JEE MAIN 2016 Previous Year Questions (PYQs) – Page 1 of 7
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For $x \in \mathbb{R}$,
$f(x) = |\log 2 - \sin x|$
and
$g(x) = f(f(x))$,
then:
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Solution
Let
$ p = \displaystyle \lim_{x \to 0^{+}} \left(1 + \tan^{2}\sqrt{x}\right)^{\tfrac{1}{x}} $
then $\log p$ is equal to:
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Solution
A value of $\theta$ for which
$ \displaystyle \frac{2 + 3i \sin \theta}{1 - 2i,} \cdot \frac{1}{\sin \theta} $
is purely imaginary, is:
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Solution
If the standard deviation of the numbers $2, 3, a,$ and $11$ is $3.5$,
then which of the following is true?
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Solution
Let two fair six-faced dice $A$ and $B$ be thrown simultaneously.
If $E_{1}$ is the event that die $A$ shows up four,
$E_{2}$ is the event that die $B$ shows up two,
and $E_{3}$ is the event that the sum of numbers on both dice is odd,
then which of the following statements is NOT true?
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Solution
If a curve $y = f(x)$ passes through the point $(1,-1)$ and satisfies the differential equation
$ y(1+xy),dx = x,dy $,
then $ f\left(-\dfrac{1}{2}\right) $ is equal to:
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Solution
The area (in sq. units) of the region
$ {(x,y) : y^{2} \ge 2x \ \text{and} \ x^{2} + y^{2} \le 4x,\ x \ge 0,\ y \ge 0} $
is:
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Solution
The integral
$ \displaystyle \int \frac{2x^{12} + 5x^{9}}{(x^{5} + x^{2} + 1)^{3}}, dx $
is equal to:
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Solution
The system of linear equations
$ x + \lambda y - z = 0 $
$ \lambda x - y - z = 0 $
$ x + y - \lambda z = 0 $
has a non-trivial solution for:
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Solution
A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $= x$ units and a circle of radius $= r$ units.
If the sum of the areas of the square and the circle so formed is minimum, then:
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Solution
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