1
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.

2
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 $P(X \geq 3)$.

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

(a) If $A=\left[\begin{array}{ccc}1 & 2 & -3 \\ 2 & 0 & -3 \\ 1 & 2 & 0\end{array}\right]$, then find $A^{-1}$ and hence solve the following system of equations:

$$\begin{array}{r} x+2 y-3 z=1 \\ 2 x-3 z=2 \\ x+2 y=3 \end{array}$$

OR

(b) Find the product of the matrices $\left[\begin{array}{ccc}1 & 2 & -3 \\ 2 & 3 & 2 \\ 3 & -3 & -4\end{array}\right]\left[\begin{array}{ccc}-6 & 17 & 13 \\ 14 & 5 & -8 \\ -15 & 9 & -1\end{array}\right]$ and hence solve the system of linear equations:

$$\begin{aligned} x+2 y-3 z & =4 \\ 2 x+3 y+2 z & =2 \\ 3 x-3 y-4 z & =11 \end{aligned}$$

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

Find the area of the region bounded by the curve $4 x^2$ $+y^2=36$ using integration.

EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12