁸θ)sec2θ = a², θ ∈ P . Then n(S) is:Not in JEE Main syllabus
- Let the vectors a = - i + j + 3 k and b = i + 3 j + k. For some λ, μ ∈ ℝ, let c = a + b. If c (3 i - 6 j + 2 k) = 10 and c ( i +...
- Let the point A be the foot of perpendicular drawn from the point P(a, b, 0) on the line x-1 2 = y-2 1 = z- 3 . If the midpoint...
- Two adjacent sides of a parallelogram PQRS are given by PQ = j + k and PS = i - j. If the side PS is rotated about the point P by...
- The value of _0^ 20 ( ^4x + ^4x)dx is equal to:
- Let f(x) be a polynomial of degree 5, and have extrema at x = 1 and x = −1. If _ x 0 ( f(x) x^3 ) = -5, then f(2) − f(−2) is...
- Let f(x) = ( 16x+24 x^2+2x-15 )dx. If f(4) = 14log_e(3) and f(7) = log_e(2^ 3^ )$, α, β ∈ ℕ, then α + β is equal to: