Let $f : [2, \infty) \to \mathbf{R}$ be a function defined by $f(x) = x^2 - 4x + 5$. The range of $f$ is :

The number of symmetric relations on set $A = \{1,2,3\}$ is

Relation R on the set $A = \{1, 2, ..., 15\}$ defined as $R = \{(x, y): y - 4x = 0\}$ is

Which of the following figures shows a bijective function from set $X_1$ to set $X_2$ :

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Consider a function $f:[-1,1] \to Y$ defined as $f(x)=\dfrac{x}{x+2}$ and $Y=range(f(x))$, then which of following statements are correct?

(A) Function $f(x)$ is one-one

(B) Function $f(x)$ is not one-one

(C) Function $f(x)$ is onto

(D) Function $f(x)$ is invertible

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Consider a function $f:\left[0,\frac{\pi}{2}\right] \to R$, given by $f(x)=\sin x$ and $g:\left[0,\frac{\pi}{2}\right] \to R$, given by $g(x)=\cos x$, Where R is a set of real numbers, Which of the following statements are correct?

(A) f and g are one-one

(B) f and g are not one-one

(C) f+g is not one-one

(D) f+g is one-one

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Which of the following are correct?

(A) If a ≡ b(mod n), then -a ≡ -b (mod n)

(B) If a + b = c, then a(mod n) + b(mod n) ≡ (a + b + c)(mod n).

(C) If a ≡ b (mod n), then ka ≡ kb(mod n), ∀ k ∈ I.

(D) If a ≡ b (mod n), then (a + k) ≡ (b + k)(mod n), ∀ k ∈ I.

Choose the correct answer from the options given below: