AIEEE Mathematics

Question

If $5^x+(2x\sqrt{3})^{2x}\underline {>} 13x$ then the solution of the set for x is

Possible Answers

Selected	Possible Answer
	$[2, \infty)$
	{2}
	$(-\infty,2]$
	[0, 2]

Question

Let OP.OQ = 1, Let O, P, Q be three points. O and Q represents the complex number 0 and z then P represents

Possible Answers

Selected	Possible Answer
	1/z
	none of these
	$1/\bar {z}$
	$\bar {z}$

Question

A shopkeeper sells three varieties of perfumes and he has a large number of bottles of the same size of each variety in his stock. There are 5 places in a row in his showcase. The number of different ways of displaying the three varieties of perfumes in the show case is

Possible Answers

Selected	Possible Answer
	6
	150
	none
	50

Question

Let $f_n(\emptyset)=$ < $\tan \frac{\emptyset}{2}C1+\sec \emptyset)(1 + \sec 2\emptyset)(1 + \sec 4\emptyset)\cdots(1 + \sec 2^n\emptyset)$ , then

Possible Answers

Selected	Possible Answer
	$f_3(\pi/32)=-1$
	$f_2(\pi/16)=1$
	$f_4(\pi/64)=1$
	$f_5(\pi/128)=1$

Question

The most general solution of $2^{\sin x}+2^{\cos x}=2^{1-\frac{1}{\sqrt{2}}}$ are

Possible Answers

Selected	Possible Answer
	$n \pi+(-1)^n\frac{\pi}{4}$
	$n \pi-\frac{\pi}{4}$
	$2n \pi+\frac{\pi}{4}$
	$n \pi+\frac{\pi}{4}$

Question

Let [x] denotes greatest integer $\underline < x.$ Then
$Lt \frac {1}{n\rightarrow \infty n^3}\{[1^2x]+[2^2x]+[3^2x]+\cdots[n^2x]\}$ equal to

Possible Answers

Selected	Possible Answer
	x/2
	x/3
	0
	x/4

Question

In an obtuse angled triangle, the obtuse angle is $3\pi/4$ and the other two angles are equal to two values of $\emptyset$ satisfying $a \tan \emptyset + b \sec \emptyset = c$

where $|b| \underline < \sqrt{a^2+c^2}$ then a^2-c^2 is equal to

Possible Answers

Selected	Possible Answer
	a/c
	none
	2ac
	ac

Question

The value of p for which the functions

$f(x)=\frac {(4^x-1)^3}{\sin (x/p) \log \{1+(x^2/3)\}} \qquad x \not=0$

$12(\log 4)^3 \qquad x=0$

may be continuous at x= 0 is

Possible Answers

Selected	Possible Answer
	1
	2
	none
	3

Question

Let f(x) =x^n , being a non-negative integer. The value of n which in equality

f' (a+b)=f'(a)+f'(b) is valid for all a, b >0 is

Possible Answers

Selected	Possible Answer
	5
	2
	4
	1

Question

Consider a circle with its centre lying on the focus of the parabola y^2 = 2 px such that it touch the directive of the parabola. Then a point of intersection of the circle and the parabola is

Possible Answers