JEE Main Mathematics Mock

QUESTION: 1

if the pair of lines ax² + 2hxy + by² + 2gx + 2fy + c = 0

A.
2f gh = bg² + ch²
B.
bg² ≠ ch²
C.
abc = 2fgh
D.
none of these

Solution:

QUESTION: 2

The circle x² + y² - 8x + 4y + 4 = 0 touches

A.
x-axis
B.
y-axis
C.
both x and y-axis
D.
does not touch the axis

Solution:

QUESTION: 3

The foci of the ellipse 25(x+1)² + 9(y+2)² = 225 are

A.
(-1,2),(6,1)
B.
(-1,-2),(1,6)
C.
(1-,2),(1,-6)
D.
(-1,2),(-1,-6)

Solution:

QUESTION: 4

The product of all roots of is

A.
-1
B.
1
C.
3/2
D.
-(1/2)

Solution:

QUESTION: 5

The differential equation of the family of lines passing through the origin is

A.
x dy/dx + y = 0
B.
X+dy/dx = 0
C.
dy/dx = y/x
D.
dy/dx = x

Solution:

QUESTION: 6

Log (x + y) - 2xy = 0, then y (0) =

A.
1
B.
-1
C.
2
D.
0

Solution:

QUESTION: 7

If f: R → R and g : R → R defined by f(x) = 2x + 3 and g(x) = x² + 7, then the value of x for which f(g(x)) = 25 are

A.
+ 1
B.
+ 2
C.
+ 3
D.
+ 4

Solution:

QUESTION: 8

The area bounded by the curve y = x² - 4x, x-axis and line x = 2 is

A.
(16/3) sq.unit
B.
(-16/3) sq.unit
C.
(4/7) sq.unit
D.
cannot be calculated

Solution:

QUESTION: 9

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): f (x) = log x³ and g (x) = 3 log x are equal .
Reason(R) : Two functions f and g are said to be equal if their domains, ranges are equal and f (x) = g (x) ∀ x in the domain .

A.
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B.
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
C.
Assertion is true but Reason is false.
D.
Assertion is false but Reason is true.

Solution:

QUESTION: 10

Which of the following statements are true ?
(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.
(2) For any polynomial f(x) =0 with real co-efficients, imaginary roots occurs in conjugate paris.
(3) Order relation exists in complex numbers whereas it does not exist in real numbers.
(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.

A.
(1) and (2) only
B.
(2) and (4) only
C.
(3) and (4) only
D.
(1),(2) and (4) only

Solution:

QUESTION: 11

A tangent is drawn at the point (3√3 cos θ, sin θ) 0 < θ < (π/2) of an ellipse (x²/27) + (y²/1) = 1 the least value of the sum of the intercepts on the co-ordinate axes by this tangent is attained at θ =

A.
π/6
B.
π/3
C.
π/8
D.
π/4

Solution:

QUESTION: 12

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion (A):
Reason (R): The non zero vectors are always linearly independent

A.
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B.
Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
C.
Assertion is true but Reason is false.
D.
Assertion is false but Reason is true.

Solution:

QUESTION: 13

How many numbers between 99 and 1000 can be formed from the digits 2,3,7,0,8,6 so that in each number each digit may occur once only?

A.
100
B.
90
C.
120
D.
80

Solution:

QUESTION: 14

If two dice are thrown, find the probability of getting an odd number of on one and multiple of 3 on the other is

A.
1/3
B.
2/3
C.
1/6
D.
13/36

Solution:

Odd no. on the first die

1, 3, 5

multiple of 3 on the other die

3, 6

now let's see the combination of these two events happening simultaneously

as the question says

(1,3) , (1,6) , (3,3) , (3,6) , (5,6) , (5,3)

total no of favourable events = 6

total no of events throwing two dice simultaneously = 6² = 36

so probability = 6/36 = 1/6

QUESTION: 15

The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved is

A.
1/4
B.
1/2
C.
3/4
D.
1/3

Solution:

We have, probability that A can solve the problem = P(A) = 1/2 ,
And in this way P(B) = 1/3 and P(C) = 1/4.
P(A cannot solve the problem) = 1 – P(A) = 1/2 ,
P(B cannot solve the problem) = 1 – P(B) = 1 – 1/3 = 2/3,
P(C cannot solve the problem) = 1 – P(C) = 1 – 1/4 = 3/4.
P(A, B, and C cannot solve the problem) = 1/2 x 2/3 x 3/4 = 1/4.
Therefore , P(Problem will be solve) = 1 – P(Problem is not solved by any of them)
= 1 – 1/4 = 3/4

QUESTION: 16

If the roots of ax² + bx + c = 0 are α,β and roots of Ax² + Bx + C = 0 are α + K, β + K, then B² - 4AC/b² - 4ac is equal to

A.
a/A
B.
A/a
C.
(a/A)²
D.
(A/a)²

Solution:

QUESTION: 17

Let f(x) be a polynominal function of second degree,If f(1) = f(-1) and a,b,c are in A.P., then f'(a),f'(b) and f'(c) are in

A.
A.P.
B.
G.P.
C.
H.P.
D.
Arithmetico-geometric progression

Solution:

QUESTION: 18

The total expenditure incurred by an industry under different heads is best presented as a

A.
bar diagram
B.
pie diagram
C.
histogram
D.
frequency polygon

Solution:

QUESTION: 19

The orthocentre of a triangle whose vertices are [(2),((√3-1)/2)], ((1/2),-(1/2)) and (2,-(1/2)) is

A.
[(3/2),((√3-2)/2)]
B.
[(2),(-1/2)]
C.
[(5/4),((√3-2)/4)]
D.
[(1/2),-(1/2)]

Solution:

QUESTION: 20