Maharashtra HSC Maths & Statistics Question Paper 2025, Download PDF Here

Maharashtra Board Class 12 Maths & Statistics Answer Key 2025

Question:

If $A=\{1,2,3,4,5\}$ then which of the following is not true?
(a) $\exists x \in A$ such that $x+3=8$
(b) $\exists x \in A$ such that $x+2<9$
(c) $\forall x \in A, x+6 \geq 9$
(d) $\exists x \in A$ such that $x+6<10$

Correct Answer: C

Question:

In $\triangle A B C,(a+b) \cdot \cos C+(b+c) \cos A+(c+a) \cdot \cos B$ is equal to $\qquad$
(a) $a-b+c$
(b) $a+b-c$
(c) $a+b+c$
(d) $a-b-c$

Correct Answer: C

Question:

If $|\bar{a}|=5,|\bar{b}|=13$ and $|\bar{a} \times \bar{b}|=25$ then $|\bar{a} \cdot \bar{b}|$ is equal to
$\qquad$ .
(a) 30
(b) 60
(c) 40
(d) 45

Correct Answer: B

Question:

The vector equation of the line passing through the point having position vector $4 \hat{i}-\hat{j}+2 \hat{k}$ and parallel to vector $-2 \hat{i}-\hat{j}+\hat{k}$ is given by $\qquad$ .
(a) $(4 \hat{i}-\hat{j}-2 \hat{k})+\lambda(-2 \hat{i}-\hat{j}+\hat{k})$
(b) $(4 \hat{i}-\hat{j}+2 \hat{k})+\lambda(2 \hat{i}-\hat{j}+\hat{k})$
(c) $(4 \hat{i}-\hat{j}+2 \hat{k})+\lambda(-2 \hat{i}-\hat{j}-\hat{k})$
(d) $(4 \hat{i}-\hat{j}+2 \hat{k})+\lambda(-2 \hat{i}-\hat{j}+\hat{k})$

Correct Answer: D

Question:

Let $f(1)=3, f^{\prime}(1)=-\frac{1}{3}, g(1)=-4$ and $g^{\prime}(1)=-\frac{8}{3}$. The derivative of $\sqrt{[f(x)]^2+[g(x)]^2}$ w.r.t. $x$ at $x=1$ is $\qquad$ -.
(a) $-\frac{29}{25}$
(b) $\frac{7}{3}$
(c) $\frac{31}{15}$
(d) $\frac{29}{15}$

Correct Answer: D

Question:

If the mean and variance of a binomial distribution are 18 and 12 respectively, then $n$ is equal to $\qquad$
(a) 36
(b) 54
(c) 18
(d) 27

Correct Answer: B

Question:

The area bounded by the line $y=x$, X -axis and the lines $x=-1$ and $x=4$ is equal to $\qquad$ (in square units)
(a) $\frac{2}{17}$
(b) 8
(c) $\frac{17}{2}$
(d) $\frac{1}{2}$

Correct Answer: C

Question:

$\begin{aligned}
&\text { Write the order of the differential equation }\\
&\sqrt{1+\left(\frac{d y}{d x}\right)^2}=\left(\frac{d^2 y}{d x^2}\right)^{\frac{3}{2}}
\end{aligned}$

Answer:

$\text { The highest derivative is } \frac{d^2 y}{d x^2} \text {, so the order is } \mathbf{2} \text {. }$

Question:

Write the condition for the function $f(x)$, to be strictly increasing, for all $x \in R$.

Answer:

For a function $f(x)$ to be strictly increasing for all $x \in \mathbb{R}$, the following condition must hold:

$
f^{\prime}(x)>0 \quad \text { for all } x \in \mathbb{R}
$

This means the derivative of $f(x)$ must be positive everywhere on the real number line.

$
f^{\prime}(x)>0 \quad \forall x \in \mathbb{R}
$