1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{f}(x)=(x-1)(x-2)(x-3), x \in[0,4]$. Values of C will be __________ if L.M.V.T. (Lagrange's Mean Value Theorem) can be applied.

A
$\frac{4-2 \sqrt{3}}{3}, \frac{4+2 \sqrt{3}}{3}$
B
$\frac{6-2 \sqrt{3}}{3}, \frac{6+2 \sqrt{3}}{3}$
C
$\frac{6-\sqrt{3}}{3}, \frac{6+\sqrt{3}}{3}$
D
$2-\sqrt{3}, 2+\sqrt{3}$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $\mathrm{e}^{y-x} \frac{\mathrm{~d} y}{\mathrm{~d} x}=y\left(\frac{\sin x+\cos x}{1+y \log y}\right)$ is

A
$\mathrm{e}^y \log y=\mathrm{e}^{\mathrm{x}} \sin x+\mathrm{c}$, where c is a constant of integration.
B
$\mathrm{e}^y=\mathrm{e}^x \sin x+\mathrm{c}$, where c is a constant of integration.
C
$\log y=\mathrm{e}^x \sin x+\mathrm{c}$, where c is a constant of integration.
D
$y \log y=\mathrm{e}^x \sin x+\mathrm{c}$, where c is a constant of integration.
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Minimum number of times a fair coin must be tossed, so that the probability of getting at least one head, is more than $99 \%$ is

A
5
B
6
C
7
D
8
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The vector of magnitude 6 units and perpendicular to vectors $2 \hat{i}+\hat{j}-3 \hat{k}$ and $\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ is

A
$2 \sqrt{3}(-\hat{i}+\hat{j}+\hat{k})$
B
$2 \sqrt{3}(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$
C
$2 \sqrt{3}(\hat{i}+\hat{j}+\hat{k})$
D
$2 \sqrt{3}(-\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$
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