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This mock test of Mathematics Test 10 - Trigonometry for JEE helps you for every JEE entrance exam.
This contains 30 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)/(mâ€“n) =

Solution:

QUESTION: 7

Minimum value of 3cosx + 4sinx +5?

Solution:

QUESTION: 8

The expression ) lies between

Solution:
5 cos a+3 cos (a +Â Ï€3)+3 â‡’Â 5 cos a + 3 [ Â cos(Ï€3)cos a - sin (Ï€3)Â sin a ]+ 3 As we know ( cosÂ ( a + b ) = cos a cos bÂ - sin a sin b ) â‡’5 cos a + 3(12)cos a - 3(32)Â sin a+3 since cos(Ï€3) =Â 12, sin(Ï€3) =Â 32 â‡’132Â cos a - 3(32Â )Â sin a + 3 a cos a +Â b sin a +Â c Â Â Â minimum value is Â c-a2Â +Â b2 â‡’132Â cosÂ a - 3(32Â )Â sin a + 3 minimum value Â 3-Â 13222Â +33222 â‡’Â 3 -Â 1694Â +Â 274 â‡’Â 3 -Â 49 â‡’Â 3 - Â 7 â‡’Â -4 maximum value is Â 3 +Â 13222Â +33222Â â‡’Â 3 +Â 1694Â +Â 274 â‡’Â 3 + 7 â‡’Â 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:

QUESTION: 26

The equation ,where x is a variable has real roots. Then the interval of p may be any of the following

Solution:

QUESTION: 27

The number of solutions of the equation which lie between 0 and 2 is

Solution:

QUESTION: 28

Simplify 15ax^{2} ⁄ 5x

Solution:

QUESTION: 29

if then =

Solution:

QUESTION: 30

If then =

Solution:
âˆš3cosx+sinx=1=>âˆš3/2cosx+1/2sinx=1/2=>(cosa)(cosx)+(sina)(sinx)=1/2(( let âˆš3/2 be cosa and 1/2 be sina) =>cosÏ€/6cosx+sinÏ€/6sinx=1/2 =>cos( Ï€/6-x)=1/2 =>cos(x-Ï€/6)=cosÏ€/3 =>x-Ï€/6=2nÏ€+/-Ï€/3 =>x=2nÏ€+Ï€/2 or x=2nÏ€-Ï€/6 => here we can have all the values given in option.

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