1
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int_\limits1^2 \frac{\mathrm{d} x}{\left(x^2-2 x+4\right)^{\frac{3}{2}}}=\frac{\mathrm{k}}{\mathrm{k}+5} \text {, then } \mathrm{k} \text { has the value }$$

A
1
B
2
C
$$-$$1
D
$$-$$2
2
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The sides of a rectangle are given by the equations $$x=-2, x=4, y=-2$$ and $$y=5$$

Then the equation of the circle, whose centre is the point of intersection of the diagonals, lying within the rectangle and touching only two opposite sides, is

A
$$x^2+y^2+2 x+3 y+9=0$$
B
$$x^2+y^2-2 x+3 y+9=0$$
C
$$x^2+y^2+2 x-3 y-9=0$$
D
$$x^2+y^2-2 x-3 y-9=0$$
3
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{b}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}$$, then vector $$\overline{\mathrm{r}}$$ satisfying $$\overline{\mathrm{a}} \times \overline{\mathrm{r}}=\overline{\mathrm{b}}$$ and $$\overline{\mathrm{a}} \cdot \overline{\mathrm{r}}=3$$ is

A
$$\frac{5}{3} \hat{\mathrm{i}}+\frac{2}{3} \hat{\mathrm{j}}+\frac{2}{3} \hat{\mathrm{k}}$$
B
$$-\frac{5}{3} \hat{\mathrm{i}}+\frac{2}{3} \hat{\mathrm{j}}+\frac{2}{3} \hat{\mathrm{k}}$$
C
$$\frac{5}{3} \hat{\mathrm{i}}-\frac{2}{3} \hat{\mathrm{j}}+\frac{2}{3} \hat{\mathrm{k}}$$
D
$$-\frac{5}{3} \hat{\mathrm{i}}+\frac{2}{3} \hat{\mathrm{j}}+\frac{1}{3} \hat{\mathrm{k}}$$
4
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The magnitude of the projection of the vector $$2 \hat{i}+\hat{j}+\hat{k}$$ on the vector perpendicular to the plane containing the vectors $$\hat{i}+\hat{j}+\hat{k}$$ and $$\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$$ is

A
$$\frac{2}{\sqrt{6}}$$
B
$$\frac{1}{\sqrt{6}}$$
C
$$\frac{5}{\sqrt{6}}$$
D
$$\frac{7}{\sqrt{6}}$$
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