1
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If three fair coins are tossed, then variance of number of heads obtained, is

A
0.25
B
3
C
0.75
D
1.5
2
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The plane $2 x+3 y+4 z=1$ meets $X$-axis in $A$, Y -axis in B and Z -axis in C . Then the centroid of $\triangle A B C$ is

A
$(2,3,4)$
B
$\left(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right)$
C
$\left(\frac{1}{6}, \frac{1}{9}, \frac{1}{12}\right)$
D
$\left(\frac{3}{2}, \frac{3}{3}, \frac{3}{4}\right)$
3
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $x^2+y^2=\mathrm{t}+\frac{1}{\mathrm{t}}, x^4+y^4=\mathrm{t}^2+\frac{1}{\mathrm{t}^2}$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

A
$\frac{1}{x^3 y}$
B
$\frac{1}{x y^3}$
C
$-\frac{1}{x y^3}$
D
$-\frac{1}{x^3 y}$
4
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of $\frac{\mathrm{d} y}{\mathrm{~d} x}+\sin \left(\frac{x+y}{2}\right)=\sin \left(\frac{x-y}{2}\right)$ is

A
$\log \tan \left(\frac{y}{2}\right)=\mathrm{C}-2 \sin x$
B
$\log \tan \left(\frac{y}{4}\right)=\mathrm{C}-2 \sin \left(\frac{x}{2}\right)$
C
$\log \tan \left(\frac{y}{2}+\frac{\pi}{4}\right)=\mathrm{C}-2 \sin x$
D
$\log \tan \left(\frac{y}{2}+\frac{\pi}{4}\right)=\mathrm{C}-2 \sin \left(\frac{x}{2}\right)$
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