JEE Maths
Sample Paper 4 | 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:
In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the selected student has opted neither for NCC nor for NSS is
(a) 
(b) 
(c) 
(d) 
Question 2:
Given both 
and 
are acute angles and 
then the value of 
belongs to
(a) 
(b) 
(c) 
(d) 
.
Question 3:
Let 
. The number of different ordered pairs (Y, Z) that can be formed such that 
and 
is empty is
(a) 
(b) 
(c) 
(d) 
.
Question 4:
If a point R(4, y, z) lies on the line segment joining the points P(2,
, 4) and Q(8,0,10), then the equation of line containing R and origin is
(a) 
(b) 
(c) 
(d) 
Question 5:
If a point R(4, y, z) lies on the line segment joining the points P(2, , 4) and Q(8,0,10), then the distance of R from the origin is [Level: Difficult]
(a) 6
(b) 2
(c) 
(d) 2
Question 6:
The Evaluation of 
is
(a) 
(b) 
(c) 
(d) 
Question 7:
is equal to
(a) 
(b) 
(c) 
(d) 
Question 8:
If 
then the number of values of x for which 
is
(a) 
(b) 
(c) 5
(d) 8.
Question 9:
If the tangent at 
and 
on the parabola meet in 
, then 
, 
and 
are in
(a) 
(b) 
(c) 
(d) 
Question 10:
The solution of 
is
(a) 
(b) 
(c) 
(d) none of these.
Question 11:
The equation of the smallest circle passing through the points (2, 2) and (3, 3) is. [Level: Moderate]
(a) 
(b) 
(c) 
(d) 
Question 12:
A straight line L with negative slope passes through the point 
and cuts the positive co-ordinates axes at points 
and Q as L varies ,the absolute minimum value of OP+OQ is (O is origin)
(a) 
(b) 
(c) 
(d) 
Question 13:
The line 
meets the circle 
at only one point, if 
is
(a) 
(b) 
(c) 
(d) 
Question 14:
is equal to
(a)
(b) 
(c)
(d) 
Question 15:
If the difference between the roots of the equation 
is less than 
, then set of possible values of p is
(a) 
(b) 
(c) 
(d) 
Question 16:
A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that all the letters are in the wrong envelopes.
(a) 720
(b) 360
(c) 265
(d) 180
Question 17:
If 
, then x lies in the interval
(a) 
(b) 
(c) 
(d) none of these
Question 18:
An ellipse inscribed in a circle and a point within the circle is chosen at random. If the probability that this point lies outside the ellipse is 
then the eccentricity of the ellipse is
(a) 
(b) 
(c) 
(d)
Question 19:
The locus of middle points of chords of hyperbola 
parallel to 
is
(a) 
(b) 
(c) 
(d) 
Question 20:
equals
(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 value of 
is __________ .
Question 2:
If 
= 
and 
, then 
at x = 1, is __________ .
Question 3:
If the area above the x-axis bounded by the curves 
and 
and 2 is 
the the value of k is __________ .
Question 4:
If for some p, q, r 
R, not all have same sign, one of the roots of the equation 
is also a root of the equation 
, then 
is equal to __________ .
Question 5:
Let A = 
and B = 
where a, b, c R. If 
AB = 
, then number of ordered triplets (a, b, c) is __________ .
Question 6:
The value of 
is __________ .
Question 7:
The exponent of 7 in 
is ___________ .
Question 8:
If 
, 
, 
, then the value of 
is __________ ._______ .
Question 9:
The positive value of 
, if the following equations 
, 
are consistent, is __________ .
Question 10:
The eccentric angle (in degree) of the point of contact of the line 
with the ellipse 
, is __________ .
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