Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

1.

मान ज्ञात कीजिए sinx+sin2x+sin3x=cosx+cos2x+cos3x`

Answer» Correct Answer - `(i) (1)/(8)(4n+1)pi, 2n pi+- (2pi)/(3), n in I " " (ii) n=(npi)/(4), (2n+1) (pi)/(24), n in I`
Discussion
2.

हल करें `cos3 theta+ sin 3 theta= cos theta+sin theta`

Answer» प्रश्न से `cos3 theta+ sin 3 theta= cos theta+sin theta" "....(1)`
या `sin 3 theta- sin theta = cos theta-cos3 theta`
या `2"cos" (3 theta+ theta)/(2)."sin"(3 theta- theta)/(2)=2"sin"(theta+3 theta)/(2)."sin"(3theta-theta)/(2)`
या `2 cos 2 sin theta- sin 2 theta. sin theta=0`
या `sin theta(cos2 theta-sin 2theta)=0`
`:. sin theta=0` या `cos 2 theta-sin 2 theta=0`
जब `sin theta=0` तो `theta=n pi, n in I`
जब `cos 2 theta- sin 2 theta=0` तो `cos 2 theta= sin theta`
या `tan 2 theta=1` [जहाँ `cos2 theta` से भाग दिया जा सकता है क्यकिं `cos2 thetane0`]
या `tan 2 theta="tan"(pi)/(4) " " :. 2 theta =n pi+(pi)/(4)`
या `theta=(n pi)/(2)+(pi)/(8), n in Z`
अतः `theta=n pi, (n pi)/(2)+(pi)/(8), n in Z`
Discussion
3.

हल करें `(1- tan theta)(1+ sin 2 theta)=(1+tan theta)`

Answer» प्रश्न से `(1-tan theta)(1+(2tan theta)/(1+tan^(2) theta))=1+ tan theta`
या `(1-tan theta) ((1+tan^(2)theta+ 2 tan theta))/(I+ tan^(2) theta)=1+ tan theta`
या `(t-tan theta) (1+tan theta)^(2)-(1+tan theta)(1+tan^(2) theta)`
या `(1+ tan theta)[(1-tan theta)(1+tan theta)-(1+ tan^(2) theta)]=0`
या `(t+tan theta)[1-tan^(2) theta-1-tan^(2)theta]=0`
या `(1+tan theta)(-2 tan^(2) theta)=0`
या `tan^(2) theta(1+ tan theta)=0`
यदि `tan^(2) theta=0`, तो `tan theta=0 rArr 0 n pi`
यदि `1+tan theta=0` तो `tan theta=-1= tan (-(pi)/(4))`
`:. theta=npi+(-(pi)/(4))=npi-(pi)/(4)`
अतः `theta=npi, n pi-(pi)/(4), n in Z`
Discussion
4.

समीकरण `tan theta= cot alpha` का व्यापक हल होगाA. `theta= n pi+(pi)/(2)-alpha`B. `theta= n pi-(pi)/(2)+alpha`C. `theta= n pi+(pi)/(2)+alpha`D. `theta= n pi+(pi)/(2)-alpha`

Answer» Correct Answer - A
Discussion
5.

`theta` का वह मान जो समीकरण `sin5 theta=cos2 theta` को संतुष्ट करता हैA. `(14n-1)(pi)/(6)`B. `(6n-1)(pi)/(14)`C. `(4n+1)(pi)/(14)`D. `(6n+1)(pi)/(14)`

Answer» Correct Answer - C
Discussion
6.

हल करें (i) `cosmx+cosnx=0` (ii) `tan x+tan 4x=1` `(iii) tan 5 theta=cos 2 theta)` (iv) `tan x=-cost (x+(pi)/(3))`

Answer» Correct Answer - `((2r+1)pi)/(m+-n)r, in I " " (ii) (2n+1)(pi)/(10), n in I`
(iii) `((2n+1)pi)/(14), n in I " " (iv) x=n pi+(5pi)/(6)n, in Z`
Discussion
7.

यदि `cot theta=(1/2)"cosec"theta`, तो `theta`=A. `3npi+-(pi)/(2)`B. `npi+-(pi)/(3)`C. `2npi+-(pi)/(3)`D. `npi+(-1)^(n)(pi)/(6)`

Answer» Correct Answer - C
Discussion
8.

`theta` का वह मान जो समीकरण `cos theta=-(1)/(sqrt(2))` तथा `tan theta=1` को संतुष्ट करता है से कौन होगाA. `2npi+(4pi)/(5)`B. `2npi-(5pi)/(4)`C. `2npi+(5pi)/(4)`D. `2npi-(4pi)/(5)`

Answer» Correct Answer - C
Discussion
9.

हल करें (i) `cos6x+cos4x= sin 3x+sinx` (ii) `cos5x+cos3x+cosx=0` `(iii) cos theta-sin3 theta=cos2 theta` `(iv) cos x+cos3x+cos5x+cos7x+0` (v) `sin 3 theta+sin2 theta+ sin theta =0` (vi) `sin 2x-sin4x+sin6x=0`

Answer» Correct Answer - `(i) (2n+1)(pi)/(2),(4n+1)(pi)/(14)(4n-1)(pi)/(6)n in I`
(ii) `(2n+1)(pi)/(6), n pi +-(pi)/(3), n in I " " (iii) (2npi)/(3),(4n+1)(pi)/(4),(4n-1)(pi)/(2)n in I`
(iv) ` (2n+1)(pi)/(6),(2n+1)(pi)/(4),(2n+1) pi`
(v) `(npi)/(2), 2n pi+-(2pi)/(3), n in I " " (vi) n=(n pi)/(4)` या `x=npi+-(pi)/(6), n in Z`
Discussion
10.

हल करें (i) ` 2sin^(2)+sinx=3(0^(@) lex le 1000^(@))` (ii) `2 cos^(2)x-cosx=3,(theta lex le 1000^(@))` `(iii) 2sin^(2)x+sin^(2)x=2` (iv) `2 cos^(2)x+3sinx=0`

Answer» Correct Answer - `(i) 180^(@),540^(@),900^(@) " " (ii) 90^(@),450^(@),810^(@)`
(ii) `(2n+1)(pi)/(2),npi +-(pi)/(2)n in I " " (iv) x-npi+(-1)^(n)(7pi)/(6)n, in Z`
Discussion
11.

हल करें (i) `sinx+cosx+secx+"cosecx"=0` (ii) `cos 3 theta sin^(3) theta cos^(3) theta=0`

Answer» Correct Answer - `(i) n pi-(pi)/(4), n in I (ii) (npi)/(4) ; n in I`
Discussion
12.

हल करें (i) `cos theta =(1)/(2) " " (ii) sin theta=-1` (iii) `3 tan^(2)theta=1 " " (iv) 2 sin theta =sqrt(3)` (iv) `sin=x-(sqrt(3))/(2)`

Answer» Correct Answer - `(i) 2n pi pm (pi)/(3), n in I " " (ii) n pi+(-1)^(n+1)(pi)/(2)n in I`
(iii) ` n +- (pi)/(6)n in I " " (iv) n pi +(-1)^(n)(pi)/(3)n in I`
(v) `x=xn pi(-1)^(n)(4pi)/(3), n in Z`
Discussion
13.

हल करें `sin theta =-(sqrt(3))/(2)`

Answer» प्रश्न से `sin theta=-(sqrt(3))/(2)=sin (-(pi)/(3))`
`:. theta =n pi +(-1)^(n)(-(pi)/(3))`
अतः `theta=npi-(-1)^(n)(pi)/(3), n=0pm1pm2`
Discussion