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This mock test of Mathematics Test 10 - Trigonometry for JEE helps you for every JEE entrance exam.
This contains 25 Multiple Choice Questions for JEE Mathematics Test 10 - Trigonometry (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If m= sin^{6}x + cos^{6}x, then m belongs to the interval

Solution:

m=sin^6x+cos^6x=(sin^2x+cos^2x)(sin4x+cos^4x-sin^2xcos^2x)

as a^3+b^3=(a+b)(a^2-ab+b^2)

we know that,

sin^2x+cos^2x=1

m=((sin^2x+cos^2x)^2-3sin^2xcos^2x)

m=1-3sin^2xcos^2x

m=1-3/4(sin2x)^2

we know 0<=sin^2A<=1,

so -1<=-sin^2 2x<=0 multiply with -1,

-3/4<=-3/4(sin^2 2x)<=0 multiply with 3/4,

1/4<=1-3/4(sin^2 2x)<=1 add 1,

1/4<=m<=1

therefore "m" belongs to[1,1/4].

QUESTION: 2

Solution:

QUESTION: 3

if then the value of

Solution:

QUESTION: 4

if

Solution:

QUESTION: 5

In a triangle .If tan (P/2) and than (Q/2) are the roots of the equation then

Solution:

QUESTION: 6

If m then (m n)/(m–n) =

Solution:

QUESTION: 7

Minimum value of 3cosx + 4sinx +5?

Solution:

QUESTION: 8

The expression ) lies between

Solution:
5 cos a+3 cos (a + π3)+3 ⇒ 5 cos a + 3 [ cos(π3)cos a - sin (π3) sin a ]+ 3 As we know ( cos ( a + b ) = cos a cos b - sin a sin b ) ⇒5 cos a + 3(12)cos a - 3(32) sin a+3 since cos(π3) = 12, sin(π3) = 32 ⇒132 cos a - 3(32 ) sin a + 3 a cos a + b sin a + c minimum value is c-a2 + b2 ⇒132 cos a - 3(32 ) sin a + 3 minimum value 3- 13222 +33222 ⇒ 3 - 1694 + 274 ⇒ 3 - 49 ⇒ 3 - 7 ⇒ -4 maximum value is 3 + 13222 +33222 ⇒ 3 + 1694 + 274 ⇒ 3 + 7 ⇒ 10

QUESTION: 9

The maximum value of is

Solution:

QUESTION: 10

if then x+y+z =

Solution:

QUESTION: 11

The value of expression is equal to

Solution:

QUESTION: 12

Solution:

QUESTION: 13

If the angle A of a triangle ABC is given by the equation 5 cos A 3 = 0, then sin A and tan A are the roots of the equation

Solution:

QUESTION: 14

Solution:

QUESTION: 15

If A B = then (tanA + 1)(tanB + 1) is equal to

Solution:

QUESTION: 16

For a positive integer n,let

,Then

,Then

Solution:

QUESTION: 17

=

Solution:

QUESTION: 18

Solution:

QUESTION: 19

If q = then

Solution:

QUESTION: 20

the =

Solution:

QUESTION: 21

Solution:

QUESTION: 22

The number of solutions of

Solution:

QUESTION: 23

The maximum value of sin in the interval is attained at

Solution:

QUESTION: 24

The equation asinx + bcosx = c where |c|> has

Solution:

QUESTION: 25

If satisfying the equation then value of is

Solution:

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