Question 1: Palette 1/13

BITSAT 2025 MCQ

If $f: X \rightarrow Y$ be a function defined by $f(x)=a \sin \left(x+\frac{\pi}{4}\right)+b \cos x+c$ and $f$ is bijective, then the set $X$ with $\theta=\tan ^{-1}\left(\frac{a+\sqrt{2} b}{a}\right)$ is

A

$\left[-\frac{\pi}{2}+\theta, \frac{\pi}{2}+\theta\right]$

B

$[\pi-\theta, \pi+\theta]$

C

$\left[-\frac{\pi}{2}-\theta, \frac{\pi}{2}-\theta\right]$

D

$\left[2 \pi-\frac{\theta}{2}, \frac{\pi}{2}+\theta\right]$

Question 2: Palette 2/13

BITSAT 2025 MCQ

If the function $f: R \rightarrow R$ is defined by $f(x)=x^2+5 x+9$, then $f^{-1}(9)$ is equal to

A

$\{-5,9\}$

B

$\{0,-5\}$

C

$\{0,9\}$

D

$\{0,2\}$

Question 3: Palette 3/13

BITSAT 2024 MCQ

Let $ [x] $ denote the greatest integer $ \leq x $. If $ f(x)=[x] $ and $ g(x)=|x| $, then the value of $ f\left(g\left(\frac{8}{5}\right)\right)-g\left(f\left(-\frac{8}{5}\right)\right) $ is

A

2

B

-2

C

1

D

-1

Question 4: Palette 4/13

BITSAT 2023 MCQ

If $f(x)=x^2-2 x+1$ and $f \circ g(x)=x^2+2 x+1$, then $g(x)$ is equal to

A

$x-2$

B

$x+2$

C

$-x-2$

D

$-x+2$

Question 5: Palette 5/13

BITSAT 2022 MCQ

If g(x) = x² + x $-$ 2 and $\frac{1}{2}gof(x)=2x^2-5x+2$, then f(x) is equal to

A

2x $-$ 3

B

2x + 3

C

2x² + 3x + 1

D

2x² $-$ 3x + 1

Question 6: Palette 6/13

BITSAT 2021 MCQ

If f(x) = 4x $-$ x², x$\in$R, and f(a + 1) $-$ f(a $-$ 1) = 0, then a is equal to

A

0

B

2

C

1

D

3

Question 7: Palette 7/13

BITSAT 2021 MCQ

The maximum value of the function y = x(x $-$ 1)², is

A

0

B

${4 \over {27}}$

C

$-$4

D

None of these

Question 8: Palette 8/13

BITSAT 2021 MCQ

Find the area enclosed by the loop in the curve 4y² = 4x² $-$ x³.

A

${{128} \over {15}}$

B

${{15} \over {128}}$

C

${{130} \over {17}}$

D

${{17} \over {130}}$

Question 9: Palette 9/13

BITSAT 2020 MCQ

If $2f(xy) = {(f(x))^x} + {(f(y))^x}$ for all $x,y \in R$ and $f(1) = a( \ne 1)$. Then $\sum\limits_{k = 1}^n {f(k) = } $

A

$({a^n} - 1)/(a - 1)$

B

$a({a^{n - 1}} - 1)/(a - 1)$

C

$a({a^n} - 1)/(a - 1)$

D

$({a^n} - 1)/a + 1$

Question 10: Palette 10/13

BITSAT 2020 MCQ

Let f(x) = x $-$ 3, g(x) = 4 $-$ x. Then the set of values of x for which $|f(x) + g(x)|\, < \,|f(x)| + |g(x)|$ is true, is given by :

A

R

B

R $-$ (3, 4)

C

R $-$ [3, 4]

D

None of these

Question 11: Palette 11/13

BITSAT 2020 MCQ

$\left\{ {x \in R:{{2x - 1} \over {{x^3} + 4{x^2} + 3x}} \in R} \right\}$ is equal to

A

$R - \{ 0\} $

B

$R - \{ 0,1,3\} $

C

$R - \{ 0, - 1, - 3\} $

D

$R - \left\{ {0, - 1, - 3,{1 \over 2}} \right\}$

Question 12: Palette 12/13

BITSAT 2020 MCQ

The solution set of ${{|x - 2|\, - 1} \over {|x - 2|\, - 2}} \le 0$ is

A

[0, 1] $\cup$ (3, 4)

B

[0, 1] $\cup$ [3, 4]

C

[$-$1, 1] $\cup$ (3, 4]

D

None of these

Question 13: Palette 13/13

BITSAT 2020 MCQ

Let $f(x) = {x \over {\sqrt {1 + {x^2}} }}$, $\underbrace {fofofo.....of(x)}_{x\,times}$ is

A

${x \over {\sqrt {1 + \left( {\sum\limits_{r = 1}^n r } \right){x^2}} }}$

B

${x \over {\sqrt {1 + \left( {\sum\limits_{r = 1}^n 1 } \right){x^2}} }}$

C

${\left( {{x \over {\sqrt {1 + {x^2}} }}} \right)^x}$

D

${x \over {\sqrt {1 + n{x^2}} }}$