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JEE Mathematics Solved Question Paper 2020

Multiple Choice Questions

A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be :

$If S is the sum of the first 10 terms of the series \tan^{- 1} (\frac{1}{3}) + \tan^{- 1} (\frac{1}{7}) + \tan^{- 1} (\frac{1}{13}) + \tan^{- 1} (\frac{1}{3}) + \tan^{- 1} (\frac{1}{21}) + . . ., then \tan (S) = ?$

$- \frac{6}{5}$
$\frac{5}{11}$
$\frac{5}{6}$
$\frac{10}{11}$

$If 2^{10} + 2^{9} . 3^{1} + 2^{8} . 3^{2} + . . . + 2 . 3^{9} + 3^{10} = 3^{10} = S - 2^{11} Then S = ?$

$3^{11}$
$2 . 3^{11}$
$\frac{3^{11}}{2} + 2^{10}$
$3^{11} - 2^{11}$

If the common tangent to the parabolas, y² = 4x and x² = 4y also touches the circle, x² + y² = c², then c is equal to :

$\frac{1}{\sqrt{2}}$
$\frac{1}{2 \sqrt{2}}$
$\frac{1}{2}$
$\frac{1}{4}$

5.
$If α is the positive root of the equation, p (x) = x^{2} - x - 2 = 0, then \lim_{x \to α} \frac{\sqrt{1 - \cos (p (x))}}{x + α - 4} = ?$

$\frac{3}{2}$

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

$\frac{1}{\sqrt{2}}$

$\frac{1}{2}$

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

$P (x) = 0 x^{2} - x - 2 = 0 (x - 2) (x + 1) = 0 x = 2, - 1 ∴ α = 2 Now \lim_{x \to 2^{+}} \frac{\sqrt{1 - \cos (x^{2} - x - 2)}}{x - 2} \Rightarrow \lim_{x \to 2^{+}} \frac{\sqrt{2 \sin (\frac{x^{2} - x - 2}{2})}}{x - 2} \lim_{x \to 2^{+}} 2 \frac{|\sin (\frac{x^{2} - x - 2}{2})|}{x - 2} \Rightarrow for x \to 2^{+}, \frac{x^{2} - x - 2}{2} \to 0^{+} \lim_{x \to 2^{+}} \frac{\sqrt{2} \sin (\frac{x^{2} - x - 2}{2})}{\sin (\frac{x^{2} - x - 2}{2})} . \frac{(\frac{x^{2} - x - 2}{2})}{x - 2} \Rightarrow \lim_{x \to 2^{+}} \frac{1}{\sqrt{2}} . \frac{(x - 2) (x + 1)}{(x - 2)} = \frac{3}{\sqrt{2}}$

If the co–ordinates of two points A and B are $(\sqrt{7}, 0) and (- \sqrt{7}, 0)$ respectively and P is any point on the conic, 9x² + 16y² = 144, then PA + PB is equal to :

The product of the roots of the equation 9x² – 18|x| + 5 = 0 is

$\frac{25}{81}$
$\frac{5}{27}$
$\frac{25}{9}$
$\frac{5}{9}$

If the point P on the curve, 4x² + 5y² = 20 is farthest from the point Q(0, – 4), then PQ² is equal to :

If (a, b, c) is the image of the point (1, 2, – 3) in the line,

$\frac{x + 1}{2} = \frac{y - 3}{- 2} = \frac{z}{- 1}$ , then a + b + c is equal to :

10.

If the four complex numbers $z, z, z - 2 Re (z) and z - 2 Re (z)$ represent the vertices of a square of side 4 units in the Argand plane, then |z| is equal to :