1
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\int \frac{(x-1) \mathrm{e}^x}{(x+1)^3} \mathrm{~d} x$ is equal to

A
$\frac{\mathrm{e}^x}{(x+1)}+\mathrm{c}$, (where c is constant of integration)
B
$\frac{\mathrm{e}^{\mathrm{x}}}{(x+1)^2}+\mathrm{c}$, (where c is constant of integration)
C
$\frac{-\mathrm{e}^x}{(x+1)}+\mathrm{c}$, (where c is constant of integration)
D
$\frac{-\mathrm{e}^x}{(x+1)^2}+\mathrm{c}$, (where c is constant of integration)
2
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{P}(2,3,6)$ be a point in space and Q be a point on the line $\bar{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(-3 \hat{i}+\hat{j}+5 \hat{k})$. Then the value of $\mu$ for which vector $\overline{\mathrm{PQ}}$ is parallel to the plane $x-4 y+4 z=1$ is

A
$\frac{13}{6}$
B
$-\frac{6}{13}$
C
$\frac{6}{13}$
D
$-\frac{13}{6}$
3
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Consider the following statements

p : the switch $\mathrm{S}_1$ is closed.

q : the switch $\mathrm{S}_2$ is closed.

$r$ : the switch $\mathrm{S}_3$ is closed.

Then the switching circuit represented by the statement $(p \wedge q) \vee(\sim p \wedge(\sim q \vee p \vee r))$ is

A
MHT CET 2024 3rd May Morning Shift Mathematics - Mathematical Reasoning Question 39 English Option 1
B
MHT CET 2024 3rd May Morning Shift Mathematics - Mathematical Reasoning Question 39 English Option 2
C
MHT CET 2024 3rd May Morning Shift Mathematics - Mathematical Reasoning Question 39 English Option 3
D
MHT CET 2024 3rd May Morning Shift Mathematics - Mathematical Reasoning Question 39 English Option 4
4
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\bar{a}, \bar{b}, \bar{c}$ be three non-coplanar vectors and $\overline{\mathrm{p}}, \overline{\mathrm{q}}, \overline{\mathrm{r}}$ defined by the relations

$$\overline{\mathrm{p}}=\frac{\overline{\mathrm{b}} \times \overline{\mathrm{c}}}{[\overline{\mathrm{a}} \overline{\mathrm{~b}} \overline{\mathrm{c}}]}, \overline{\mathrm{q}}=\frac{\overline{\mathrm{c}} \times \overline{\mathrm{a}}}{[\overline{\mathrm{a}} \overline{\mathrm{~b}} \overline{\mathrm{c}}]}, \overline{\mathrm{r}}=\frac{\overline{\mathrm{a}} \times \overline{\mathrm{b}}}{[\overline{\mathrm{a}} \overline{\mathrm{~b}} \overline{\mathrm{c}}]}$$

then the value of the expression $(\overline{\mathrm{a}}+\overline{\mathrm{b}}) \cdot \overline{\mathrm{p}}+(\overline{\mathrm{b}}+\overline{\mathrm{c}}) \cdot \overline{\mathrm{q}}+(\overline{\mathrm{c}}+\overline{\mathrm{a}}) \cdot \overline{\mathrm{r}}$ is equal to

A
0
B
1
C
2
D
3
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