Practice questions
88551 published questions with worked solutions.
- If 0 < x < 1, then 1+x^2 [ x ( ^ -1 x) + ( ^ -1 x) ^2 - 1 ]^ 1 2 =
- The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors a , b , c such that a b = b c = c...
- Let a and b be non-zero real numbers. Then, the equation (ax^2 + by^2 + c)(x^2 - 5xy + 6y^2) = 0 represents
- Let g(x) = (x-1)^n ^m(x-1) ; 0 < x < 2, m and n are integers , m 0, n > 0, and let p be the left hand derivative of |x-1| at x =...
- The total number of local maxima and local minima of the function f(x) = cases (2+x)^3, & -3 < x -1 x^ 2/3 , & -1 < x < 2 cases is
- Let P(x_1, y_1) and Q(x_2, y_2), y_1 < 0, y_2 < 0, be the end points of the latus rectum of the ellipse x^2 + 4y^2 = 4. The...
- Let S_n = _ k=1 ^ n n n^2+kn+k^2 T_n = _ k=0 ^ n-1 n n^2+kn+k^2 , for n = 1, 2, 3, . Then,
- Let f(x) be a non-constant twice differentiable function defined on (- , ) such that f(x) = f(1-x) and f' ( 1 4 ) = 0. Then,
- Let f and g be real valued functions defined on interval (-1,1) such that g''(x) is continuous, g(0) 0, g'(0) = 0, g''(0) 0, and...
- Consider three planes P_1: x - y + z = 1, P_2: x + y - z = -1, P_3: x - 3y + 3z = 2. Let L_1, L_2, L_3 be the lines of...
- Consider the system of equations x - 2y + 3z = -1, -x + y - 2z = k, x - 3y + 4z = 1. STATEMENT-1: The system of equations has no...
- Consider the system of equations ax + by = 0, cx + dy = 0, where a, b, c, d 0, 1 . STATEMENT-1: The probability that the system...
- Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?
- Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60°). In the position of...
- An ideal gas is expanding such that PT^2 = constant. The coefficient of volume expansion of the gas is
- Two balls, having linear momenta p _1 = p , and p _2 = -p , , undergo a collision in free space. There is no external force...
- STATEMENT-1: In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put...
- STATEMENT-1: An astronaut in an orbiting space station above the Earth experiences weightlessness. STATEMENT-2: An object moving...
- STATEMENT-1: Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are...
- Hyperconjugation involves overlap of the following orbitals
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