JEE Maths
Sample Paper 3 | JEE Maths
SECTION-A
(One Options Correct Type)
This section contains 20 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE option is correct.
Question 1:
is equal to
(a) 
(b) 
(c) 
(d) 
Question 2:
If 
and 
are linearly independent vectors and 
, then
(a) 
(b) 
(c) 
(d) 
Question 3:
If the circles 
and 
intersect orthogonally, then k is
(a) 
(b) 
(c) 
(d)
Question 4:
The vertex of the parabola whose parametric equation is 
, 
, 
, is
(a) 
(b) 
(c) 
(d) 
Question 5:
If 
then k is equal to
(a) 1
(b) – 1
(c) 2
(d) – 2.
Question 6:
Find the remainder, when 
is divided by 25
(a) 7
(b) 14
(c) 18
(d) 21
Question 7:
The function g(x) = 
has a local minimum at
(a) x = 2
(b) x = 
(c) x = 0
(d) x = 1
Question 8:
The set of points where f(x) = 
is differentiable, is
(a) 
(b) 
(c) 
(d) 
Question 9:
If f(x) is differentiable and strictly increasing function, then the value of 
is
(a) 1
(b) 0
(c) 
(d) 2
Question 10:
,if
(a) 
(b) 
(c) 
(d) a = 8
Question 11:
The value of 
is
(a) 
(b) 
(c) 
(d) 
Question 12:
If y = 
has its extremum values at x = 
and x = 2, then 
is
(a) 
(b) 
(c) 3
(d) 1
Question 13:
If the normal at 
on the parabola 
meets the parabola again at the point 
,then the value of 
is
(a) 
(b) 
(c) 
(d)
Question 14:
Area bounded by the curve 
and -axis between 
and 
is
(a) 
(b) 
(c) 
(d) 
Question 15:
If y(t) is a solution of 
and y(0) = , then y(1) is equal to
(a) 
(b) 
(c) 1
(d)
Question 16:
Period of 
is
(a) 
(b) 
(c) 2
(d) 
Question 17:
If A = 
, then A is
(a) invertible only if t =
(b) invertible only if t = 
(c) not invertible for any t 
R
(d) invertible for all t R
Question 18:
If 
are in HP, then 
is equal to
(a) 
(b) 
(c) 
(d) 
Question 19:
Let X and Y be two arbitrary, 3
3 non-zero, skew-symmetric matrices and Z be an arbitrary 3 3, non-zero, symmetric matrix. Then which of the following matrices is skew-symmetric matrix ?
(a) 
(b) 
(c) 
(d) 
Question 20:
A speaks truth in 80% cases and B in 75% cases. What is the probability that they contradict each other in stating the same fact ?
(a) 
(b) 
(c) 
(d) 
SECTION - B
(Numerical Answer Type)
This section contains 10 questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to the second decimal place).
Question 1:
The number of 4 letter words that can be formed from the letters of the word CALCUTTA, are ____________ .
Question 2:
The area of the triangle formed by -axis, the straight line L passing through 
and 
and the straight line perpendicular to the line L and passing through 
(a) 
(b) 
(c) 
(d) 
Question 3:
Let f: R
R be a function defined by f(x) = 
. If the function g(x) = f(f(f(x))) + f(f(x)), then the greatest integer less than or equal to g(1) is __________ .
Question 4:
If the equation of normal to the circle 
at (1, 1) is ax + by = c, then (a + b + c) is __________ .
Question 5:
The area enclosed between the curves 
and 
in the interval 
is (in square units) __________ .
Question 6:
If the mean deviation about the median of the numbers a, 2a, ……., 50a is 50, then |a| is __________ .
Question 7:
If the sum to n terms of the series 
f(0) is __________ .
Question 8:
The number of four digit numbers that can be formed with only even digits without repetition, is __________ .
Question 9:
If z is a complex number such that |z| 
2, then the minimum value of 
is ___________ .
Question 10:
The product of the roots of the equation 
is __________ .
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