1
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $$y = {{\sin x} \over {1 + {{\cos x} \over {1 + {{\sin x} \over {1 + {{\cos x} \over {...}}}}}}}}$$, then $\frac{dy}{dx}$ is given by
A
$\frac{y \sin x+(1+y) \cos x}{1+2 y+\cos x-\sin x}$
B
$\frac{y \cos x+(1+y) \sin x}{1+2 y+\cos x-\sin x}$
C
$\frac{y \sin x-(1+y) \cos x}{1+2 y+\cos x-\sin x}$
D
$\frac{y \cos x-(1+y) \sin x}{1+2 y+\cos x-\sin x}$
2
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\quad \overline{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{k}}, \overline{\mathrm{b}}=x \hat{\mathrm{i}}+\hat{\mathrm{j}}+(1-x) \hat{\mathrm{k}} \quad$ and $\overline{\mathrm{c}}=y \hat{\mathrm{i}}+x \hat{\mathrm{j}}+(1+x-y) \hat{\mathrm{k}}$ then $\overline{\mathrm{a}} \cdot(\overline{\mathrm{b}} \times \overline{\mathrm{c}})$ depends on

A
only $x$
B
only $y$
C
neither $x$ nor $y$
D
both $x$ and $y$
3
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let a line intersect the co-ordinate axes in points $A$ and $B$ such that the area of the triangle $O A B$ is 12 sq. units. If the line passes through the point $(2,3)$, then the equation of the line is

A
$x+y=5$
B
$3 x+2 y=12$
C
$2 x+y=7$
D
$2 x+3 y=13$
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If for certain $x, 3 \cos x \neq 2 \sin x$, then the general solution of, $\sin ^2 x-\cos 2 x=2-\sin 2 x$, is

A
$(2 \mathrm{n}+1) \frac{\pi}{2}, \mathrm{n} \in \mathbb{Z}$
B
$(2 \mathrm{n}+1) \frac{\pi}{4}, \mathrm{n} \in \mathbb{Z}$
C
$\mathrm{n} \pi+(-1)^{\mathrm{n}} \frac{\pi}{3}, \mathrm{n} \in \mathbb{Z}$
D
$\frac{\mathrm{n} \pi}{2}+1, \mathrm{n} \in \mathbb{Z}$
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