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

(a) Evaluate: $\int_0^\pi \frac{e^{\cos x}}{e^{\cos x}+e^{-\cos x}} d x$

OR

(b) Find: $\int \frac{2 x+1}{(x+1)^2(x-1)} d x$

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

(a) Find the particular solution of the differential equation $\frac{d y}{d x}-2 x y=3^{x^2} e^{x^2} ; y(0)=5$.

OR

(b) Solve the following differential equation: $$ x^2 d y+y(x+y) d x=0 $$

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

Find a vector of magnitude 4 units perpendicular to each of the vectors $2 \hat{i}-\hat{j}+\hat{k}$ and $\hat{i}+\hat{j}-\hat{k}$ and hence verify your answer.

4
CBSE 12th Mathematics Delhi Set 1 - 2024
Subjective
+3
-0

The random variable $X$ has the following probability distribution where $a$ and $b$ are some constants:

X 1 2 3 4 5
P(X) 0.2 a a 0.2 b

If the mean $E(X)=3$, then find values of $a$ and $b$ and hence determine $P(X \geq 3)$.

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