Mathematics · JEE

Binomial Theorem and Its Simple Applications Mock Test for JEE

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Q1MathsUnit 5: Binomial Theorem and Its Simple Applications

The coefficient of

x^{9}

in the expansion of

\left(x^{3}+\frac{1}{2^{t}}\right)^{11},

where

t=\log _{\sqrt{2}}\left(x^{\frac{3}{2}}\right)

Q2MathsUnit 5: Binomial Theorem and Its Simple Applications

Sum of coefficients in the expeansion of

(a+b+c)^{8}

Q3MathsUnit 5: Binomial Theorem and Its Simple Applications

If it is known that the third term of the binomial expansion

\left(x+x^{\log _{10} x}\right)^{3}

10^{6}

then

x

is equal to

Q4MathsUnit 5: Binomial Theorem and Its Simple Applications

If the middle term in the expansion of

\left(x^{2}+\frac{1}{x}\right)^{n}

924 x^{6},

then

n=

Q5MathsUnit 5: Binomial Theorem and Its Simple Applications

Evaluate the following

(0.98)^{2}

Q6MathsUnit 5: Binomial Theorem and Its Simple Applications

The coeffcient of

x^{10}

in the expansion of

(1+x)^{2}\left(1+x^{2}\right)^{3}\left(1+x^{3}\right)^{4}

is equal to

Q7MathsUnit 5: Binomial Theorem and Its Simple Applications

The number of terms with integral coefficients in the expansion of

\left(7^{1 / 3}+5^{1 / 2} \cdot x\right)^{600}

Q8MathsUnit 5: Binomial Theorem and Its Simple Applications

\forall n \in N, 3^{3 n}-26^{n}

is divisible by

Q9MathsUnit 5: Binomial Theorem and Its Simple Applications

Using identities, evaluate

998^{2}

Q10MathsUnit 5: Binomial Theorem and Its Simple Applications

Coefficient of

\boldsymbol{x}^{\mathbf{5 0}}

(x>0),

(1+x)^{1000}+2 x(1+

\boldsymbol{x})^{999}+\mathbf{3} \boldsymbol{x}^{2}(\mathbf{1}+\boldsymbol{x})^{998}+\ldots

Q11MathsUnit 5: Binomial Theorem and Its Simple Applications

The number of dissimilar terms in the expansion of

\left(1-3 x+3 x^{2}-x^{3}\right)^{20}

Q12MathsUnit 5: Binomial Theorem and Its Simple Applications

Using the formula for squaring a binomial the value of

(999)^{2}

is:

Q13MathsUnit 5: Binomial Theorem and Its Simple Applications

For every positive integer

n, \frac{n^{7}}{7}+\frac{n^{5}}{5}+

\frac{2 n^{3}}{3}-\frac{n}{105}

Q14MathsUnit 5: Binomial Theorem and Its Simple Applications

Evaluate using expansion of

(a+b)^{2}

(a-b)^{2}:

(9.4)^{2}

Q15MathsUnit 5: Binomial Theorem and Its Simple Applications

The total number of terms in the expansion of

(x+y)^{50}+(x-y)^{50}

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