CBSE 12th Mathematics Delhi Set 1 - 2023
CBSE 2023 Previous Year
3 hDuration
75Total Marks
20Questions
1Sections
Instructions
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Paper Structure
Mathematics
Mathematics
Q1.
mcq single
+1 / 0
Two vector $$\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k} \quad$$ and $$\vec{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}$$ are collinear if:
Q2.
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The magnitude of the vector $$6 \hat{i}-2 \hat{j}+3 \hat{k}$$ is :
Q3.
mcq single
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$$\sin \left[\frac{\pi}{3}+\sin ^{-1}\left(\frac{1}{2}\right)\right]$$ is equal to:
Q4.
mcq single
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The function $$f(x)=[x]$$, where $$[x]$$ denotes the greatest integer less than or equal to $$x$$, is continuous at:
Q5.
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If $$x=A \cos 4 t+B \sin 4 t$$, then $$\frac{d^2 x}{d t^2}$$ is equal to:
Q6.
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Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is:
Q7.
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If for any two events $$\mathrm{A}$$ and $$\mathrm{B}, P(A)=\frac{4}{5}$$ and $$P(A \cap B)=\frac{7}{10}$$, then $$P(B / A)$$ is equals to:
Q8.
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Assertion (A): Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is $$\frac{1}{3}$$.
Reason (R): Let E and F be two events with a random experiment, then $$\mathrm{P}(\mathrm{F} / \mathrm{E})=\frac{\mathrm{P}(\mathrm{E} \cap \mathrm{F})}{\mathrm{P}(\mathrm{E})}$$.
Q9.
mcq single
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Let $$A=\{3,5\}$$. Then number of reflexive relations of $$A$$ is:
Q10.
mcq single
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The derivative of $$x^{2 x}$$ w.r.t. $$x$$ is:
Q11.
mcq single
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The interval in which the function $$f(x)=2 x^3+9 x^2 +12 x-1$$ is decreasing is :
Q12.
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The angle between the lines $$2 x=3 y=-z$$ and $$6 x=-y=-4 z$$ is:
Q13.
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If a line makes angles of $$90^{\circ}, 135^{\circ}$$ and $$45^{\circ}$$ with the $$x, y$$ and $$z$$ axes respectively, then its direction cosines are:
Q14.
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The sum of the order and the degree of the differential equation $$\frac{d}{d x}\left(\left(\frac{d y}{d x}\right)^3\right)$$ is:
Q15.
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Assertion (A): $$\int_\limits2^8 \frac{\sqrt{10-x}}{\sqrt{x}+\sqrt{10-x}} d x=3$$
Reason (R): $$\int_\limits a^b f(x) d x=\int_a^b f(a+b-x) d x$$
Q16.
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$$\int_\limits{-1}^1 \frac{|x-2|}{x-2} d x, x \neq 2 \text { is equal to: }$$
Q17.
mcq single
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If for a square matrix $$\mathrm{A}, A^2-A+I=\mathrm{O}$$, then $$\mathrm{A}^{-1}$$ equals:
Q18.
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$$\text { If } A=\left[\begin{array}{ll}
1 & 0 \\
2 & 1
\end{array}\right], B=\left[\begin{array}{ll}
x & 0 \\
1 & 1
\end{array}\right] \text { and } A=B^2 \text {, then } x \text { equals: }$$
Q19.
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$$\text { If }\left|\begin{array}{lll}
\alpha & 3 & 4 \\
1 & 2 & 1 \\
1 & 4 & 1
\end{array}\right|=0 \text {, then the value of } \alpha \text { is: }$$
Q20.
mcq single
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$$\int \frac{\sec x}{\sec x-\tan x} d x$$ equals: