In the expansion of $(x+a)^n$, if the sum of odd terms be $P$ and the sum of even terms be $Q$, then $4 P Q=$ ?
- A$(x+a)^n=(x-a)^n$
- B$(x+a)^{2 n}-(x-a)^{2 n}$
- C$(x+a)^n+(x-a)^n$
- D$(x+a)^{2 n}+(x-a)^{2 n}$
Question types
Model Paper 8 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→022 Marks Questions
7 Q→033 Marks Question
9 Q→045 Marks Questions
6 Q→05Assertion (A) & Reason (B) MCQ
2 Q→06Case study (4 Marks)
3 Q→Sample Questions
Model Paper 8 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The value of $\left({ }^7 C_0+{ }^7 C_1\right)+\left({ }^7 C_1+{ }^7 C_2\right)+\ldots .+\left({ }^7 C_6+{ }^7 C_7\right)$ is
- A$2^8-2$
- B$2^8=1$
- C$2^7-1$
- D$2^8$
$\lim _{x \rightarrow \pi} \frac{\sin x}{x-\pi}$ is equal to
- A1
- B-1
- C2
- D-2
If $x$ is a real number and $|x|<3$, then
- A- 3 < x < 3
- B$x \geq-3$
- C$x \geq 3$
- D$-3 \leq x \leq 3$
If $\left(1-x+x^2\right)^n=a_0+a_1 x+a_2 x^2+\ldots+a_{2 n} x^{2 n}$, then $a_0+a_2+a_4+\ldots+a_{2 n}$ equals.
- A$3^n+\frac{1}{2}$
- B$\frac{3^n+1}{2}$
- C$\frac{3^n-1}{2}$
- D$\frac{1-3^n}{2}$
In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?
Check whether the probabilities $P ( A )$ and $P ( B )$ are consistently defined $P ( A )=0.5, P ( B )=0.4, P(A \cup B)=0.8$
View full solution →Find the length of perpendicular from the origin to the lines 7x + 24y = 50.
Evaluate $\lim _{x \rightarrow 1} \frac{x^3-1}{x-1}$
View full solution →Find the domain and the range of the real function: $f ( x )=\frac{|x-4|}{x-4}$
View full solution →he sum of three numbers a, b, c in A.P. is 18. If a and b are each increased by 4 and c is increased by 36, the new numbers form a G.P. Find a, b, c.
Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{2 x}{\sqrt{a+x}-\sqrt{a-x}}$.
View full solution →Are the $E=\left\{x: x \in Z, x^2 \leq 4\right\}$ and $F=\left\{x: x \in Z, x^2=4\right\}$ pairs of equal set?
View full solution →If A.M. and G.M. of roots of a quadratic equation are 8 and 5 respectively then obtain the quadratic equation.
Differentiate $e ^{ ax + b }$ from first principle.
View full solution →Fine the lengths major and minor axes, coordinates of the vertices, coordinates of the foci, eccentricity, and length of the latus rectum of the ellipse $25 x^2+4 y^2=100$.
View full solution →The mean and standard deviation of 100 observations were calculated as 40 and 5.1, respectively by a student who took by mistake 50 instead of 40 for one observation. What are the correct mean and standard deviation?
If $A + B + C =\pi$, prove that $\frac{\sin 2 A+\sin 2 B+\sin 2 C}{\sin A+\sin B+\sin C}=8 \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$
View full solution →Prove that: $\cot x+\cot \left(\frac{\pi}{3}+x\right)+\cot \left(\frac{2 \pi}{3}+x\right)=3 \cot 3 x$
View full solution →Assertion (A): The collection of all natural numbers less than 100' is a set.
Reason (R): A set is a well-defined collection of the distinct objects.
Reason (R): A set is a well-defined collection of the distinct objects.
- 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.
- 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.
Two complex numbers $Z _1= a + ib$ and $Z _2= c + id$ are said to be equal, if $a = c$ and $b = d$.
i. If $(x+i y)(2-3 i)=4+i$ then find the value of $(x, y)$.
ii. If $\frac{(1+i)^2}{2-i}=x+i y$, then find the value of $x+y$. (1)
iii. If $\left(\frac{1-i}{1+i}\right)^{100}=a+i b$, then find the values of $a$ and $b$. (2)
OR
If $(a-2,2 b+1)=(b-1, a+2)$, then find the real values of $a$ and $b$. (2)
View full solution →i. If $(x+i y)(2-3 i)=4+i$ then find the value of $(x, y)$.
ii. If $\frac{(1+i)^2}{2-i}=x+i y$, then find the value of $x+y$. (1)
iii. If $\left(\frac{1-i}{1+i}\right)^{100}=a+i b$, then find the values of $a$ and $b$. (2)
OR
If $(a-2,2 b+1)=(b-1, a+2)$, then find the real values of $a$ and $b$. (2)
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