Practice questions
90156 published questions with worked solutions.
- Consider the relation R on the set −2, −1, 0, 1, 2 defined by (a, b) ∈ R if and only if 1 + ab > 0. Then, among the statements:...
- The number of values of z ∈ ℂ, satisfying the equations |z − (4 + 8i)| = √10 and |z − (3 + 5i)| + |z − (5 + 11i)| = 4√5, is:
- If the system of linear equations: x + y + z = 6, x + 2y + 5z = 10, 2x + 3y + λz = μ has infinitely many solutions, then the...
- Let A= bmatrix &1&2 2&3&0 0&4&5 bmatrix and B= bmatrix 1&0&0 0&-5 &0 0&4 &-2 bmatrix + adj (A). If det(B) = 66, then det(adj(A))...
- Let α = 3 + 4 + 8 + 9 + 13 + 14 + … upto 40 terms. If ( )^ 1020 is a root of the equation x² + x − 2 = 0, β ∈ (0, π/2), then...
- A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation...
- A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the...
- If 26 ( 2^3 3 12 2+ 2^5 5 12 4+ 2^7 7 12 6+ + 2^ 13 13 12 12 )=3^ 13 - , then α is equal to:
- A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so...
- If a straight line drawn through the point of intersection of the lines 4x + 3y − 1 = 0 and 3x + 4y − 1 = 0, meets the...
- Let O be the vertex of the parabola y² = 4x and its chords OP and OQ are perpendicular to each other. If the locus of the...
- Let α = 3 sin⁻¹(6/11) and β = 3 cos⁻¹(4/9), where inverse trigonometric functions take only the principal values. Given below are...
- For the function f(x) = e^ sin|x| − |x|, x ∈ ℝ, consider the following statements: Statement I: f is differentiable for all x ∈...
- Let a=4 i- j+3 k, b=10 i+2 j- k and a vector c be such that 2( a b)+3( b c)= 0. If a c=15, then c ( i+ j-3 k) is equal to:
- Let the foot of perpendicular from the point (λ, 2, 3) on the line x-4 1= y-9 2= z-5 1 be the point (1, μ, 2). Then the distance...
- Let y = y(x) be the solution of the differential equation x 1-x^2 ,dy+ (y 1-x^2 -x ^ -1 x )dx=0, x ∈ (0, 1), _ x 1^- y(x)=1. Then...
- Let f : (1, ∞) → ℝ be a function defined as f(x)= x-1 x+1 . Let fⁱ⁺¹(x) = f(fⁱ(x)), i = 1, 2, …, 25, where f¹(x) = f(x). If g(x)...
- Let f(x)= cases 13, & x /2 [2mm] b(1- x) ( -2x)^2 , & x> /2 cases . If f is continuous at x = π/2, then the value of _0^ 3b-6...
- Let x^2 f(a^2+7a+3) + y^2 f(3a+15) =1 represent an ellipse with major axis along y-axis, where f is a strictly decreasing...
- The sum of squares of all the real solutions of the equation _ (x+1) (2x^2+5x+3)=4- _ (2x+3) (x^2+2x+1) is equal to _______.