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Class 12 Maths previous year question paper 2023
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Jkbose previous year question paper 2023 SET X, Y, Z Maths
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Class 12 maths previous year question paper 2023 Set y

B-12-Y

https://www.jkboseoldpapers.com
Roll No.
Total No of Questions ….. 29
Total No. of Printed Pages: 8
XIIARJKUT23
9112-Y
MATHEMATICS
Time : 3 Hours
[Maximum Marks : 100]
SECTION-A
(MULTIPLE CHOICE QUESTIONS) ….. 1 each

1. Range of the function $$f(x)=4 x+3, x>0$$ is :
(A) $$(3, ∞ )$$
(B) $$[3 , ∞)$$
(C) $$(-∞, 3)$$
(D) $$(-∞, 3]$$
2. $$\tan ^{-1} x+\cot ^{-1} x, x \in \mathbf{R}$$ is equal to :
(A) $$\frac{\pi}{2}$$
(B) $$\frac{\pi}{3}$$
(C) $$\frac{\pi}{4}$$
(D) $$\pi$$
3. If $$\vec{a}$$ and $$\vec{b}$$ are two unit vectors, then $$|\vec{a} \times \vec{b}|=$$ :
(A) $$\cos \theta$$
(B) $$\sin \theta$$
(C) (ab) $$\cos \theta$$
(D) (ab) $$\sin \theta$$
4. If A is a square matrix of order n , then $$|{adj}(A)|=$$
(A) $$|\mathrm{A}|^{n}$$
(B) $$|A|^{n-1}$$
(C) $$|A|^{n+1}$$
(D) None of these

XIIARJKUT23-9112-Y
B-12-Y

{SECTION-B}
(VERY SHORT ANSWER TYPE QUESTIONS) 2 each

5. Using properties of determinants. prove that :
$$
\left|\begin{array}{lll}
1 & a & b+c \\
1 & b & c+a \\
1 & c & a+b
\end{array}\right|=0
$$
6. Prove that the function $$f(x)=5 x-3$$ is continums at $$x=0$$.
7. Differentiate $$\cos (\sin x)$$ with respect to $$x$$.
8. Find :
$$
\int \frac{(\log . x)^{2}}{x} d x
$$
9. A coin is tossed three times. Find P(F/E), where E is the event “at least two heads” and F is the event “at most two heads.”
10. Compute $$P(A / B)$$ if $$P(B)=0.5$$ and $$P(A \cap B)=0.32$$.
11. Find the vector in the direction of vector $$5 \hat{i}-\hat{j}+2 \hat{k}$$ and having magnitude of 8 units.
12. Define Linear Constraints.

XIIARJKUT23-9112-Y
B-12-Y

{SECTION-C}
(SHORT ANSWER TYPE QUESTIONS)

13. Find fog and gof if $$f(x)=8 x^{3}$$ and $$g(x)=x^{1/3}$$.
14. Prove that :
$$
\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{2}{11}=\tan ^{-1} \frac{3}{4}
$$
15.
$$
A=\left[\begin{array}{lll}
1 & 0 & 2 \\
0 & 2 & 1 \\
2 & 0 & 3
\end{array}\right]
$$
prove that $$A^{3}-6 A^{2}+7 A+21=0$$.
16. Find local maxima and local minima if any of the function :
$$
f(x)=x^{3}-6 x^{2}+9 x+15
$$
17. Find general solution of differential equation :
$$
x \frac{d y}{d x}-y+x \sin \left(\frac{y}{x}\right)=0
$$
18. Find $$\frac{d y}{d x}$$ if $$x^{3}+x^{2} y+x y^{2}+y^{3}=81$$.

{B-12-Y}

19. Prove that:
$$
\int \sqrt{a^{2}-x^{2}} d x=\frac{x \sqrt{a^{2}-x^{2}}}{2}+\frac{a^{2}}{2} \sin ^{-1}\left(\frac{x}{a}\right)+C
$$
20. If $$y=\left(\tan ^{-1} x\right)^{2}$$, show that :
$$
\left(x^{2}+1\right)^{2} y_{2}+2 x\left(x^{2}+1\right) y_{1}=2
$$
21. If $$\vec{a}, \vec{b}, \vec{c}$$ are unit vectors such that $$\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$$. find the value of $$\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}$$.
22. Find the Vector and Cartesian equations of the line that passes through the points (3, -2,-5 ) and (3, 2,6 ).
23. Solve the following graphically :

Minimise :
$$
\mathrm{Z}=x+2 y
$$

Subject to the constraints :
$$
\begin{aligned}
2 x+y & \geq 3 \\
x+2 y & \geq 6 \\
x, y & \geq 0
\end{aligned}
$$

{(SECTION-D)}

{(LONG ANSWER TYPE QUESTIONS)}
24. Using properties of determinants show that :
$$
\left.\left|\begin{array}{lll}
a & a^{2} & b c \\
b & b^{2} & c a \\
c & c^{2} & a b
\end{array}\right|=(a-b)(b-c)(c-a)(a b+b c+c a\right)
$$

Or
Solve the system of linear equations using matrix method :
$$
\begin{aligned}
2 x+y+z & =1 \\
x-2 y-z & =\frac{3}{2} \\
3 y-5 z & =9
\end{aligned}
$$
25. Find $$\frac{d y}{d x}$$ if $$x=a\left(\cos t+\log \tan \frac{1}{2}\right) \cdot y=a \sin t$$
Or

Find $$\frac{d y}{d x}$$ if $$(\cos x)^{y}=(\cos y)^{x}$$.
26. Find $$\int_{0}^{\pi / 2} \sqrt{\sin \phi} \operatorname{cos}^{5} \phi d\phi /$$.
Or
Using integration, find the area of region bounded by triangle whose vertices are (-1. 0). (1, 3), (3. 2).
27. If $$\vec{a}=\hat{i}+4 \hat{j}+2 \hat{k} \cdot \vec{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}, \vec{c}=2 \hat{i}-\hat{j}+4 \hat{k}$$. find the vector $$\vec{d}$$ which is perpendicular to both $$\vec{a}$$ and $$\vec{b}$$ and $$\vec{c} \cdot \vec{d}=15$$.

Or

Find the shortest distance between the lines $$\frac{x+1}{7}=\frac{y+1}{-6}=\frac{z+1}{1}$$ and $$\frac{x-3}{1}=\frac{y-5}{-2}=\frac{z-7}{1}$$. https://www.jkboseoldpapers.com
28. Find the intervals in which the function $$f(x)=(x+1)^{3}(x-3)^{3}$$ is strictly increasing or decreasing.
Or

Evaluate :
$$
\int_{0}^{\pi / 2} \log \sin x d x
$$

29. There are $$5 \%$$ defective items in a large bulk of items. What is the probability that a sample of $$\mathbf{1 0}$$ items will include not more than one defective item.

Or

Find the mean and variance of the number obtained on a throw of an unbiased die.

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