Practice questions
88551 published questions with worked solutions.
- If the function f(x) = cases 2 x (k_1+1)x + (k_2-1)x , & x < 0 4, & x=0 2 x _e ( 2+k_1x 2+k_2x ), & x>0 cases is continuous at x...
- If the line 3x – 2y + 12 = 0 intersects the parabola 4y = 3x^2 at the points A and B, then at the vertex of the parabola, the...
- Let a curve y = f(x) pass through the points (0, 5) and ( _e2, k). If the curve satisfies the differential equation 2(3+y)e^ 2x...
- Let f(x) = _ex and g(x) = x^4-2x^3+3x^2-2x+2 2x^2-2x+1 . Then the domain of fog is-
- If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms,...
- Let | z -i 2 z +i | = 1 3 , Z ∈ C, be the equation of a circle with center at C. If the area of the triangle, whose vertices are...
- The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come...
- Let the area of a ΔPQR with vertices P(5, 4), Q(–2, 4) and R(a, b) be 35 square units. If its orthocenter and centroid are O (2,...
- If 2 x 3 4 , then ^ -1 ( 12 13 x + 5 13 x ) is equal to-
- The value of (sin70°)(cot10°cot70° – 1) is
- Marks obtains by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the...
- If A, B and (adj(A^ -1 ) + adj(B^ -1 )) are non-singular matrices of same order, then the inverse of A(adj(A^ -1 ) + adj(B^ -1...
- If the system of equations (λ – 1)x + (λ – 4)y + λz = 5 λx + (λ – 1)y + (λ –4)z = 7 (λ + 1)x + (λ + 2)y – (λ + 2)z = 9 has...
- One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1,...
- The sum of all rational terms in the expansion of (1 + 2^ 1/3 + 3^ 1/2 )^6 is equal to _____
- Let the circle C touch the line x – y + 1 = 0, have the centre on the positive x-axis, and cut off a chord of length 4 13 along...
- If the set of all values of a, for which the equation 5x^3 - 15x - a = 0 has three distinct real roots, is the interval (α, β),...
- Regarding self-inductance : A : The self-inductance of the coil depends on its geometry. B : Self-inductance does not depend on...
- A light hollow cube of side length 10 cm and mass 10g, is floating in water. It is pushed down and released to execute simple...
- A radioactive nucleus n_2 has 3 times the decay constant as compared to the decay constant of another radioactive nucleus n_1. If...