• Statement −1 is false, Statement −2 is true

• Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

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).

• Statement −1 is false, Statement −2 is true

• Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

The statement p → (q → p) is equivalent to

• p → (p → q) 

• p → (p ∨ q)

• p → (p ∧ q)

• p → (p ∧ q)

The value of cot 

• 6/17

• 5/17

• 4/17

• 4/17

The quadratic equations x² – 6x + a = 0 and x² – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

• 1

• 4

• 3

• 3

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

• 8 . ⁶C₄ . ⁷C₄

• 6 . 7 . ⁸C₄

• 6 . 8 . ⁷C₄

• 6 . 8 . ⁷C₄

Let f : N → Y be a function defined as f (x) = 4x + 3, where Y = {y ∈ N : y = 4x + 3 for some x ∈ N}.Show that f is invertible and its inverse is 

Let R be the real line. Consider the following subsets of the plane R × R.
S = {(x, y) : y = x + 1 and 0 < x < 2}, T = {(x, y) : x − y is an integer}. Which one of the following is true?

• neither S nor T is an equivalence relation on R

• both S and T are equivalence relations on R

• S is an equivalence relation on R but T is not 

• S is an equivalence relation on R but T is not 

19.

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 A₂= 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.

• Statement −1 is false, Statement −2 is true

• Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

Let f(x) = Then which one of the following is true?

• f is neither differentiable at x = 0 nor at x = 1

• f is differentiable at x = 0 and at x = 1

• f is differentiable at x = 0 but not at x = 1 

• f is differentiable at x = 0 but not at x = 1