1
KCET 2021
MCQ (Single Correct Answer)
+1
-0

If $$a$$ and $$b$$ are fixed non-zero constants, then the derivative of $$\frac{a}{x^4}-\frac{b}{x^2}+\cos x$$ is $$m a+n b-p$$, where

A
$$m=4 x^3, n=\frac{-2}{x^3}$$ and $$p=\sin x$$
B
$$m=\frac{-4}{x^5}, n=\frac{2}{x^3}$$ and $$p=\sin x$$
C
$$m=\frac{-4}{x^5}, n=\frac{-2}{x^3}$$ and $$p=\sin x$$
D
$$m=4 x^3, n=\frac{2}{x^3}$$ and $$p=-\sin x$$
2
KCET 2021
MCQ (Single Correct Answer)
+1
-0

If $$y=\left(\cos x^2\right)^2$$, then $$\frac{d y}{d x}$$ is equal to

A
$$-4 x \sin 2 x^2$$
B
$$-x \sin x^2$$
C
$$-2 x \sin 2 x^2$$
D
$$-x \cos 2 x^2$$
3
KCET 2021
MCQ (Single Correct Answer)
+1
-0

For constant $$a, \frac{d}{d x}\left(x^x+x^a+a^x+a^a\right)$$ is

A
$$x^x(1+\log x)+a x^{a-1}$$
B
$$x^x(1+\log x)+a x^{a-1}+a^x \log a$$
C
$$x^x(1+\log x)+a^a(1+\log x)$$
D
$$x^x(1+\log x)+a^a(1+\log a)+a x^{a-1}$$
4
KCET 2021
MCQ (Single Correct Answer)
+1
-0

Consider the following statements

Statement 1 : If $$y=\log _{10} x+\log _e x$$, then $$\frac{d y}{d x}=\frac{\log _{10} e}{x}+\frac{1}{x}$$

Statement 2 : If $$\frac{d}{d x}\left(\log _{10} x\right)=\frac{\log x}{\log 10}$$ and $$\frac{d}{d x}\left(\log _e x\right)=\frac{\log x}{\log e}$$

A
Statement 1 is true, Statement 2 is false.
B
Statement 1 is false, statement 2 is true.
C
Both statements 1 and 2 are true.
D
Both statements 1 and 2 are false.
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