[ Question Bank ] - Rajasthan Board (RBSE) STD 12 Science MATHS Questions

If matrix $A+B=\left[\begin{array}{ll}2 & 4 \\ 1 & 2\end{array}\right], A-B=\left[\begin{array}{ll}0 & 1 \\ 2 & 2\end{array}\right]$, then find matrix $A$.

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Q 112 Marks Questions2 Marks

If A = {1, 2, 3}, B {2, 1), then find the number of non empty relations from A to B.

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Q 122 Marks Questions2 Marks

Find the area of that parallelogram whose diagonals are denoted by vectors $2 \hat{i}-\hat{j}+5 \hat{k}$ and $3 \hat{i}+\hat{j}+2 \hat{k}$.

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Q 132 Marks Questions2 Marks

If $A=[1 \ 2 \ 3], B=\left[\begin{array}{l}3 \\ 2 \\ 1\end{array}\right]$ then find $AB$ and $BA$.

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Q 142 Marks Questions2 Marks

Find a vector of magnitude 8 along with the vector $i+2 j+2 k$.

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Q 152 Marks Questions2 Marks

If $A$ and $B$ are independent events show that the probability of happening at least one of $A$ and $B$ will be $1-P\left(A^{\prime}\right) P\left(B^{\prime}\right)$

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Q 163 Marks Question3 Marks

Solve : $\tan ^{-1} 2 x+\tan ^{-1} 3 x=\frac{\pi}{4}$.

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Q 173 Marks Question3 Marks

Find the value of $\int \frac{\sin x}{\sin (x-a)} d x$.

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Q 183 Marks Question3 Marks

Prove that $\cos ^{-1} \frac{63}{65}+2 \tan ^{-1} \frac{1}{5}=\sin ^{-1} \frac{3}{5}$.

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Q 193 Marks Question3 Marks

Find the value of $\int \frac{\mathrm{dx}}{\mathrm{e}^{\mathrm{x}}-1}$.

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Q 203 Marks Question3 Marks

Find the value of $\int \frac{1}{1-\tan x} d x$.

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Q 21Fill In The Blanks[1 Marks ]1 Mark

The value of $\int x \cdot e^x d x$ will be

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Q 22Fill In The Blanks[1 Marks ]1 Mark

If $y=\tan x^2$ then $\frac{d y}{d x}=$……..

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Q 23Fill In The Blanks[1 Marks ]1 Mark

The angle between the line $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$ and the plane $x+2 y+3 z-5=0$ will be.....

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Q 24Fill In The Blanks[1 Marks ]1 Mark

The value of $\int \frac{\sin ^{-1} x}{\sqrt{1-x^2}} d x$ will be………

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Q 25Fill In The Blanks[1 Marks ]1 Mark

The tangent of normal on curve $y=x^2+2$ at point $(1,3)$ will be.....

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Q 26Answer the question [ 4 mark question ]4 Marks

A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs. 5 each for type A and Rs. 6 each for type B souvenirs. How many souvenirs of each type should be manufactured for maximum profit.

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Q 27Answer the question [ 4 mark question ]4 Marks

Find the particular solution of differential equation $\frac{d y}{d x}+y \cot x=2 x+x^2 \cot x,(x \neq c)$ given that, $y =0$ at $x=\frac{\pi}{2}$

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Q 28Answer the question [ 4 mark question ]4 Marks

Find the value of $\int_0^\pi \frac{x \sin x}{1+\cos ^2 x} d x$

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Q 29Answer the question [ 4 mark question ]4 Marks

Find the value of $\int_0^{\pi / 2} \frac{\cos x}{(1+\sin x)(2+\sin x)} d x$

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Q 30Answer the question [ 4 mark question ]4 Marks

Find $\int \frac{x^2}{x^6+x^3} d x$