Practising JEE Main mock tests is crucial for effective exam preparation. These tests help students understand the exam pattern, improve time management, and identify strengths and weaknesses. Regular practice boosts confidence, enhances problem-solving speed, and ensures better performance in the actual exam.

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JEE Main Binomial Theorem Practice Questions with Solutions

The Mathematics section is a very important section of the JEE Main entrance exam, and the Binomial Theorem are an essential part of Mathematics. The JEE Main Binomial Theorem Practice Test is a valuable resource for all JEE Main aspirants to learn about the main concepts of the Binomial Theorem and enhance their problem-solving abilities. The JEE Main Binomial Theorem Practice Questions with Solutions have a variety of questions from this chapter for students to practice and strengthen their mathematics section for the JEE Main entrance test.

About 2 to 3 questions may appear from the Binomial Theorem on the JEE Main question paper. Usually, the question will be in the form of multiple choice questions as well as integer type questions, testing both your conceptual knowledge and numerical abilities. JEE Main is a highly competitive entrance exam for all engineering aspirants. Therefore, it is essential for candidates to attempt these practice tests at least once a week to develop knowledge and precision of the topic.

Around 15 to 20 questions are available from this chapter in the JEE Main Binomial Theorem Practice Questions with Solutions, covering all the essential topics. The important topics of this chapter, from which questions may appear in the exam, are General Term in the Expansion, Properties of Binomial Coefficients, Middle Term, Simple Applications, Special Results and Identities, and Identifying or Manipulating Expressions. The practice tests, containing questions on all these topics along with their detailed solutions, will allow aspirants to understand the basic concepts well by going through the detailed explanations provided.

Practising the JEE Main Binomial Theorem practice questions with solutions on a regular basis will help students to improve their accuracy and manage their time better during the examination. It will also allow them to memorise formulas, understand concepts, and gain confidence in solving questions from this topic with ease in the JEE Main exam.

JEE Main Mathematics Binomial Theorem Practice Questions

Chemistry Physics

Question 1.

The sum of the coefficient of $x^{2 / 3}$ and $x^{- 2 / 5}$ in the binomial expansion of ${(x^{2 / 3} + \frac{1}{2} x^{- 2 / 5})}^{9}$ is

19/4

69/16

63/16

21/4

Question 2.

The coefficient of $x^{70}$ in $x^{2} (1 + x)^{98} + x^{3} (1 + x)^{97} + x^{4} (1 + x)^{96} + \dots + x^{54} (1 + x)^{46}$ is $^{99} C_{p} -^{46} C_{q}$ . Then a possible value of $p + q$ is :

Question 3.

If the term independent of $x$ in the expansion of ${(\sqrt{a} x^{2} + \frac{1}{2 x^{3}})}^{10}$ is 105 , then $a^{2}$ is equal to :

Question 4.

If the constant term in the expansion of ${(\frac{\sqrt[5]{3}}{x} + \frac{2 x}{\sqrt[3]{5}})}^{12}, x \neq 0$ , is $α \times 2^{8} \times \sqrt[5]{3}$ , then $25 α$ is equal to :

724

742

693

639

Question 5.

If the coefficients of $x^{4}, x^{5}$ and $x^{6}$ in the expansion of $(1 + x)^{n}$ are in the arithmetic progression, then the maximum value of $n$ is:

Question 6.

The sum of all rational terms in the expansion of ${(2^{\frac{1}{5}} + 5^{\frac{1}{3}})}^{15}$ is equal to :

633

6131

3133

931

Question 7.

Let

m

and

n

be the coefficients of seventh and thirteenth terms respectively

in the expansion of

{(\frac{1}{3} x^{\frac{1}{3}} + \frac{1}{2 x^{\frac{2}{3}}})}^{18}

. Then

{(\frac{n}{m})}^{\frac{1}{3}}

is :

\frac{1}{9}

\frac{1}{4}

\frac{4}{9}

\frac{9}{4}

Question 8.

Let $a$ be the sum of all coefficients in the expansion of ${(1 - 2 x + 2 x^{2})}^{2023} {(3 - 4 x^{2} + 2 x^{3})}^{2024}$ and $b = lim_{x \to 0} (\frac{\int_{0}^{x} \frac{\log (1 + t)}{t^{2024} + 1} d t}{x^{2}})$ . If the equation $c x^{2} + d x + e = 0$ and $2 b x^{2} + a x + 4 = 0$ have a common root, where $c, d, e \in R$ , then $d : c :$ e equals

2 : 1 : 4

1 : 1 : 4

1 : 2 : 4

4 : 1 : 4

Question 9.

^{n - 1} C_{r} = (k^{2} - 8)^{n} C_{r + 1}

if and only if :

2 \sqrt{2} < k < 2 \sqrt{3}

2 \sqrt{2} < k \leq 3

2 \sqrt{3} < k < 3 \sqrt{3}

2 \sqrt{3} < k \leq 3 \sqrt{2}

Question 10.

If A denotes the sum of all the coefficients in the expansion of

{(1 - 3 x + 10 x^{2})}^{n}

and B denotes the sum of all the coefficients in the expansion of

{(1 + x^{2})}^{n}

, then :

B = A^{3}

3 A = B

A = 3 B

A = B^{3}

Great Job! continue working on more practice questions?

Question 1.

Let

{(a + b x + c x^{2})}^{10} = \sum_{i = 0}^{20} p_{i} x^{i}, a, b, c \in N

.

If

p_{1} = 20

and

p_{2} = 210

, then

2 (a + b + c)

is equal to :

Question 2.

The coefficient of $x^{5}$ in the expansion of ${(2 x^{3} - \frac{1}{3 x^{2}})}^{5}$ is :

\frac{26}{3}

\frac{80}{9}

Question 3.

Fractional part of the number $\frac{4^{2022}}{15}$ is equal to

\frac{8}{15}

\frac{4}{15}

\frac{1}{15}

\frac{14}{15}

Question 4.

If $\frac{1}{n + 1}^{n} C_{n} + \frac{1}{n}^{n} C_{n - 1} + \dots + \frac{1}{2}^{n} C_{1} +^{n} C_{0} = \frac{1023}{10}$ then $n$ is equal to :

Question 5.

The sum, of the coefficients of the first 50 terms in the binomial expansion of $(1 - x)^{100}$ , is equal to

^{99} C_{49}

^{101} C_{50}

-^{99} C_{49}

-^{101} C_{50}

Question 6.

The sum of the coefficients of three consecutive terms in the binomial expansion of $(1 + x)^{n + 2}$ , which are in the ratio $1 : 3 : 5$ , is equal to :

Question 7.

If the $1011^{th}$ term from the end in the binominal expansion of ${(\frac{4 x}{5} - \frac{5}{2 x})}^{2022}$ is 1024 times $1011^{th}$ R term from the beginning, then $| x |$ is equal to

\frac{5}{16}

Question 8.

Let the number $(22)^{2022} + (2022)^{22}$ leave the remainder $α$ when divided by 3 and $β$ when divided by 7. Then $(α^{2} + β^{2})$ is equal to :

Question 9.

If the coefficients of $x$ and $x^{2}$ in $(1 + x)^{p} (1 - x)^{q}$ are 4 and $-$ 5 respectively, then $2 p + 3 q$ is equal to :

Question 10.

If the coefficient of $x^{7}$ in ${(a x - \frac{1}{b x^{2}})}^{13}$ and the coefficient of $x^{- 5}$ in ${(a x + \frac{1}{b x^{2}})}^{13}$ are equal, then $a^{4} b^{4}$ is equal to :

Great Job! continue working on more practice questions?

JEE Main Binomial Theorem Practice Questions With Solutions