1
CBSE 12th Mathematics Delhi Set 1 - 2024
MCQ (Single Correct Answer)
+1
-0

Assertion (A): The vectors

$$\begin{aligned} & \vec{a}=6 \hat{i}+2 \hat{j}-8 \hat{k} \\ & \vec{b}=10 \hat{i}-2 \hat{j}-6 \hat{k} \\ & \vec{c}=4 \hat{i}-4 \hat{j}+2 \hat{k} \end{aligned}$$

represent the sides of a right angled triangle.

Reason (R): Three non-zero vectors of which none of two are collinear forms a triangle if their resultant is zero vector or sum of any two vectors is equal to the third.

A
Both Assertion (A) and Reason (R) are true and the Reason ( $R$ ) is the correct explanation of the Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of the Assertion (A).
C
Assertion (A) is true, but Reason (R) is false.
D
Assertion (A) is false, but Reason (R) is true.
2
CBSE 12th Mathematics Delhi Set 1 - 2024
Subjective
+2
-0

Find value of $k$ if $\sin ^{-1}\left[k \tan \left(2 \cos ^{-1} \frac{\sqrt{3}}{2}\right)\right]=\frac{\pi}{3}$.

3
CBSE 12th Mathematics Delhi Set 1 - 2024
Subjective
+2
-0

(a) Verify whether the function $f$ defined by $f(x)=\left\{\begin{array}{cl}x \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.$ is continuous at $x=0$ or not.

OR

(b) Check for differentiability of the function $f$ defined by $f(x)=|x-5|$, at the point $x=5$.

4
CBSE 12th Mathematics Delhi Set 1 - 2024
Subjective
+2
-0

The area of the circle is increasing at a uniform rate of $2 \mathrm{~cm}^2 / \mathrm{s}$. How fast is the circumference of the circle increasing when the radius $r=5 \mathrm{~cm}$ ?

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