1
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ are unit vectors such that $|\overline{\mathrm{a}}+\overline{\mathrm{b}}|=\sqrt{3}$, then the angle between $\bar{a}$ and $\bar{b}$ is

A
$\frac{\pi}{6}$
B
$\frac{\pi}{3}$
C
$\frac{\pi}{4}$
D
$\frac{\pi}{2}$
2
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\int_0^2\left[x^2\right] \mathrm{d} x$ is (where $[x]$ denotes the greatest integer function not greater than $x$ )

A
$5-\sqrt{2}-\sqrt{3}$
B
$5+\sqrt{2}-\sqrt{3}$
C
$5+\sqrt{2}+\sqrt{3}$
D
$5-\sqrt{2}+\sqrt{3}$
3
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\quad \int \frac{3 \sin x \cos x}{4 \sin x+7} \mathrm{~d} x=\mathrm{A} \sin x-\mathrm{Blog}(4 \sin x+7)+\mathrm{c}$ where c is the constant of integration, then the value of $\mathrm{A}+\mathrm{B}$ is equal to

A
$\frac{9}{16}$
B
$\frac{-9}{16}$
C
$\frac{33}{16}$
D
$\frac{-33}{16}$
4
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

Three vectors $\hat{\mathrm{i}}-\hat{\mathrm{k}}, \lambda \hat{\mathrm{i}}+\hat{\mathrm{j}}+(1-\lambda) \hat{\mathrm{k}}$ and $\mu \hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+(1+\lambda-\mu) \hat{\mathrm{k}}$ represents coterminous edges of a parallelopiped, then the volume of the parallelopiped depends on.

A
only $\lambda$
B
only $\mu$
C
both $\lambda$ and $\mu$
D
neither $\lambda$ nor $\mu$
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