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

$$\int_\limits0^a \frac{x-a}{x+a} d x=$$

A
$a-2 a \log 2$
B
$a-a \log 2$
C
$\mathrm{a}+2 \mathrm{a} \log 2$
D
$a+a \log 2$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius $r$. If PS and RQ intersect at a point X on the circumference of the circle, then 2 r equals

A
$\sqrt{\mathrm{PQ} \cdot \mathrm{RS}}$
B
$\frac{\mathrm{PQ}+\mathrm{RS}}{2}$
C
$\frac{2 \cdot P Q \cdot R S}{P Q+R S}$
D
$\sqrt{\frac{\mathrm{PQ}^2+\mathrm{RS}^2}{2}}$
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A random variable X assumes values $1,2,3, \ldots \ldots ., \mathrm{n}$ with equal probabilities. If $\operatorname{var}(X): E(X)=4: 1$, then $n$ is equal to

A
20
B
15
C
25
D
10
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{b}}=4 \hat{\mathrm{i}}-2 \hat{j}+3 \hat{k}, \overline{\mathrm{c}}=\hat{i}-2 \hat{j}+\hat{k}$, then $a$ vector of magnitude 6 units, which is parallel to the vector $2 \bar{a}-\bar{b}+3 c$, is

A
$2 \hat{i}-4 \hat{j}+4 \hat{k}$
B
$\hat{i}-\hat{j}+2 \hat{k}$
C
$4 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}$
D
$2 \hat{i}+4 \hat{j}+4 \hat{k}$
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