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This mock test of Mathematics Test 3 - Entire XI Syllabus for JEE helps you for every JEE entrance exam.
This contains 25 Multiple Choice Questions for JEE Mathematics Test 3 - Entire XI Syllabus (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Value of lim_{x → 0}(1+Sin(x))^{Cosec(x)}

Solution:

lim_{x → 0}(1+Sin(x))^{Cosec(x)}

Put sin(x) = t we get

lim_{t → 0}(1+t)^{(1⁄t)} = e.

QUESTION: 2

The number of straight lines that can be drawn out of 10 points of which 7 are collinear is

Solution:

1. One line passing through 7 collinear points

2. 7 lines passing from each collinear point to non collinear one (3 times as there are 3 non-collinear points)

3. 3 lines joining each pair of non-collinear points 1+(7*3)+3 1+21+3 =25

QUESTION: 3

If the correlation coefficient between two variables is 1, then the two least square lines of regression are

Solution:

QUESTION: 4

The real part of is

Solution:

First we consider theta as x

1/1-cosx+isinx=1/2cos^2 x/2 + 2isinx/2cosx/2

=sec(x/2)/2 {1/cosx/2 + isinx/2}

=sec(x/2)/2 (1/e^ix/2). (e^ix=cosx+isinx){eulers theorem)

=sec(x/2)/2 e^-ix/2

=sec(x/2)/2 [ cos(-x/2) + i sun(-x/2)]

=1/2secx/2.cosx/2.-1/2itanx/2

=1/2.-i(1/2tanx/2)

=Re(z)=1/2

QUESTION: 5

The value of log3 tan1º + log3 tan2º +....+log3 tan 89º is

Solution:

Loga+log=log(ab)

tan(90-A)=cotA

log(tab.tan2......tan45........cot2.cot1). tan45=1

tanA.cotA=1

=log(1)=0

QUESTION: 6

If the solution of quadratic equation x^{2}-11x+22 are x=3 and x=6, then the base of the number is

Solution:

QUESTION: 7

1^{2} + (1^{2} + 2^{2}) + (1^{2} + 2^{2} + 3^{2 })+..... upto 22^{nd} term is

Solution:

QUESTION: 8

In ΔABC, ∠B = 90^{o} and b a = 4. The area of the triangle is the maximum when ∠C is

Solution:

QUESTION: 9

Let E be the ellipse and C be the circle x^{2} y^{2} = 4. Let P and Q be the point (1,2) and (2,1) respectively. Then

Solution:

QUESTION: 10

The third term of a G.P. is 4. The products of the first five term is

Solution:

QUESTION: 11

The sum of the infinIte of terms of G.P. is 20, and the sum of their square is 100, then the first term of

Solution:

QUESTION: 12

If cos^{-1} x/2 + cos ^{-1} y/3 = θ Then 9x^{2} - 12xy cos θ + 4y^{2} is

Solution:

QUESTION: 13

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

Solution:

QUESTION: 14

If A_{1}, A_{2 }be two A.M’s and G_{1}, G_{2} be two G..M.’s between a and b, then ( A_{1}, A_{2 })/G_{1},G_{2} is equal to

Solution:

QUESTION: 15

A tree is broken by wind, its upper part touches the ground at a point 10 meters from the foot of the tree and makes an angle of 60º with the ground the entire lenght of the tree of

Solution:

QUESTION: 16

How many diagonals can be drawn in a polygon of 15 sides ?

Solution:

QUESTION: 17

9x^{2} - 16y^{2} = 144 represents

Solution:

QUESTION: 18

If then r is equal to

Solution:

QUESTION: 19

Coefficient of X^{4} in the expansion of is

Solution:

QUESTION: 20

The locus of the mid-point of the chords of a circle x^{2} + y^{2} =4, which subtended a right angle at the centre is

Solution:

*Answer can only contain numeric values

QUESTION: 21

If α and β are roots of eq. λ(x^{2}–x) + x + 5 = 0

If λ_{1}, λ_{2} are two values of λ for which then

Solution:

*Answer can only contain numeric values

QUESTION: 22

If graph of x^{2} + bx + d is following.

ΔOBC is right angled isosceles triangle and A is mid point of OB then d =

Solution:

f(0) = d

OC = d ⇒ OB = d

OA = d/2

Roots of eq. are d & d/2

Product of roots d × d/2 = d

*Answer can only contain numeric values

QUESTION: 23

Sum of non real roots of eq.

(x^{2} + x – 2) · (x^{2} + x – 3) = 12 is …..

Solution:

x^{2} + x = t

t^{2} – 5t – 6 = 0

t = 6 or t = –1

x^{2} + x = 6 x^{2} + x = –1

x^{2} + x – 6 = 0 x^{2} + x + 1 = 0

Roots are real sum of roots = –1

*Answer can only contain numeric values

QUESTION: 24

2^{1/4} . 4^{1/8} . 8^{1/16}-------- ∞ is equal to?

Solution:

*Answer can only contain numeric values

QUESTION: 25

If ƒ(x) = |x – 3| + |x – 16| + |22 – x|, ∀ x ∈ R increases in (a,∞), then a/4 is equal to

Solution:

⇒ ƒ'(x) > 0 ∀ x ≥ 16 ⇒ a = 16

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