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 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
D.
S is an equivalence relation on R but T is not
T = {(x, y) : x−y ∈ I}
as 0 ∈ I T is a reflexive relation.
If x − y ∈ I ⇒ y − x ∈ I
∴ T is symmetrical also
If x − y = I1 and y − z = I2
Then x − z = (x − y) + (y − z) = I1 + I2 ∈ I
∴ T is also transitive.
Hence T is an equivalence relation.
Clearly x ≠ x + 1 ⇒ (x, x) ∉ S
∴ S is not reflexive.
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