IIT-JEE 2005 Screening | Mathematical Induction and Binomial Theorem Question 8 | Mathematics

1

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)

+2

-0.5

The value of $$$\left( {\matrix{ {30} \cr 0 \cr } } \right)\left( {\matrix{ {30} \cr {10} \cr } } \right) - \left( {\matrix{ {30} \cr 1 \cr } } \right)\left( {\matrix{ {30} \cr {11} \cr } } \right) + \left( {\matrix{ {30} \cr 2 \cr } } \right)\left( {\matrix{ {30} \cr {12} \cr } } \right)....... + \left( {\matrix{ {30} \cr {20} \cr } } \right)\left( {\matrix{ {30} \cr {30} \cr } } \right)$$$
is where $$\left( {\matrix{ n \cr r \cr } } \right) = {}^n{C_r}$$

A

$$\left( {\matrix{ {30} \cr {10} \cr } } \right)$$

B

$$\left( {\matrix{ {30} \cr {15} \cr } } \right)$$

C

$$\left( {\matrix{ {60} \cr {30} \cr } } \right)$$

D

$$\left( {\matrix{ {31} \cr {10} \cr } } \right)$$

2

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

+2

-0.5

If $${}^{n - 1}{C_r} = \left( {{k^2} - 3} \right)\,{}^n{C_{r + 1,}}$$ then $$k \in $$

A

$$\left( { - \infty , - 2} \right)$$

B

$$\left[ {2,\infty } \right)$$

C

$$\left[ { - \sqrt 3 ,\sqrt 3 } \right]$$

D

$$\left( {\sqrt 3 ,2} \right]$$

3

IIT-JEE 2003 Screening

MCQ (Single Correct Answer)

+2

-0.5

Coefficient of $${t^{24}}$$ in $${\left( {1 + {t^2}} \right)^{12}}\left( {1 + {t^{12}}} \right)\left( {1 + {t^{24}}} \right)$$ is

A

$${}^{12}{C_6} + 3$$

B

$${}^{12}{C_6} + 1$$

C

$${}^{12}{C_6}$$

D

$${}^{12}{C_6} + 2$$

4

IIT-JEE 2002 Screening

MCQ (Single Correct Answer)

+2

-0.5

The sum $$\sum\limits_{i = 0}^m {\left( {\matrix{ {10} \cr i \cr } } \right)\left( {\matrix{ {20} \cr {m - i} \cr } } \right),\,\left( {where\left( {\matrix{ p \cr q \cr } } \right) = 0\,\,if\,\,p < q} \right)} $$ is maximum when $$m$$ is

A

5

B

10

C

15

D

20