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REPEATER 2024 Maths - REPEATER 2024

Maharashtra Board - STD 12 Science - Maths (MSBSHSE - English Medium). 44 questions in this chapter.

Question types

REPEATER 2024 question types

44 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

44
Questions
5
Question groups
5
Question types
Sample Questions

REPEATER 2024 questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ2 Marks
The approximate value of $\tan \left(44^{\circ} 30^{\prime}\right)$, given that $1^{\circ}=0.0175^c$, is  __________.
  • A
    0.8952
  • B
    0.9528
  • C
    0.9285
  • ✓
    0.9825

Answer: D.

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Q 2MCQ2 Marks
Given that $X \sim B(n, p)$. If $n=10$ and $p=0.4$ then $E(X)$ and $\operatorname{Var}(X)$ respectively are  __________.
  • A
    $4,0.24$
  • B
    $0.4,0.24$
  • ✓
    $4,2.4$
  • D
    $3, 0.24$

Answer: C.

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Q 3MCQ2 Marks
$y=c^2+\frac{c}{x}$ is solution of  __________ .
  • ✓
    $x^4\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}-y=0$
  • B
    $x^2\left(\frac{d y}{d x}\right)^2+y=0$
  • C
    $x^3\left(\frac{d^2 y}{d x^2}\right)-x \frac{d y}{d x}+y=0$
  • D
    $x \frac{d^2 y}{d x^2}=4 y$

Answer: A.

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Q 4MCQ2 Marks
If $x=e^{\frac{x}{y}}$ then $\frac{d y}{d x}=........$
  • A
    $1-\frac{y}{x}$
  • B
    $1+\frac{y}{x}$
  • ✓
    $\frac{x-y}{x \log x}$
  • D
    $\frac{x+y}{x \log x}$

Answer: C.

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Q 5MCQ2 Marks
The perpendicular distance of the plane $\hat{r} .(2 \hat{i}+3 \hat{j}-\hat{k})=5$, from the origin is ..........
  • ✓
    $\frac{5}{\sqrt{14}}$ units
  • B
    $\frac{5}{14}$ units
  • C
    5 units
  • D
    $\frac{\sqrt{14}}{5}$ units

Answer: A.

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Q 21Solve the Following Question.(4 Marks)4 Marks
$\begin{aligned}
\int_{-a}^a f(x) \cdot d x & =2 \int_0^a f(x) \cdot d x 0, & & \text { if } f(x) \text { is an even function. } \\
& =0, & & \text { if } f(x) \text { is an odd function }
\end{aligned}$
Hence find the value of $\int_{-1}^1 \tan ^{-1} x \cdot d x$
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Q 23Solve the Following Question.(4 Marks)4 Marks
If $y=f(u)$ is a differentiable function of $u$ and $u= g (x)$ is a differentiable function of $x$ such that the composite function $y=f(g(x))$ is a differentiable function of $x$ then prove that: $\frac{d y}{d x}=\frac{d y}{d u} \times \frac{d u}{d x}$
Hence find $\frac{d}{d x}\left(\frac{1}{\sqrt{\sin x}}\right)$.
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Q 24Solve the Following Question.(4 Marks)4 Marks
A firm manufactures two products $A$ and $B$ on which profit earned per unit are $₹.3$ and $₹.4$ respectively. Each product is processed on two machines $M_1$ and $M_2$. The product A requires one minute of processing time on $M_1$ and two minutes on $M_2$, while product $B$ requires one minute on $M_1$ and one minute on $M_2$. Machine $M_1$ is available for use not more than $450$ minutes, while $M_2$ is available for $600$ minutes during any working day. Find the number of units of product $A$ and $B$ to be manufactured to get the maximum profit.
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