In how many ways can a committee of 5 members be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?
- A50
- B200
- C25
- D100
Question types
Model Paper 9 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 9 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
For any positive integer $n,(-\sqrt{-1})^{4 n+3}=$ ?
- A1
- Bi
- C-i
- D-1
Mark the Correct alternative in the following: $8 \sin \frac{x}{8} \cos \frac{x}{2} \cos \frac{x}{4} \cos \frac{x}{8}$ is equal to
- ✓$\sin x$
- B$8 \cos x$
- C$\cos x$
- D$8 \sin x$
Answer: A.
View full solution →If $A$ and $B$ are two given sets, then $A \cap(A \cap B)^C$ is equal to
- AB
- BA
- C$A \cap B ^{ C }$
- D$\phi$
The solution set of $6x - 1 > 5$ 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 each of the observations $x _1, x _2, \ldots, x _{ n }$ is increased by $a,$ where a is a negative or positive number, then the variance remains unchanged.
Reason $(R):$ Adding or subtracting a positive or negative number to $($or from$)$ each observation of a group does not affect the variance.
Reason $(R):$ Adding or subtracting a positive or negative number to $($or from$)$ each observation of a group does not affect the variance.
- ✓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 expansion of $(1+ x )^{ n }=n_{c_0}+n_{c_1} x+n_{c_2} x^2 \ldots+n_{c_n} x^n$.
Reason $(R):$ If $x=-1$, then the above expansion is zero.
Reason $(R):$ If $x=-1$, then the above expansion is zero.
- ABoth $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- ✓Both $A$ 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: B.
View full solution →if $O$ is the origin and $Q$ is a variable point on $y^2 = x.$ Find the locus of the mid$-$point of $OQ.$
View full solution →Write down all possible subsets of A = (1, {2, 3}).
Find the equations to the circles which pass through the origin and cut off equal chords of length $'a\ '$ from the straight lines $y = x$ and $y = -x.$
View full solution →Find equation of circle whose end points of its diameter are $(-2, 3)$ and $(0, -1).$
View full solution →Evaluate $\lim _{x \rightarrow 0} \frac{e^{k x}-1}{x}$.
View full solution →If $u=\{1,2,3,4,5,6,7,8,9,10,12,24\}$
$A=\{x: x$ is prime and $x \leq 10\}$
$B=\{x: x$ is a factor of $24\}$
Verify the following result
$i. A - B = A \cap B^{\prime}$
$ii. (A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$
$iii. (A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$
View full solution →$A=\{x: x$ is prime and $x \leq 10\}$
$B=\{x: x$ is a factor of $24\}$
Verify the following result
$i. A - B = A \cap B^{\prime}$
$ii. (A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}$
$iii. (A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$
Evaluate $\left[\frac{1}{1-4 i}-\frac{2}{1+i}\right]\left[\frac{3-4 i}{5+i}\right]$ to the standard form.
View full solution →Express $(1-2 i)^{-3}$ in the form of $(a+i b)$.
View full solution →Find the expansion of $\left(3 x^2-2 a x+3 a^2\right)^3$ using binomial theorem.
View full solution →Find n , if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of $\left(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}}\right)^n$ is $\sqrt{6}: 1$
View full solution →$24 \ 3 \ 32 \ 1 $ A state cricket authority has to choose a team of $11$ members, to do it so the authority asks $2$ coaches of a government academy to select the team members that have experience as well as the best performers in last $15$ matches. They can make up a team of $11$ cricketers amongst $15$ possible candidates. In how many ways can the final eleven be selected from $15$ cricket players if:
$i$. Two of them being leg spinners, in how many ways can be the final eleven be selected from $15$ cricket players if one and only one leg spinner must be included? $(1)$
$ii$. If there are $6$ bowlers, $3$ wicketkeepers, and $6$ batsmen in all. In how many ways can be the final eleven be selected from $15$ cricket players if $4$ bowlers, $2$ wicketkeepers and $5$ batsmen are included. $(1)$
$iii$. In how many ways can be the final eleven be selected from $15$ cricket players if there is no restriction? $(2)$
OR
In how many ways can be the final eleven be selected from $15$ cricket players if one particular player must be included. $(2)$
View full solution →$i$. Two of them being leg spinners, in how many ways can be the final eleven be selected from $15$ cricket players if one and only one leg spinner must be included? $(1)$
$ii$. If there are $6$ bowlers, $3$ wicketkeepers, and $6$ batsmen in all. In how many ways can be the final eleven be selected from $15$ cricket players if $4$ bowlers, $2$ wicketkeepers and $5$ batsmen are included. $(1)$
$iii$. In how many ways can be the final eleven be selected from $15$ cricket players if there is no restriction? $(2)$
OR
In how many ways can be the final eleven be selected from $15$ cricket players if one particular player must be included. $(2)$
Consider the data
$i.$ Find the standard deviation. $(1)$
$ii.$ Find the variance.$ (1)$
$iii$. Find the mean. $(2)$
$OR$
Write the formula of variance? $(2)$
View full solution →| $x_i$ | $4$ | $8$ | $11$ | $17$ | $20$ | $24$ | $32$ |
| $f _{ i }$ | $3$ | $5$ | $9$ | $5$ | $4$ | $3$ | $1$ |
$ii.$ Find the variance.$ (1)$
$iii$. Find the mean. $(2)$
$OR$
Write the formula of variance? $(2)$
A satellite dish has a shape called a paraboloid, where each cross section is parabola. Since radio signals $($parallel to axis$)$ will bounce off the surface of the dish to the focus, the receiver should be placed at the focus. The dish is $12$ ft across, and $4.5$ ft deep at the vertex
$i$. Name the type of curve given in the above paragraph and find the equation of curve? $(1)$
$ii.$ Find the equation of parabola whose vertex is $(3, 4)$ and focus is $(5, 4). (1)$
$iii.$ Find the equation of parabola Vertex $(0, 0)$ passing through $(2, 3)$ and axis is along $x-$ axis. and also find the length of latus rectum. $(2)$
OR
$iv$. Find focus, length of latus rectum and equation of directrix of the parabola $x^2=8 y. (2)$
View full solution →$i$. Name the type of curve given in the above paragraph and find the equation of curve? $(1)$
$ii.$ Find the equation of parabola whose vertex is $(3, 4)$ and focus is $(5, 4). (1)$
$iii.$ Find the equation of parabola Vertex $(0, 0)$ passing through $(2, 3)$ and axis is along $x-$ axis. and also find the length of latus rectum. $(2)$
OR
$iv$. Find focus, length of latus rectum and equation of directrix of the parabola $x^2=8 y. (2)$
Prove the following identity: $\cos ^3 2 x+3 \cos 2 x=4\left(\cos ^6 x-\sin ^6 x\right)$.
View full solution →Prove that: $\tan 20^{\circ} \tan 30^{\circ} \tan 40^{\circ} \tan 80^{\circ}=1$
View full solution →Find the sum of the following series up to n terms:
$i. 5 + 55 + 555 + ……$
$ii. 6 + .66 + .666 + …..$
View full solution →$i. 5 + 55 + 555 + ……$
$ii. 6 + .66 + .666 + …..$
Differentiate $\frac{\cos x}{x}$ from first principle.
View full solution →Differentiate If $y=\sqrt{\frac{\sec x-\tan x}{\sec x+\tan x}}$ show that $\frac{d y}{d x}=\sec x(\tan x+\sec x)$
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