Practice questions
88551 published questions with worked solutions.
- Consider the following reaction, the rate expression of which is given below A + B → C, rate = k [A]^ 1/2 [B]^ 1/2 . The reaction...
- The total number of 'sigma' and 'Pi' bonds in 2-oxohex-4-ynoic acid is____.
- A first row transition metal with highest enthalpy of atomisation, upon reaction with oxygen at high temperature forms oxides of...
- If the function f(x) = cases 72^x - 9^x - 8^x + 1 2 - 1 + x , & x 0 a _e2 _e3, & x = 0 cases is continuous at x = 0, then the...
- If λ > 0, let θ be the angle between the vectors a = i + j - 3 k and b = 3 i - j + 2 k. If the vectors a + b and a - b are...
- Let C be a circle with radius 10 units and centre at the origin. Let the line x + y = 2 intersects the circle C at the points P...
- Let a relation R on N × N be defined as: (x_1, y_1) R (x_2, y_2) if and only if x_1 ≤ x_2 or y_1 ≤ y_2. Consider the two...
- Let three real numbers a, b, c be in arithmetic progression and a + 1, b, c + 3 be in geometric progression. If a > 10 and the...
- Let A = bmatrix 1 & 2 0 & 1 bmatrix and B = I + adj(A) + (adj A)² + … + (adj A)^ 10 . Then, the sum of all the elements of the...
- The value of 1 2^2 + 2 3^2 + + 100 (101)^2 1^2 2 + 2^2 3 + + 100^2 101 is
- Let f(x) = _0^x(t + (1 - e^t))dt, x ∈ R. Then _ x 0 f(x) x^3 is equal to
- The area (in sq. units) of the region described by (x, y) : y² ≤ 2x, and y ≥ 4x − 1 is
- The area (in sq. units) of the region S = z ∈ C; |z − 1| ≤ 2; (z + z) + i(z − z) ≤ 2, Im(z) ≥ 0 is
- If the value of the integral _ -1 ^ 1 x 1 + 3^x dx is 2 . Then, a value of α is
- Let f(x) = 3 x - 2 + 4 - x be a real valued function. If α and β are respectively the minimum and the maximum values of f, then...
- If the coefficients of x⁴, x⁵ and x⁶ in the expansion of (1 + x)^n are in the arithmetic progression, then the maximum value of n...
- Consider a hyperbola H having centre at the origin and foci on the x-axis. Let C_1 be the circle touching the hyperbola H and...
- If the mean of the following probability distribution of a random variable X: | X | 0 | 2 | 4 | 6 | 8 | |---|---|---|---|---|---|...
- Let PQ be a chord of the parabola y² = 12x and the midpoint of PQ be at (4, 1). Then, which of the following point lies on the...
- Given the inverse trigonometric function assumes principal values only. Let x, y be any two real numbers in [−1, 1] such that...