1
IIT-JEE 1998
MCQ (Single Correct Answer)
+2
-0.5
Let $${T_r}$$ be the $${r^{th}}$$ term of an A.P., for $$r=1, 2, 3, ....$$ If for some positive integers $$m$$, $$n$$ we have
$${T_m} = {1 \over n}$$ and $${T_n} = {1 \over m},$$ then $${T_n} = {1 \over m},$$ equals
A
$${1 \over {mn}}$$
B
$${1 \over {mn}} + {1 \over n}$$
C
$$1$$
D
$$0$$
2
IIT-JEE 1998
MCQ (Single Correct Answer)
+2
-0.5
Let $$n$$ be an odd integer. If $$\sin n\theta = \sum\limits_{r = 0}^n {{b_r}{{\sin }^r}\theta ,} $$ for every value of $$\theta ,$$ then
A
$${b_0} = 1,\,b = 3$$
B
$${b_0} = 0,\,{b_1} = n$$
C
$${b_0} = - 1,\,{b_1} = n$$
D
$${b_0} = 0,\,{b_1} = {n^2} - 3n + 3$$
3
IIT-JEE 1998
Subjective
+8
-0
Let $$p$$ be a prime and $$m$$ a positive integer. By mathematical induction on $$m$$, or otherwise, prove that whenever $$r$$ is an integer such that $$p$$ does not divide $$r$$, $$p$$ divides $${}^{np}{C_r},$$

[Hint: You may use the fact that $${\left( {1 + x} \right)^{\left( {m + 1} \right)p}} = {\left( {1 + x} \right)^p}{\left( {1 + x} \right)^{mp}}$$]

4
IIT-JEE 1998
MCQ (More than One Correct Answer)
+2
-0.5
The number of common tangents to the circles $${x^2}\, + \,{y^2} = 4$$ and $${x^2}\, + \,{y^2}\, - 6x\, - 8y = 24$$ is
A
0
B
1
C
3
D
4
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