JEE Maths
Sample Paper 1 | 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:
Consider the line L given by the equation 
. Let Q be the mirror image of the point R(1,6,3) with respect to L. Let a line 
be such that it passes through Q and P(4,2,8). Then which of the following points is on the line ?
(a) (1,0,3)
(b) (7,4,9)
(c) (2,0,4)
(d) (2,1,-
2)
Question 2:
If the imaginary part of the complex number 
is 2 for 
, then the value of the integral 
is
(a) 0
(b) 1
(c) 2
(d) 3
Question 3:
If 
= 
and 
= 
then
(a) 
(b) 
(c) 
(d) 
Question 4:
If in the expansion of 
, the coefficients of x and 
are 3 and – 6 respectively, then p + q is
(a) 9
(b) 12
(c) 18
(d) 21
Question 5:
The value of 
is
(a) 
(b) 
(c) 
(d) 
Question 6:
f: R
R is given by f(x) = .
If L = 
, then the value of 6L is
(a) 2
(b) 4
(c) 6
(d) 8
Question 7:
The shortest distance between the line x – 2y + 3 = 0 and the curve 
is
(a) 
(b) 
(c) 
(d) 2
Question 8:
Let 
,. . . . be an A.P. with 
= 1. Then the common difference of this A.P., such that the product 
is minimum, is
(a) 1
(b) 
(c) 
(d) None of these
Question 9:
A circle passes through (0,p) and cuts a chord of length 2q on the x-axis. Then then locus of the centre of this circle is
(a) a straight line
(b) a parabola
(c) an ellipse
(d) a hyperbola
Question 10:
The mean of a set of numbers is 
. If each of the number is increased by 
, then the mean of the new set of numbers is
(a)
(b) 
(c) +
(d) None of these
Question 11:
If y = y(x) is the solution of the differential equation, 
satisfying (1,2), then 
is
(a) 1
(b) 0
(c) 1
(d) 3
Question 12:
The inverse function of f(x) = 
is
(a) 
(b) 
(c) 
(d) 
Question 13:
If the straight lines 
and 
are coplanar, then 
is
(a) 
(b) 
(c) 1
(d) 2
Question 14:
Let 
and 
be two vectors such that 
and the angle between and is 
. If 
is a unit vector, then 
is equal to
(a) 8
(b) 4
(c) 5
(d) 6
Question 15:
The domain of the function 
is
(a) 
(b) 
(c) 
(d) R – 
Question 16:
If 1, 
are the cube roots of unity, then the roots of the equation 
, are
(a) 
(b) 
(c) 
(d) 1,
Question 17:
If 
, 
, 1 are in A.P., then x is equal to
(a) 
(b) 
(c) 
(d) 
Question 18:
(a) 
and 
(b) 
and
(c) 
and
(d) none
Question 19:
The number of distinct solutions of sec x + tan x = 
, for x 
(a) 0
(b) 1
(c) 2
(d) 3
Question 20:
If from each of the three bags containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is
(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:
Number of sides of the polygon whose interior angles are in A.P. with smallest angle and common difference of 120° and 5° respectively, are __________ .
Question 2:
The value of 
is equal to ___________ .
Question 3:
If the lines 
,
and 
are concurrent, then b is __________ .
Question 4:
If the length of the latus rectum of a parabola, whose focus is (a, a) and the tangent at its vertex is x + y = a, is 16, then 
|a| is __________ .
Question 5:
Let A = 
. If 
= 25, then a value of 5
equals _________ .
Question 6:
Let 
, 
and 
. If the vectors, 
, 
and 
are coplanar, then 
is equal to __________ .
Question 7:
f(x) and g(x) are two differentiable function on [0,2] such that 
, 
, f(2) = 3g(2) = 9 then f(x) – g(x) at x = 
is _________.
Question 8:
If 
are such that 1 – 2i 
is a root of 
, then 
is ____________ .
Question 9:
If |x| >1 then sum of the series 
Then the value of 
is __________ .
Question 10:
The number of points, at which the function f(x) = 
, x 
R is not differentiable, is __________ .
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