AIEEE Maths Papers

Question

In a triangle ABC, if A, B, C are acute angles, then $\cot A. \cot B. \cot C$ is

Possible Answers

Selected	Possible Answer
	not greater than $\frac {1}{3 \sqrt {3}}$
	greater than $\frac {1}{3 \sqrt {3}}$
	greater than $2 \sqrt {3}$
	less than $2 \sqrt {3}$

Question

If f (x) is a function satisfying $f (x + y)= f(x) f(y) \forall x, y \in N$ , such that f(1)=3 and $\overset{n}{\underset{x=1}{\sum}}f(x)=120.$ Then the value of n is

Possible Answers

Selected	Possible Answer
	5
	4
	6
	none

Question

If $f(x)=\cos [\pi^2]x+\cos[-\pi^2]x$ where [x] denotes greatest integer function

Possible Answers

Selected	Possible Answer
	$f(\pi/4)=2$
	$f(\pi/2)=-1$
	$f(-\pi)=3$
	$f(\pi)=1$

Question

A particle moves in a straight line with a velocity given by $\frac {dx}{dt}=x+1$ . (x is the distance described). The time taken by the particle to traverse a distance of 99 meters is

Possible Answers

Selected	Possible Answer
	$\log_{10}e$
	$\frac {1}{2}\log_{10}e$
	$2 \log_{10}e$
	$2\log_e10$

Question

The value of b and c for which the identity f(x+1)-f(x)=8x+3 is satisfied, where f(x)=bx^2+cx+d are

Possible Answers

Selected	Possible Answer
	none
	b = 4, c = -1
	b = -1, c = 4
	b = 2, c = 1

Question

If $\overrightarrow {a}, \overrightarrow {b}, \overrightarrow {c}$ are non-coplanar unit vectors such that $\overrightarrow {a}* (\overrightarrow {b} * \overrightarrow {c})=$ $\frac {\overrightarrow {b} + \overrightarrow {c}}{\sqrt {2}}$ . Then the angle between $\overrightarrow {a}$ and $\overrightarrow {b}$ is

Possible Answers