Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

491.
For a, b $\in$ R, define $a * b = \frac{a}{a + b}$ , where a + b $\neq$ 0. If a * b = 5, then the value of b * a is

5

- 5

4

- 4

- 4

$We have, a * b = \frac{a}{a + b} \Rightarrow \frac{1}{a * b} = \frac{a + b}{a} = 1 + \frac{b}{a} \Rightarrow \frac{1}{5} = 1 + \frac{b}{a} \Rightarrow \frac{b}{a} = - \frac{4}{5} \Rightarrow \frac{a}{b} = - \frac{5}{4} Now, \frac{1}{b * a} = \frac{b + a}{b} = 1 + \frac{a}{b} = 1 - \frac{5}{4} = - \frac{1}{4} \Rightarrow b * a = - 4$

492.

Let A = {x, y, z} and B = {a, b, c, d}. Which one of the following is not a relation from A to B ?

{(x, a), (x, c)}
{(y, c), (y, d)}
{(z, a), (z, d)}
{(z, b), (y, b), (a, d)}

493.

If f(x) = x² - 1 and g(x) = (x + 1)², then (gof) (x) is

(x + 1)⁴ - 1
x⁴ - 1
x⁴
(x + 1)⁴

494.

If the function f : $[1, \infty) \to [1, \infty)$ is defined by f(x) = 2^{x(x - 1)}, then f^-1(x) is

${(\frac{1}{2})}^{x (x - 1)}$
$\frac{1}{2} (1 - \sqrt{1 + 4 \log_{2} (x)})$
$\frac{1}{2} \sqrt{1 + 4 \log_{2} (x)}$
$\frac{1}{2} [1 + \sqrt{1 + 4 \log_{2} (x)}]$

495.

If n(A) = 8 and $n (A \cap B) = 2$ , then $n ((A \cap B)' \cap A)$ is equal to

496.

If f(x) = $\sin (x) + \cos (x)$ , $x \in (- \infty, \infty)$ and g(x) = x², $x \in (- \infty, \infty)$ , then (fog)(x) is equal to

1
0
$\sin^{2} (x) + \cos (x^{2})$
$\sin (x^{2}) + \cos (x^{2})$

497.

If n(A) = 5 and n(B) = 7, then the number of relations on A x B is

2³⁵
2⁴⁹
2²⁵
$2^{35 \times 35}$

498.

Let $ϕ (x) = \frac{b (x - a)}{b - a} + \frac{a (x - b)}{a - b}$ , where x $\in$ R and a and b are fixed real numbers with $a \neq b$ . Then, $ϕ (a + b)$ is equal to