1
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the curves $$y^2=6 x$$ and $$9 x^2+b y^2=16$$ intersect each other at right angle, then value of '$$b$$' is

A
$$\frac{9}{2}$$
B
6
C
$$\frac{7}{2}$$
D
4
2
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The circles $$x^2+y^2+2 \mathrm{a} x+\mathrm{c}=0$$ and $$x^2+y^2+2 b y+c=0$$ touch each other externally, if

A
$$\frac{1}{\mathrm{a}^2}-\frac{1}{\mathrm{~b}^2}=\frac{1}{\mathrm{c}}$$
B
$$\frac{1}{\mathrm{a}^2}+\frac{1}{\mathrm{~b}^2}=\frac{1}{\mathrm{c}}$$
C
$$\frac{1}{\mathrm{a}^2}+\frac{1}{\mathrm{~b}^2}=\frac{1}{\mathrm{c}^2}$$
D
$$\frac{1}{\mathrm{a}^2}-\frac{1}{\mathrm{~b}^2}=\frac{1}{\mathrm{c}^2}$$
3
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Given $$\mathrm{f}(x)=\left\{\begin{array}{cc}\frac{1-\cos 4 x}{x^2} & , \text { if } x<0 \\ \mathrm{a} & , \text { if } x=0 \\ \frac{\sqrt{x}}{\sqrt{16-\sqrt{x}-4}}, & \text { if } x>0\end{array}\right.$$

If $$\mathrm{f}(x)$$ is continuous at $$x=0$$, then value of a is

A
$$-$$8
B
2
C
$$-$$2
D
8
4
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$A, B, C, D$$ are four points in a plane with position vectors $$\bar{a}, \bar{b}, \bar{c}, \bar{d}$$ respectively such that $$(\bar{a}-\bar{d}) \cdot(\bar{b}-\bar{c})=(\bar{b}-\bar{d}) \cdot(\bar{c}-\bar{a})=0$$. The point $$D$$, then is the ___________ of $$\triangle \mathrm{ABC}$$

A
centroid
B
circumcentre
C
incentre
D
orthocentre
MHT CET Papers
EXAM MAP