1
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \log x \cdot[\log (e x)]^{-2} d x=\ldots$$

A
$\frac{x}{1+\log x}+c$
B
$x(1-\log x)+c$
C
$x(1+\log x)+c$
D
$\frac{x}{1-\log x}+c$
2
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\log \left[\frac{x+\sqrt{x^2+25}}{\sqrt{x^2+25}-x}\right]$ then $\frac{d y}{d x}=\ldots \ldots$

A
$\frac{1}{\sqrt{x^2+25}}$
B
$\frac{2}{\sqrt{x^2+25}}$
C
$\frac{-1}{\sqrt{x^2+25}}$
D
$\frac{-2}{\sqrt{x^2+25}}$
3
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the scalar triple product of the vectors $-3 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, 3 \hat{\mathbf{i}}-7 \hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}$ and $7 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ is 272 then $\lambda=\ldots \ldots$

A
9
B
11
C
8
D
10
4
MHT CET 2019 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

- The edge of a cube is decreasing at the rate of $0.04 \mathrm{~cm} / \mathrm{sec}$. If the edge of the cube is 10 cms , then rate of decrease of surface area of the cube is...

A
$4.8 \mathrm{~cm}^2 / \mathrm{sec}$
B
$4.08 \mathrm{~cm}^2 / \mathrm{sec}$
C
$48 \mathrm{~cm}^2 / \mathrm{sec}$
D
$4.008 \mathrm{~cm}^2 / \mathrm{sec}$
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