1

JEE Main 2021 (Online) 18th March Evening Shift

Numerical

+4

-1

Let $${}^n{C_r}$$ denote the binomial coefficient of x

^{r}in the expansion of (1 + x)^{n}. If $$\sum\limits_{k = 0}^{10} {({2^2} + 3k)} {}^{10}{C_k} = \alpha {.3^{10}} + \beta {.2^{10}},\alpha ,\beta \in R$$, then $$\alpha$$ + $$\beta$$ is equal to ___________.Your input ____

2

JEE Main 2021 (Online) 17th March Evening Shift

Numerical

+4

-1

Let the coefficients of third, fourth and fifth terms in the expansion of $${\left( {x + {a \over {{x^2}}}} \right)^n},x \ne 0$$, be in the ratio 12 : 8 : 3. Then the term independent of x in the expansion, is equal to ___________.

Your input ____

3

JEE Main 2021 (Online) 17th March Morning Shift

Numerical

+4

-1

If (2021)

^{3762}is divided by 17, then the remainder is __________.Your input ____

4

JEE Main 2021 (Online) 16th March Evening Shift

Numerical

+4

-1

Let n be a positive integer. Let

$$A = \sum\limits_{k = 0}^n {{{( - 1)}^k}{}^n{C_k}\left[ {{{\left( {{1 \over 2}} \right)}^k} + {{\left( {{3 \over 4}} \right)}^k} + {{\left( {{7 \over 8}} \right)}^k} + {{\left( {{{15} \over {16}}} \right)}^k} + {{\left( {{{31} \over {32}}} \right)}^k}} \right]} $$. If

$$63A = 1 - {1 \over {{2^{30}}}}$$, then n is equal to _____________.

$$A = \sum\limits_{k = 0}^n {{{( - 1)}^k}{}^n{C_k}\left[ {{{\left( {{1 \over 2}} \right)}^k} + {{\left( {{3 \over 4}} \right)}^k} + {{\left( {{7 \over 8}} \right)}^k} + {{\left( {{{15} \over {16}}} \right)}^k} + {{\left( {{{31} \over {32}}} \right)}^k}} \right]} $$. If

$$63A = 1 - {1 \over {{2^{30}}}}$$, then n is equal to _____________.

Your input ____

Questions Asked from Mathematical Induction and Binomial Theorem (Numerical)

Number in Brackets after Paper Indicates No. of Questions

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