If $A=\left[\begin{array}{ll}3 & 4 \\ 5 & 2\end{array}\right]$ and 2A + B is a null matrix, then B is equal to:
View full solution →Question types
Model Paper 3 question types
45 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
45
Questions
6
Question groups
5
Question types
01
M.C.Q (1 Marks)
18 Q→02Assertion (A) & Reason (B) MCQ
2 Q→032 Marks Questions
7 Q→043 Marks Question
9 Q→055 Marks Questions
6 Q→06Case study (4 Marks)
3 Q→Sample Questions
Model Paper 3 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $A=\left[3 1 7 5\right]$ and $A ^2+ xI = yA$ then the values of $x$ and $y$ are
View full solution →Range of $\operatorname{coses}^{-1} X$ is
View full solution →If $x, y, z$ are non$-$zero real numbers, then the inverse of matrix $A=\left[\begin{array}{lll}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{array}\right]$ is
View full solution →The solution of the differential equation $\left(x^2+1\right) \frac{d y}{d x}+\left(y^2+1\right)=0$, is
View full solution →Let R be any relation in the set A of human beings in a town at a particular time.
Assertion (A): If $R=\{(x, y): x$ is wife of $y\}$, then $R$ is reflexive.
Reason (R): If $R=\{(x, y): x$ is father of $y\}$, then R is neither reflexive nor symmetric nor transitive.
View full solution →Assertion (A): If $R=\{(x, y): x$ is wife of $y\}$, then $R$ is reflexive.
Reason (R): If $R=\{(x, y): x$ is father of $y\}$, then R is neither reflexive nor symmetric nor transitive.
Assertion $(A):$ A particle moving in a straight line covers a distance of $x$ cm in t second, where $x=t^3+3 t^2-6 t +18$ The velocity of particle at the end of $3$ seconds is $39$ cm/s.
Reason $(R):$ Velocity of the particle at the end of $3$ seconds is $\frac{d x}{d t}$ at $t =3$
View full solution →Reason $(R):$ Velocity of the particle at the end of $3$ seconds is $\frac{d x}{d t}$ at $t =3$
A ladder $13 \ m$ long is leaning against a vertical wall. The bottom of the ladder is dragged away from the wall along the ground at the rate of $2 \ cm/ \sec$. How fast is the height on the wall decreasing when the foot of the ladder is $5\ m$ away from the wall?
View full solution →Show that $f(x)=\frac{1}{1+x^2}$ is neither increasing nor decreasing on $R$ .
View full solution →Evaluate : $- \tan ^{-1}\left(-\frac{1}{\sqrt{3}}\right)+\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)+\tan ^{-1}\left(\sin \left(-\frac{\pi}{2}\right)\right)$
View full solution →$\tan ^{-1}\left(\tan \frac{3 \pi}{4}\right) =?$
View full solution →Find values of $k$ if area of triangle is $35$ square units having vertices as $(2, -6), (5, 4), (k, 4)$.
View full solution →If with reference to the right handed system of mutually perpendicular unit vectors $\hat{i}, \hat{j}$ and $\hat{k}, \vec{\alpha}=3 \hat{i}-\hat{j.}$
$\vec{\beta}=2 \hat{i}+\hat{j}-3 \hat{k.}$ then express $\vec{\beta}$ in the form $\vec{\beta}=\vec{\beta}_1+\vec{\beta}_2$, where $\vec{\beta}_1$ is $\|$ to $\vec{\alpha}$ and $\vec{\beta}_2$ is perpendicular to $\vec{\alpha}$.
View full solution →$\vec{\beta}=2 \hat{i}+\hat{j}-3 \hat{k.}$ then express $\vec{\beta}$ in the form $\vec{\beta}=\vec{\beta}_1+\vec{\beta}_2$, where $\vec{\beta}_1$ is $\|$ to $\vec{\alpha}$ and $\vec{\beta}_2$ is perpendicular to $\vec{\alpha}$.
Evaluate $\int_0^{\pi / 2} \frac{x+\sin x}{1+\cos x} d x$
View full solution →A factory has two machines $A$ and $B$. Past records show that the machine $A$ produced $60\%$ of the items of output and machine $B$ produced $40\%$ of the items. Further $2\%$ of the items produced by machine $A$ were defective and $1\%$ produced by machine $B$ were defective. If an item is drawn at random, what is the probability that it is defective?
View full solution →Evaluate: $\int \frac{x+2}{\sqrt{x^2+2 x-1}} d x$
View full solution →Evaluate the integral : $\int \sqrt{\cot \theta} d \theta$
View full solution →Show that the relation $R$ in the set $A=\{1,2,3,4,5\}$ given by $R=\{(a, b):|a-b|$ is even $\}$, is an equivalence relation. Show that all the elements of $\{1,3,5\}$ are related to each other and all the elements of $\{2,4\}$ are related to each other. But no element of $\{1,3,5\}$ is related to any element of $\{2,4\}$.
View full solution →Find the area bounded by the circle $x^2+y^2=16$ and the line $\sqrt{3} y=x$ inthe first quadrant, using integration
View full solution →Prove that the semi $-$ vertical angle of the right circular cone of given volume and least curved surface area is $\cot ^{-1} \sqrt{2}$
View full solution →Show that a cylinder of a given volume which is open at the top has minimum total surface area, when its height is equal to the radius of its base
Express the matrix $B=\left[\begin{array}{ccc}2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3\end{array}\right]$ as the sum of a symmetric and a skew-symmetric matrix.
View full solution →Read the following text carefully and answer the questions that follow:
Two motorcycles $A$ and $B$ are running at the speed more than allowed speed on the road along the lines
$\vec{r}=\lambda(\hat{i}+2 \hat{j}-\hat{k})$ and $\vec{r}=3 \hat{i}+3 \hat{j}+\mu(2 \hat{i}+\hat{j}+\hat{k})$, respectively.
$i.$ Find the cartesian equation of the line along which motorcycle $A$ is running.$ (1)$
$ii.$ Find the direction cosines of line along which motorcycle $A$ is running. $(1)$
$iii.$ Find the direction ratios of line along which motorcycle $B$ is running. $(2)$
$OR$
Find the shortest distance between the given lines. $(2)$
View full solution →Two motorcycles $A$ and $B$ are running at the speed more than allowed speed on the road along the lines
$\vec{r}=\lambda(\hat{i}+2 \hat{j}-\hat{k})$ and $\vec{r}=3 \hat{i}+3 \hat{j}+\mu(2 \hat{i}+\hat{j}+\hat{k})$, respectively.
$i.$ Find the cartesian equation of the line along which motorcycle $A$ is running.$ (1)$
$ii.$ Find the direction cosines of line along which motorcycle $A$ is running. $(1)$
$iii.$ Find the direction ratios of line along which motorcycle $B$ is running. $(2)$
$OR$
Find the shortest distance between the given lines. $(2)$
Read the following text carefully and answer the questions that follow :
To hire a marketing manager, it's important to find a way to properly assess candidates who can bring radical
changes and has leadership experience.
Ajay, Ramesh and Ravi attend the interview for the post of a marketing manager. Ajay, Ramesh and Ravi
chances of being selected as the manager of a firm are in the ratio $4:1:2$ respectively. The respective probabilities for them to introduce a radical change in marketing strategy are $0.3, 0.8,$ and $0.5$. If the change does take place.
i. Find the probability that it is due to the appointment of Ajay $(A). (1)$
ii. Find the probability that it is due to the appointment of Ramesh $(B). (1)$
iii. Find the probability that it is due to the appointment of Ravi $(C). (2)$
OR
Find the probability that it is due to the appointment of Ramesh or Ravi. $(2)$
View full solution →To hire a marketing manager, it's important to find a way to properly assess candidates who can bring radical
changes and has leadership experience.
Ajay, Ramesh and Ravi attend the interview for the post of a marketing manager. Ajay, Ramesh and Ravi
chances of being selected as the manager of a firm are in the ratio $4:1:2$ respectively. The respective probabilities for them to introduce a radical change in marketing strategy are $0.3, 0.8,$ and $0.5$. If the change does take place.
i. Find the probability that it is due to the appointment of Ajay $(A). (1)$
ii. Find the probability that it is due to the appointment of Ramesh $(B). (1)$
iii. Find the probability that it is due to the appointment of Ravi $(C). (2)$
OR
Find the probability that it is due to the appointment of Ramesh or Ravi. $(2)$
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