1
MHT CET 2025 26th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The circumcenter of the triangle formed by lines $x y+2 x+2 y+4=0$ and $x+y+2=0$ is

A

$(0,0)$

B

$(-2,-2)$

C

$(-1,-1)$

D

$(-1,-2)$

2
MHT CET 2025 26th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

A triangle ABC is formed by $\mathrm{A}(1,-1,0)$, $B(3,5,3), C(-11,-5,6)$. The equation of internal angle bisector of angle $A$ is

A

$\frac{(1-x)}{2}=\frac{y-(-1)}{2}=\frac{\mathrm{z}}{3}$

B

$\frac{x+1}{2}=\frac{y-1}{2}=\frac{z}{3}$

C

$\frac{x+2}{1}=\frac{y-2}{1}=\frac{z}{3}$

D

$\frac{x-2}{1}=\frac{y+3}{2}=\frac{z}{3}$

3
MHT CET 2025 26th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\quad \overline{\mathrm{a}}=\lambda x \hat{\mathrm{i}}+y \hat{\mathrm{j}}+4 z \hat{\mathrm{k}}, \quad \overline{\mathrm{b}}=y \hat{\mathrm{i}}+x \hat{\mathrm{j}}+3 y \hat{\mathrm{k}}$, $\overline{\mathrm{c}}=-z \hat{\mathrm{i}}-2 z \hat{\mathrm{j}}-(\lambda+1) \hat{\mathrm{k}} x$ are the sides of the triangle ABC , where $x, y, \mathrm{z}$ are not all zero, such that $\bar{a}+\bar{b}-\bar{c}=\overline{0}$, then value of $\lambda$ is

A
0
B
1
C
2
D
3
4
MHT CET 2025 26th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The cumulative distribution function of a discrete random variable X is

$$ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \mathrm{X}=x & -4 & -2 & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline \mathrm{~F}(\mathrm{X}=x) & 0.1 & 0.3 & 0.5 & 0.65 & 0.75 & 0.85 & 0.90 & 1 \\ \hline \end{array} $$

then $\frac{P(X \leqslant 0)}{P(X>0)}=$

A

$\frac{1}{2}$

B

1

C

$\frac{1}{3}$

D

$\frac{1}{5}$

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