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This mock test of JEE Main Mathematics Mock - 1 for JEE helps you for every JEE entrance exam.
This contains 25 Multiple Choice Questions for JEE JEE Main Mathematics Mock - 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

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):If *C _{r}* is the coefficient of

Reason(R) : Cr = C_{n − r} for any positive integer *n*

Solution:

QUESTION: 2

The area (in square units) bounded by the curves y^{2} = 4x and x^{2} = 4y in the plane is

Solution:

QUESTION: 3

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 inverse of does not exist.

Reason(R) :The matrix is non singular.

Solution:

QUESTION: 4

If sin θ is real, then θ =

Solution:

QUESTION: 5

If the line 3x-4y=λ touches the circle x^{2}+y^{2}-4x-8y-5=0, λ can have the values

Solution:

QUESTION: 6

The length of the tangent from (0,0) to the circle *2x ^{2} + 2y^{2} + x - y + 5 = 0* is

Solution:

QUESTION: 7

The differential equation which represents the family of plane curves y=exp. (cx) is

Solution:

y = e^{cx}

dy/dx = c. e^{cx}

y' = cy

QUESTION: 8

If sin y = x sin (a + y), then (dy/dx) =

Solution:

QUESTION: 9

If A, B, C are represented by 3 + 4i, 5 - 2i, -1 + 16i respectively, then A, B, C are

Solution:

QUESTION: 10

The fundamental period of the function f(x) = 2 cos 1/3(x - π) is

Solution:

QUESTION: 11

Which of the following is not a statement ?

Solution:

QUESTION: 12

In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-

Consider the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5.

Statement-1:

The parametric equations of the line of intersection of the given planes are

x = 3 + 14t, y = 1 + 2t, z = 15t.

Statement-2:

The vector 14î+2ĵ+15k̂ is parallel to the line of intersection of given planes

Consider the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5.

Statement-1:

The parametric equations of the line of intersection of the given planes are

x = 3 + 14t, y = 1 + 2t, z = 15t.

Statement-2:

The vector 14î+2ĵ+15k̂ is parallel to the line of intersection of given planes

Solution:

QUESTION: 13

In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-

Tangents are drawn from the point (17,7) to the circle x^{2}+y^{2}=169.

Statement-1:

The tangents are mutually perpendicular.

Statement-2:

The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^{2}+y^{2}=338.

Solution:

Clearly, m_{1}m_{2} = - 1.

Hence, the two tangents arc mutually perpendicular.

Statement 1 is true.

Now, the locus of the point of intersection of two mutually perpendicular tangents to the circle x^{2} + y^{2} = r^{2} is the director circle i.e. the circle x^{2} +y^{2 }= 2r^{2}.

For the given circle r = 13. ..

Its director circle is x^{2} + y^{2} = 338.

Hence, statement 2 is true and a cogect explanation of statement as the point (17, 7) lies on the director circle of the circle (i).

QUESTION: 14

The value of a for which the system of equations

a^{3}x+(a+1)^{3}y+(a+2)^{3}z = 0

ax+(a+1)y+(a+2)z = 0

x+y+z = 0

has a non-zero solution, is

Solution:

The system of equation has a non-zero solution

QUESTION: 15

The pole of the line 2x + 3y − 4 = 0 with respect to the parabola y^{2} = 4 x is

Solution:

QUESTION: 16

If ^{n}C_{12}=^{n}C_{8}, then n=

Solution:

QUESTION: 17

The chance of getting a doublet with 2 dice is

Solution:

Total outcomes = 36

Doublet are 6 (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)

Probability of getting doublet = 6/36

= 1/6

QUESTION: 18

If cov. (x, y) = 0, then ρ(x, y) equals

Solution:

Covariance is a quantitative measure of the extent to which the deviation of one variable from its mean matches the deviation of the other from its mean. It is a mathematical relationship that is defined as:

Cov(X,Y) = E[(X − E[X])(Y − E[Y])]

Correlation between two random variables, ρ(X,Y) is the covariance of the two variables normalized by the variance of each variable. This normalization cancels the units out and normalizes the measure so that it is always in the range [0, 1]:

QUESTION: 19

The two opposite vertices of a square on xy-plane are A(-1,1) and B(5,3), the equation of other diagonal (not passing through A and B) is

Solution:

Given: Here,AB is the diagonal of square.

The vertices of a square A

Let the mid−point of AB be EThen coordinates of E are

Therefore equation of other diagonal is

QUESTION: 20

If the normal to the curve y=f(x) at the point (3,4) makes an angle 3π/4 with the positive x-axis, then f'(3)

Solution:

Given y = f(x)

differentiating w.r.t x

y' = f'(x) which is the slope of the tangent

Hence the slope of the normal is - 1/f'(x) = 3pi/4 = -1

therefore f'(x) = 1

Hence f'(3) = 1

*Answer can only contain numeric values

QUESTION: 21

Assume e^{-4/5} = 2/5. If x, y satisfy, y = e^{x} and the minimum value of (x^{2} + y^{2}) is expressed in the form of m/n then (2m - n)/5 equals (where m & n are coprime natural numbers)

Solution:

OP^{2} = x^{2} + y^{2}

y = e^{x}, y' = e^{x},

*Answer can only contain numeric values

QUESTION: 22

Let ƒ(x) be non-constant thrice differentiable function defined on (–∞, ∞) such that ƒ(x) = ƒ(6 – x) and ƒ'(0) = 0 = ƒ'(2) = ƒ'(5). If 'n' is the minimum number of roots of (ƒ"(x))^{2} + ƒ'(x)ƒ"'(x) = 0 in the interval x ∈ [0, 6] then sum of digits of n equals

Solution:

ƒ(x) = ƒ(6 – x)

⇒ ƒ'(x) = –ƒ'(6 – x) .... (1)

put x = 0, 2, 5

ƒ'(0) = ƒ'(6) = ƒ'(2) = ƒ'(4) = ƒ'(5) = ƒ'(1) = 0

and from equation (1) we get ƒ'(3) = –ƒ'(3)

⇒ ƒ'(3) = 0

So ƒ'(x) = 0 has minimum 7 roots in

x ∈ [0, 6] ⇒ ƒ"(x) has min 6 roots in x ∈ [0,6]

h(x) = ƒ'(x).ƒ"(x)

h'(x) = (ƒ"(x))^{2} + ƒ'(x) ƒ"'(x)

h(x) = 0 has 13 roots in x ∈ [0, 6]

h'(x) = 0 has 12 roots in x ∈ [0, 6]

*Answer can only contain numeric values

QUESTION: 23

If a, b, c, x, y, z are non-zero real numbers and then the value of (a^{3} + b^{3} + c^{3} + abc) equals

Solution:

x^{2}(y + z)y^{2}(z + x)z^{2}(x + y) = a^{3}b^{3}c^{3} = x^{3}y^{3}z^{3}

⇒ (x + y) (y + z) (z + x) = xyz

⇒ x^{2}(y + z) + y^{2}(z + y) + z^{2}(x + y) + xyz = 0

⇒ a^{3} + b^{3} + c^{3} + abc = 0

*Answer can only contain numeric values

QUESTION: 24

If the co-ordinate of the vertex of the parabola whose parametric equation is x = t^{2} – t + 1 and y = t^{2} + t + 1, t ∈ R is (a, b) then (2a + 4b) equals

Solution:

x = t^{2} – t + 1 .... (1)

y = t^{2} + t + 1 .... (2)

y – x = 2t & x + y = 2(t^{2} + 1)

________on elminating 't' we get

⇒ (x + y – 2) = 2(y - x)/2^{2}

(x – y)^{2} = 2(x + y – 2)

Axis : x – y = 0

Tangent at vertex : x + y – 2 = 0

Vertex : (1, 1) = (x, y)

*Answer can only contain numeric values

QUESTION: 25

Solution:

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