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## 2016 JEE Maths Solved paper

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Title: 2016 JEE Maths Solved paper

1
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Previous Year Paper Mathematics - 2016
2
Mathematics JEE 2016
Exam Year 2016
Study, Assignments, Solved Previous Year Papers .
• Multiple Choice Questions
• The sum of all real values of x satisfying the
equation is
• 3
• -4
• 6
• 5
• If all the words (with or without meaning) having
?ve letters, formed using the letters of the word
SMALL and arranged as in a dictionary then the
position of the word SMALL is
• 46th
• 59th 52nd 58th

is 28, then the sum of the coe?cients of all
3. If the number of terms in the expansion of the
terms in this expansion is 64 2187 243 729 Answer
• If the 2nd, 5th and 9th terms of a non-constant
A.P. are in G.P., then the common ratio of this
G.P. is
• 8/5
• 4/3
• 1
• 7/4
• If the sum of the ?rst ten terms of the series,

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3
Mathematics JEE 2016
Exam Year 2016
Study, Assignments, Solved Previous Year Papers .
• is 16/5 m, the m is equal to
• 102
• 101
• 100
• 99
• Let then log p is equal to 2
• 1
• 1/2
• 1/4
• A man is walking towards a vertical pillar in a
straight path, at a uniform speed. At a certain
point A on the
• path, he observes that the angle of elevation of
the top of the pillar is 30o. After walking for
10 minutes from A in the same direction, at a
point B, he observes that the angle of elevation
of the top of the pillar is
• 60o. Then the time taken (in minutes) by him,
from B to reach the pillar, is 6
• 10
• 20
• 5
• If

is an empty set contains exactly one element.
contains exactly two elements. contains more
is purely imaginary is
9. A value of ? for which p/3 p/6
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Mathematics JEE 2016
Exam Year 2016
Study, Assignments, Solved Previous Year Papers .
• If A and A adj A AAT, then 5a b is equal to
• -1
• 5
• 4
• 5
• The system of linear equations x?y-z0
?x-y-z0 xy-?z0 has a non-trivial solution for
in?nitely many values of ?.
• exactly one value of ?. exactly two values of ?.
exactly three values of ?.
• For x e R, f (x)log2-sinx and g(x)f(f(x)),
then g is not di?erentiable at x0
g'(0)cos(log2)
• g'(0)-cos(log2)
• g is di?erentiable at x0 and g'(0)-sin(log2)

. A normal to y f (x) at x p/6 also passes
through the
• Consider f(x) tan-1
• point
• (0,0)
• (0, 2p/3)
• (p/6 ,0)
• (p/4, 0)
• A wire of length 2 units is cut into two parts
which are bent respectively to form a square of
sidex units and a circle of radiusr units. If
the sum of the areas of the square and the circle
so formed is minimum, then

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Mathematics JEE 2016
Exam Year 2016
Study, Assignments, Solved Previous Year Papers .
is equal to
15.
18/e4 27/e2 9/e2 3 log 3-2 Answer
is
16. The area (in sq. units) of the region
• If a curve yf(x) passes through the point (1,
-1) and satis?es the di?erential equation,
y(1xy) dxx dy, then f(-1/2) is equal to
• -2/5
• -4/5
• 2/5
• 4/5
• Let two fair six-faced dice A and B be thrown
simultaneously. If E1 is the event that die A
shows up four, E2 is the event that die B shows
up two and E3 is the event that the sum of
numbers on both dice is odd, then which of the
following statements is NOT true?
• E1 and E2 are independent
• E2 and E3 are independent.

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Mathematics JEE 2016
Exam Year 2016
Study, Assignments, Solved Previous Year Papers .
E1 and E3 are independent. E1, E2 and E3 are
independent. Answer 19. If 0xlt2p, then the
number of real values of x, which satisfy the
equation cosxcos2xcos3xcos4x0,
is 3 5 7 9 Answer
is equal to
20. The integral
• Two sides of a rhombus are along the lines,
x-y10 and 7x-y-50. If its diagonals intersect
at (-1, -2), then which one of the following is
a vertex of this rhombus?
• (-3, -9)
• (-3, -8)
• (1/3, -8/3)
• (-10/3, -7/3)
• The centres of those circles which touch the
circle, x2y2-8x-8y-40, externally and also
touch the x- axis, lie on
• a circle
• an ellipse which is not a circle a hyperbola.
• a parabola.

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Mathematics JEE 2016
Exam Year 2016
Study, Assignments, Solved Previous Year Papers .
23. If one of the diameters of the circle, given
by the equation, x2y2-4x6y-120, is a chord of
a circle S, whose centre is at (-3, 2), then the
• 5
• 10
• Let P be the point on the parabola, y28x which
is at a minimum distance from the centre C of the
circle, x2(y6)21. Then the equation of the
circle, passing through C and having its centre
at P is
• x2y2-4x8y120 x2y2-x4y-120 x2y2- 4 x
2y-240 x2y2-4x9y180
• The eccentricity of the hyperbola whose length of
the latus rectum is equal to 8 and the length of
its conjugate axis is equal to half of the
distance between its foci, is
• 4/3

Answer 26. The distance of the point (1, -5, 9)
from the plane x-yz5 measured along the line
xyz is
lies in the plane lx my -z 9, then l2 m2 is
equal to
27. If the line
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8
Mathematics JEE 2016
Exam Year 2016
Study, Assignments, Solved Previous Year Papers .
be three unit vectors such that
then the angle
28. Let
is
between 3p/4 p/2 2p/3 5p/6 Answer
• If the standard deviation of the numbers 2, 3, a
and 11 is 3.5, then which of the following is
true?
• 3a2-26a550
• 3a2-32a840
• 3a2-34a910
• 3a2-23a440