1
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $$\frac{d y}{d x}=2^{y-x}$$ is

A
$$2^x-2^y=c$$
B
$$\frac{1}{2^x}-\frac{1}{2^y}=c$$
C
$$\frac{1}{2^x}+\frac{1}{2^y}=c$$
D
$$2^x+2^y=c$$
2
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The vector equation of the line passing through $$\mathrm{P}(1,2,3)$$ and $$\mathrm{Q}(2,3,4)$$ is

A
$$(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}+\hat{j}+\hat{k})$$
B
$$(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{j}-\hat{k})$$
C
$$(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})+\lambda(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}})$$
D
$$(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}+6 \hat{j}+12 \hat{k})$$
3
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

Range of the function $$f(x)=3+2^x+4^x$$ is

A
$$(3, \infty)$$
B
$$(-\infty, \infty)$$
C
$$[3, \infty)$$
D
$$(-\infty, 3]$$
4
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The combined equation of a pair of lines passing through the origin and inclined at $$60^{\circ}$$ and $$30=$$ respectively with $$x$$-axis is

A
$$\sqrt{3}\left(x^2+y^2\right)=2 x y$$
B
$$\sqrt{3}\left(x^2+y^2\right)=4 x y$$
C
$$4\left(x^2+y^2\right)=\sqrt{3} x y$$
D
$$2\left(x^2+y^2\right)=\sqrt{3} x y$$
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