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JEE Mathematics Solved Question Paper 2016

Multiple Choice Questions

11.

The small extremely fast RAM's are called as

cache
heaps
accumulators
stacks

12.

The value of i² + i⁴ + i⁶ + ... (2n + 1) terms is

13.

The argument of the complex number is

45°
60°
120°
150°

14.

If be the AM of a and b, then n is equal to

- 1
0
1
None of these

15.

x^1/2 . x^1/4 . x^1/8 ... $\infty$ equal to

0
1
$\infty$
x

16.

If the roots of the equation x² + px + q = 0 differ by 1, then

p² = 4q + 1
p² = 4q
p² = 4q - 1
p² = - 4q

17.

If a = 2, b = 3 and c = 5in $∆$ BC, then $∠$ C is to equal

$\frac{π}{2}$
$\frac{π}{4}$
$\frac{π}{6}$
None of these

18.

The centroid of the triangle formed by the lines x + y = 1, 2x + 3y = 6 and 4x - y = - 4 lies in the quadrant

19.
If an equilateral triangle is inscribed in the circle x² + y² = a², the lenth of its each side is

$\sqrt{2} a$

$\sqrt{3} a$

$\frac{\sqrt{3}}{2} a$

$\frac{1}{\sqrt{3}} a$

$\sqrt{3} a$

$Given equation of the circle is x^{2} + y^{2} = a^{2} where, radius = a$

let ABC be the inscribed equnateral triangle and length of its each sides be l,

$Area of ∆ ABC = \frac{\sqrt{3}}{4} l^{2} Also, OD = \sqrt{a^{2} - \frac{l^{2}}{4}} [from ∆ ODB] ∴ Area of ∆ OBC = \frac{1}{2} \times l \times \sqrt{a^{2} - \frac{l^{2}}{4}} Now, area of ∆ ABC = 3 \times Area of ∆ OBC \Rightarrow \frac{\sqrt{3}}{4} l^{2} = 3 \times \frac{l}{2} \sqrt{a^{2} - \frac{l^{2}}{4}} \Rightarrow \sqrt{3} l = 3 \sqrt{4 a^{2} - l^{2}} \Rightarrow 3 l^{2} = 9 (4 a^{2} - l^{2}) \Rightarrow l^{2} = 12 a^{2} - 3 l^{2} \Rightarrow 4 l^{2} = 12 a^{2} \Rightarrow l^{2} = 3 a^{2} \Rightarrow l = \sqrt{3} a$