Practice questions
88551 published questions with worked solutions.
- Consider 10 observations x_1, x_2, , x_ 10 such that _ i=1 ^ 10 (x_i - ) = 2 and _ i=1 ^ 10 (x_i - )^2 = 40, where α, β are...
- The number of solutions of the equation 4 sin²x − 4 cos³x + 9 − 4 cos x = 0; x ∈ [−2π, 2π] is:Not in JEE Main syllabus
- The value of _0^1(2x^3 - 3x^2 - x + 1)^3dx is equal to:
- Let A = I_2 − 2MM^T, where M is a real matrix of order 2 × 1 such that the relation M^TM = I_1 holds. If λ is a real number such...
- If three successive terms of a G.P. with common ratio r (r > 1) are the lengths of the sides of a triangle and [r] denotes the...
- The sum of squares of all possible values of k, for which area of the region bounded by the parabolas 2y² = kx and ky² = 2(y − x)...
- If y = ( x + 1)(x^2 - x) x x + x + x + 1 15 (3 ^2x - 5) ^3x, then 96 ,y' ( 6 ) is equal to ______.
- Let a = i + j + k, b = - i - 8 j + 2 k and c = 4 i + c_2 j + c_3 k, be three vectors such that b a = c a. If the angle between...
- If dx dy = 1 + x - y^2 y , x(1) = 1, then 5x(2) is equal to ______.
- Let f : (0, ∞) → R and F(x) = _0^xtf(t)dt. If F(x^2) = x^4 + x^5, then _ r=1 ^ 12 f(r^2) is equal to __________ .
- Three points O(0, 0), P(a, a²), Q(−b, b²), a > 0, b > 0, are on the parabola y = x². Let S_1 be the area of the region bounded by...
- A particle moving in a circle of radius R with uniform speed takes time T to complete one revolution. If this particle is...
- Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2V. The...
- A galvanometer has a resistance of 50 Ω and it allows maximum current of 5 mA. It can be converted into voltmeter to measure upto...
- A ball of mass 0.5 kg is a string of length 50 cm. The ball is rotated on a horizontal circular path about its vertical axis. The...
- The dimensional formula of angular impulse is:
- The pressure and volume of an ideal gas are related as PV^ 3/2 = K (Constant). The work done when the gas is taken from state...
- With rise in temperature, the Young's modulus of elasticity:
- Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume...
- A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass 10^ -2 kg moving with a speed of...