Sample Questions[ Question Bank ] questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $P(A / B)=\frac{2}{5}, P(B)=\frac{1}{5}$, then the value of $P(A \cap B)$ is
- A
$\frac{1}{5}$
- B
$\frac{2}{5}$
- ✓
$\frac{2}{25}$
- D
$\frac{1}{2}$
Answer: C.
View full solution →If $P(\operatorname{Not} A)=3 / 5$, then the value of $P(A)$ will be
- ✓
$\frac{2}{5}$
- B
$\frac{1}{5}$
- C
$\frac{4}{5}$
- D
$0$
Answer: A.
View full solution →If $P(A)=0.6, P(B)=0.3$ and $A$ and $B$ are two independent events, the value of $P(A \cap B)$ will be $-$
Answer: C.
View full solution →The distance of $(2,3,5)$ from $z-$ axis is
- A
$\sqrt{2}$
- B
$\sqrt{3}$
- C
$\sqrt{7}$
- ✓
Answer: D.
View full solution →If $\vec{a}=\hat{i}+\hat{j}+2 \hat{k}$, then the value of $\vec{a} \cdot \vec{a}$ will be
Answer: B.
View full solution →Find the probability of getting an even prime number when a die is rolled.
Find the direction cosines of Y-axis.
Find the coordinates of mid point of line joining the points $(2,-2,0)$ and $(3,1,2)$.
View full solution →Find the direction cosines of normals of the plane $\vec{r} \cdot(3 \hat{i}+\hat{j}+4 \hat{k})=5$.
View full solution →If $\vec{a}=3 \hat{i}-\hat{j}+4 \hat{k}$ and $\vec{b}=\hat{i}+\hat{j}-\hat{k}$ then find $|\vec{a}-\vec{b}|$.
View full solution →If $A$ and $B$ are independent events show that the probability of happening at least one of $A$ and $B$ will be $1-P\left(A^{\prime}\right) P\left(B^{\prime}\right)$
View full solution →If $\vec{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=-\hat{i}+2 \hat{j}+\hat{k}$ and $\vec{c}=3 \hat{i}+\hat{j}$ are such that $\vec{a}+\lambda \vec{b}$ is perpendicular on vector $\vec{c}$, then find the value of $\lambda$.
View full solution →Find a vector of magnitude 8 along with the vector $i+2 j+2 k$.
View full solution →If $y=x^x+x^a+a^x+a^a$, then find $\frac{d y}{d x}$.
View full solution →Find the area bounded by parabola $x^2=4 y$ and line $y=3$ (draw figure).
View full solution →If $\vec{a}, \vec{b}, \vec{c}$ are three vectors equal in magnitude and $\vec{a}+\vec{b}+\vec{c}=0$, then find the value of $\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}$.
View full solution →Find a unit vector along perpendicular to vectors $(\vec{a}+\vec{b})$ and $(\vec{a}-\vec{b})$ where $\vec{a}=2 \hat{i}+\hat{j}-2 \hat{k}$ and $\vec{b}=\hat{i}-2 \hat{j}+2 \hat{k}$.
View full solution →Find the value of $\int \frac{1}{1-\tan x} d x$.
View full solution →Find the value of $\int \frac{x e^x}{(x+1)^2} d x$.
View full solution →If $x^y=y^x$, then find $\frac{d y}{d x}$.
View full solution →$P(A)+P(\bar{A})=$_______
View full solution →If a line makes equal angles with direction axes, then the direction cosines of that line will be_______
The value of $\int x \cdot e^x d x$ will be
View full solution →If the radius of a sphere is changing at the rate of 0.2 cm/sec, then the rate of change in its surface area will be______
If $y=e^{x^2}$, then at $x=4$ the value of $\frac{d y}{d x}$ will be.______
View full solution →Solve the following LPP using graphical method
$
\begin{array}{ll}
\text { Minimize } & Z=600 x+400 y \\
\text { constraints } & x+2 y>12 \\
& 2 x+y<12 \\
& x+\frac{5}{4} y \geq 5 \\
& x>0, y>0
\end{array}
$
View full solution →Solve the following LPP using graphical method
$
\begin{array}{cc}
\text { Minimize } & z=3 x+5 y \\
\text { constraints } & x+3 y \geq 3 \\
& x+y \geq 2 \\
& x \geq 0, y \geq 0
\end{array}
$
View full solution →Find the solution of diffrential equation $\left(\tan ^{-1} y-x\right) d y=\left(1+y^2\right) d x$, when $x=0, y=0$.
View full solution →Find the particular solution of differential equation $\frac{d y}{d x}+y \cot x=2 x+x^2 \cot x,(x \neq c)$ given that, $y =0$ at $x=\frac{\pi}{2}$
View full solution →Find the value of $\int_{\pi / 6}^{\pi / 3} \frac{d x}{1+\sqrt{\tan x}}$
View full solution →