Mathematics Tes...

Let y be an implicit function of x defined by x^2x - 2x^x cot y - 1 = 0. Then y'(1) equals

If the straight lines (x - 1)/k = (y - 2)/2 = (Z - 3)/3 and (x - 2)/3 = (y - 3)/k = (Z - 1)/2 intersect at a point, then the integer k is equal to

The lines p(p^2 + 1)x - y + q = 0 and (p^2 + 1)^2 x + (p^2 + 1)y + 2q = 0 are perpendicular to a common line for

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

Questions are Assertion−Reason type questions.

Each of these questionscontains two statements : Statement − 1 (Assertion) and Statement−2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number iff y is a transcendental number”.Statement –1: r is equivalent to either q or p.Statement –2: r is equivalent to ∼ (p ↔ ∼ q).

If P and Q are the points of intersection of the circles x^2 + y^2 + 3x + 7y + 2p - 5 = 0 and x^2 + y^2 + 2x + 2y - p^2 = 0 , then there is a circle passing through P, Q and (1, 1) for

Questions are Assertion−Reason type questions.

Each of these questionscontains two statements : Statement − 1 (Assertion) and Statement−2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A^2 = I.Statement −1: If A ≠ I and A ≠ − I, then det A = − 1.Statement −2: If A ≠ I and A ≠ − I, then tr (A) ≠ 0.

Suppose the cube x^3 – px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?