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This mock test of JEE(MAIN) Mathematics Mock Test - 3 for JEE helps you for every JEE entrance exam.
This contains 30 Multiple Choice Questions for JEE JEE(MAIN) Mathematics Mock Test - 3 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

if the pair of lines ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0

Solution:

QUESTION: 2

The circle x^{2} + y^{2} - 8x + 4y + 4 = 0 touches

Solution:

QUESTION: 3

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

Solution:

QUESTION: 4

The product of all roots of is

Solution:

QUESTION: 5

In determinant radio of the cofactor of -3 and subdeterminant is

Solution:

QUESTION: 6

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

Solution:

QUESTION: 7

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

Solution:

QUESTION: 8

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

Solution:

QUESTION: 9

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

Solution:

QUESTION: 10

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 x^{3} 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 .

Solution:

QUESTION: 11

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.

Solution:

QUESTION: 12

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

Solution:

QUESTION: 13

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

Solution:

QUESTION: 14

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?

Solution:

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

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

Solution:

QUESTION: 17

If the roots of ax^{2} + bx + c = 0 are α,β and roots of Ax^{2} + Bx + C = 0 are α + K, β + K, then B^{2} - 4AC/b^{2} - 4ac is equal to

Solution:

QUESTION: 18

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

Solution:

QUESTION: 19

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

Solution:

QUESTION: 20

The distance of the point (2, 1, -1) from the plane x - 2y + 4z = 9 is

Solution:

QUESTION: 21

The orthocentre of a triangle whose vertices are [(2),((âˆš3-1)/2)], ((1/2),-(1/2)) and (2,-(1/2)) is

Solution:

QUESTION: 22

If a line in the octant OXYZ and it makes equal angles with the axes, then

Solution:

In the octant OXYZ, all the three components are +ve...

now the line makes equal angles with all the axes,

therefore,

angle x = angle y= angle z

we know, cos²x + cos²y + cos²z = 1

thus, cos²x + cos²x + cos²x = 1

3cos²x = 1

cosx = 1/√3.... (since, cosx is +ve in first octant)

therefore..... l= m= n = cosx = cosy = cosz = 1/√3

QUESTION: 23

If sinα=-3/5, where π<α<(3π/2), then cos(α/2)=

Solution:

QUESTION: 24

The volume of a parallelopiped whose edges are -12i+αk, 3j-k and 2i+j-15k is 546, then the value of α is

Solution:

QUESTION: 25

Solution:

QUESTION: 26

An unknown polynomial yields a remainder of 2 upon division by x − 1, and a remainder of 1 upon division by x − 2. If this polynomial is divided by (x − 1)(x − 2), then the remainder is

Solution:

QUESTION: 27

If p , x_{1} , x_{2} , … x_{i} … and q , y_{1} , y_{2} , … y_{i} … are in A.P., with common difference a and b respectively, then the centre of mean position of the points A_{i}(x_{i}, y_{i}) where i = 1, 2, ..., n lies on the line

Solution:

QUESTION: 28

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) = |x - 1| + |x - 2| + |x - 3|, where 2 < x < 3 is an identity function.

Reason(R): f : A → f(x) = x is identity function.

Solution:

QUESTION: 29

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): A five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 with repetition. The total number formed are 216.

Reason(R) : If sum of any number is divisible by 3, then the number must be divisible by 3.

Solution:

QUESTION: 30

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): The number of non-negative integral solutions of x_{1} + x_{2} + x_{3} + x_{4} ≤ 4 (where n is a +ve integer) is ^{n+4}C_{4}.

Reason(R): The number of non-negative integral solutions of x_{1} + x_{2} + .... + x_{r} = n is equal to ^{n+r-1}C_{r}.

Solution:

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