JEE Maths
Sample Paper 5 | 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:
Let y(x) be the solution of the differential equation 
, (x 
1). Then y(e) is equal to
(a) 2
(b) 2e
(c) e
(d) 0
Question 2:
The parallelism condition for two straight lines one of which is specified by the equation 
and the other being represented parametrically by 
, 
given by
(a) 
(b) none
(c) 
(d) 
Question 3:
If the coefficients of the 5th, 6th, and 7th terms in the expansion of 
are in AP, then the value of n is
(a) 7 only
(b) 14 only
(c) 7 or 14
(d) None of these
Question 4:
If 
, then the system of equations 
has
(a) infinitely many solutions
(b) a unique solution
(c) no solution
(d) exactly two solutions
Question 5:
The tangent at P , any point on the circle 
meets the coordinate axes in A and B then
(a) Length of AB is constant
(b) PA and PB are always constant
(c) The locus of the mid-point of AB is 
(d) None of these
Question 6:
For a non-zero real a, b, c 
= 
(a) 0
(b) 2
(c) 4
(d) 6
Question 7:
is equal to
(a) 
(b) 
(c) 
(d) 
Question 8:
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 9:
The value of \
is
(a) 
(b) 
(c) 1
(d) does not exist
Question 10:
If 
, then the correct statement is
(a) 
(b) 
(c) 
(d) None of these
Question 11:
If z is a complex number of unit modulus and argument θ
, then arg
equals
(a) 
(b)
(c) 
(d) 
Question 12:
The eccentric angle of the point of contact of the line 
with the ellipse 
is
(a) 0
(b) 
(c) 
(d) 
Question 13:
The locus of middle points of chords of hyperbola 
parallel to 
is
(a) 
(b) 
(c) 
(d) 
Question 14:
Let 
and 
. Then for all x 
is
(a) – 1
(b) 1
(c) f(x)
(d) g(x)
Question 15:
The number of terms common between the two series 
up to 50 terms and the series 
upto 30 terms
(a) 21
(b) 20
(c) 30
(d) 18
Question 16:
If 
such that A = {1, 2, 3, 4, 5} and B = {a, b, c, d, e, f, g}, then the total number of one-one functions is
(a) 
(b) 
(c) 7!
(d) 0
Question 17:
, (a > b) is
(a) 
(b) 
(c) 
(d) 
Question 18:
Let A + 2B = 
and 2A – B = 
. If Tr(A) denotes the sum of all diagonal elements of the matrix A, then Tr(AB) has value equal
(a) 0
(b) 2
(c) 3
(d) 1
Question 19:
What is the sum of all the 4 digit numbers formed using the digits 1, 2, 3, 4 without repeating any digits ?
(a) 11110
(b) 266640
(c) 66660
(d) None of these
Question 20:
If the standard deviation of the numbers 2, 3, 10 and p is 3.5, then which of the following is true ?
(a) 15p + 154 = 0
(b) 3
– 30p + 31 = 0
(c) – p + 49 = 0
(d) 30p + 274 = 0
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:
Let 
are in A.P. if 
and 
, then the value of 
is __________ .
Question 2:
The length of the perpendicular from the point 
on the straight line, 
is _________ .
Question 3:
If 
, then the value of ‘a’ is __________ .
Question 4:
If A = ϕ then the value of n(P(A)) is ___________ .
Question 5:
Let A and B be two independent events such that P(A) = 
and P(B) = 
. Then, the value of P(A|B) is ___________ .
Question 6:
Let 
. If the mirror image of the point P(a, 6, 9) with respect to the line 
is 
, then |a+b| is equal to __________ .
Question 7:
If the variance of first n natural numbers is 14 and the variance of first m natural numbers is 24, then m + n is equal to ___________ .
Question 8:
If 
, then the value of 
is __________ .
Question 9:
The number of Integral values of m for which the x-coordinate of the point of Intersection of the lines 
and 
also an integer, is __________ .
Question 10:
If 
then k is equal to __________ .
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