1
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0

The value of $$\lim _\limits{x \rightarrow \infty}\left[\frac{p^{1 / x}+q^{1 / x}+r^{1 / x}+s^{1 / x}}{4}\right]^{3 x}, p, q, r, s>0 \text {, }$$ is

A
$$(\text {pqrs})^3$$
B
$$(p q r s)^{3 / 2}$$
C
$$(\text {pqrs})^{3 / 4}$$
D
None of these
2
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0

If $$f(x)=\left\{\begin{array}{cc}(\sin x+\cos x)^{\operatorname{cosec} x} & ,-\frac{\pi}{2}< x<0 \\ a & ,x=0 \\ \frac{e^{1 / x}+e^{2 / x}+e^{3 / x}}{a e^{-2+\frac{1}{x}}+b e^{-1+\frac{3}{x}}} & , 0< x<\frac{\pi}{2}\end{array}\right.$$ is continuous at $$x=0$$, then the value of $$(b, a)$$ is

A
$$(-1, e)$$
B
$$(1,-e)$$
C
$$(1, e)$$
D
$$(e, 1)$$
3
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0

The image of the centre of the circle $$x^2+y^2=a^2$$ with respect to the mirror $$x+y=1$$ is

A
$$\left(\frac{1}{\sqrt{2}}, \sqrt{2}\right)$$
B
$$(\sqrt{2}, \sqrt{2})$$
C
$$(\sqrt{2,2} \sqrt{2})$$
D
$$(-\sqrt{2}, 2)$$
E
None of these
4
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0

The value of $$\lim _\limits{t \rightarrow \infty} \frac{\ln \left(\frac{3}{2} t\right)}{t^2}$$

A
2
B
1/5
C
0
D
1/2
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