1
JEE Advanced 2016 Paper 1 Offline
Numerical
+3
-0
Change Language
Let $$m$$ be the smallest positive integer such that the coefficient of $${x^2}$$ in the expansion of $${\left( {1 + x} \right)^2} + {\left( {1 + x} \right)^3} + ........ + {\left( {1 + x} \right)^{49}} + {\left( {1 + mx} \right)^{50}}\,\,$$ is $$\left( {3n + 1} \right)\,{}^{51}{C_3}$$ for some positive integer $$n$$. Then the value of $$n$$ is
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2
JEE Advanced 2016 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language
A debate club consists of 6 girls and 4 boys. A team of 4 members is to be select from this club including the selection of a captain (from among these 4 members ) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is
A
380
B
320
C
260
D
95
3
JEE Advanced 2016 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language
Let $$ - {\pi \over 6} < \theta < - {\pi \over {12}}.$$ Suppose $${\alpha _1}$$ and $${\beta_1}$$ are the roots of the equation $${x^2} - 2x\sec \theta + 1 = 0$$ and $${\alpha _2}$$ and $${\beta _2}$$ are the roots of the equation $${x^2} + 2x\,\tan \theta - 1 = 0.$$ $$If\,{\alpha _1} > {\beta _1}$$ and $${\alpha _2} > {\beta _2},$$ then $${\alpha _1} + {\beta _2}$$ equals
A
$$2\left( {\sec \theta - \tan \theta } \right)$$
B
$$2\,\sec \,\theta $$
C
$$ - 2\tan \theta $$
D
$$0$$
4
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language

Let $$f:(0,\infty ) \to R$$ be a differentiable function such that $$f'(x) = 2 - {{f(x)} \over x}$$ for all $$x \in (0,\infty )$$ and $$f(1) \ne 1$$. Then

A
$$\mathop {\lim }\limits_{x \to {0^ + }} f'\left( {{1 \over x}} \right) = 1$$
B
$$\mathop {\lim }\limits_{x \to {0^ + }} xf\left( {{1 \over x}} \right) = 2$$
C
$$\mathop {\lim }\limits_{x \to {0^ + }} {x^2}f'(x) = 0$$
D
$$\left| {f(x)} \right| \le 2$$ for all $$x \in (0,2)$$
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