In how many ways can 5 persons occupy 3 seats?
- A30
- B15
- C60
- D20
Question types
Model Paper 10 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→05Case study (4 Marks)
3 Q→065 Marks Questions
6 Q→Sample Questions
Model Paper 10 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\lim _{x \rightarrow 3} \frac{x-3}{|x-3|}$ is equal to:
- A1
- B-1
- C$0$
- DNone of these
The value of $\frac{2\left(\sin 2 x+2 \cos ^2 x-1\right)}{\cos x-\sin x-\cos 3 x+\sin 3 x}$ is
- A$\sin x$
- B$\cos x$
- ✓$\operatorname{cosec} x$
- D$\sec x$
Answer: C.
View full solution →If A = {1, 3, 5, B} and B = {2, 4}, then
- A$\{4\} \subset A$
- BNone of these
- C$B \subset A$
- D$4 \in A$
The solution set of $6 x-1 > 5$ is :
- A$\{x: x > 1, x \in N\}$
- ✓$\{x: x > 1, x \in R\}$
- C$\{x: x < 1, x \in N\}$
- D$\{x: x < 1, x \in W\}$
Answer: B.
View full solution →Assertion $(A):$ If the numbers $\frac{-2}{7}, K, \frac{-7}{2}$ are in $GP,$ then $k = \pm 1$.
Reason $(R):$ If $a_1, a_2, a_3$ are in $GP,$ then $\frac{a_2}{a_1}=\frac{a_3}{a_2}$.
Reason $(R):$ If $a_1, a_2, a_3$ are in $GP,$ then $\frac{a_2}{a_1}=\frac{a_3}{a_2}$.
- ✓Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- BBoth $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: A.
View full solution →Assertion (A): The set A = {a, b, c, d, e, g} is finite set
Reason (R): The set B = {men living presently in different parts of the world} is finite set.
Reason (R): The set B = {men living presently in different parts of the world} is finite set.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Find a point on the $y-$axis which is equidistant from $A (-4, 3)$ and $B(5, 2).$
View full solution →Is $B =\left\{ x : x ^2+2 x +1=0, x \in N \right\}$ a singleton set?
View full solution →If $A$ and $B$ are two events associated with a random experiment for which $P(A) = 0.60, P(A$ or $B) = 0.85$ and $P(A $ and $B) = 0.42,$ find $P(B).$
View full solution →If $\frac{5}{14}$ is the probability of occurrence of an event, find
i. the odds in favour of its occurrence.
ii. the odds against its occurrence.
View full solution →i. the odds in favour of its occurrence.
ii. the odds against its occurrence.
Differentiate: $\left(x^2-4 x+5\right)\left(x^3-2\right)$.
View full solution →In a class, $18$ students took Physics $, 23$ students took Chemistry and $24$ students took
Mathematics of these $13$ took both Chemistry and Mathematics, $12$ took both Physics and Chemistry and $11$ took both Physics an Mathematics. If $6$ students offered all the three subjects, find:
$i$. The total number of students.
$ii$. How many took Maths but not Chemistry.
$iii$. How many took exactly one of the three subjects.
View full solution →Mathematics of these $13$ took both Chemistry and Mathematics, $12$ took both Physics and Chemistry and $11$ took both Physics an Mathematics. If $6$ students offered all the three subjects, find:
$i$. The total number of students.
$ii$. How many took Maths but not Chemistry.
$iii$. How many took exactly one of the three subjects.
Evaluate: $\sum_{k=1}^{11}\left(2+3^k\right)$
View full solution →If the $AM$ and $GM$ of two positive numbers $a$ and $b$ are in the ratio $m : n$, show that $a : b =\left(m+\sqrt{m^2-n^2}\right):\left(m-\sqrt{m^2-n^2}\right)$
View full solution →Find the derivative of $\frac{(x-1)(x-2)}{(x-3)(x-4)}$.
View full solution →Find the derivative of $x^{-4}\left(3-4 x^{-5}\right)$
View full solution →Consider the complex number $Z = 2 - 2i.$ Complex Number in Polar Form
$i.$ Find the principal argument of $Z . (1)$
$ii.$ Find the value of $\bar{z} \bar{z}$ ? $(1)$
$iii.$ Find the value of $| Z |. (2)$
OR
Find the real part of $Z. (2)$
View full solution →$i.$ Find the principal argument of $Z . (1)$
$ii.$ Find the value of $\bar{z} \bar{z}$ ? $(1)$
$iii.$ Find the value of $| Z |. (2)$
OR
Find the real part of $Z. (2)$
There are $4$ red, $5$ blue and $3$ green marbles in a basket.
$i.$ If two marbles are picked at randomly, find the probability that both red marbles. $(1)$
$ii.$ If three marbles are picked at randomly, find the probability that all green marbles. $(1)$
$iii$. If two marbles are picked at randomly then find the probability that both are not blue marbles. $(2)$
OR
If three marbles are picked at randomly, then find the probability that atleast one of them is blue. $(2)$
View full solution →$i.$ If two marbles are picked at randomly, find the probability that both red marbles. $(1)$
$ii.$ If three marbles are picked at randomly, find the probability that all green marbles. $(1)$
$iii$. If two marbles are picked at randomly then find the probability that both are not blue marbles. $(2)$
OR
If three marbles are picked at randomly, then find the probability that atleast one of them is blue. $(2)$
Prove that $\cos 12^{\circ}+\cos 60^{\circ}+\cos 84^{\circ}=\cos 24^{\circ}+\cos 48^{\circ}$
View full solution →Prove that: $\sin 20^{\circ} \sin 40^{\circ} \sin 80^{\circ}=\frac{\sqrt{3}}{8}$
View full solution →Solve the following system of linear inequalities $\frac{4 x}{3}-\frac{9}{4}< x+\frac{3}{4}$ and $\frac{7 x-1}{3}-\frac{7 x+2}{6} > x$.
View full solution →Find the equation of the hyperbola, the length of whose latus rectum is $4$ and the eccentricity is $3$.
View full solution →Find the equation of a circle concentric with the circle $x^2+y^2+4 x+6 y+11=0$ and passing through the point $(5,4)$.
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