`sin 3A`
`cos 3A`
`sin A+ cos A`
`3`
`- cosec quad 88^0`
`- cosec quad 2^0`
`- cosec quad 44^0`
`- cosec quad 46^0`
`2`
`1`
`1/2`
`0`
` (sqrt(5) - 1) /4 `
` (sqrt(5) + 1) /4 `
` sqrt(10 + 2sqrt(5))/4`
` sqrt(10 - 2sqrt(5))/4`
` pi/6`
`pi`
`pi/2`
`pi/4`
`sin 47^0`
`cos 47^0`
`2 sin 47^0`
`2 cos 47^0`
`pi`
`pi/3`
`pi/2`
`pi/4`
`b/a`
`a/b`
`ab`
`1`
`1//4`
`1//2`
`1`
`4`
` pi/(12)`
`pi/6`
`pi/4`
`pi/3`
`1`
`2`
`-1`
`-2`
`3`
`5`
`10`
`-5`
`5`
`8`
`10`
`-10`
`60^o`
`45^o`
`30^o`
None of these
`60^0`
`45^0`
`30^0`
None of these
`0`
`1`
`2`
`3`
`2/3`
`3/2`
`2`
`1`
`I < IV < II < Ill`
`IV < II < I < Ill`
`IV < II < Ill < I`
`I < IV< Ill < II`
`c/(c^2-1)`
`c/(c^2+1)`
`(c^2-1)/(c^2+1)`
None of these
`0`
`1`
`2`
`4`
`sin A`
`cos A`
`tanA`
`0`
`0`
`1`
`2`
`-1`
`(sqrt3+1)/(sqrt3-1)`
`(sqrt3+1)/(1-sqrt3)`
`(sqrt3-1)/(sqrt3+1)`
`(sqrt3+2)/(sqrt3-1)`
`1`
`x`
`0`
`2`
`-2`
`0`
`1`
`2`
`(sqrt3-1)/(2sqrt2)`
`(sqrt3+1)/(2 sqrt2)`
`(sqrt3-1)/(sqrt3+1)`
`(sqrt3+1)/(sqrt3-1)`
`1`
`2`
`4`
None of these
`5/13`
`12/13`
`-12/13`
`-13/12`
`1`
`-1`
`-sqrt2`
`-sqrt3`
Only I
Only II
Both I and II
Neither I nor II
first quadrant
second quadrant
third quadrant
fourth quadrant
`(30^0)/pi`
`(60^0)/pi`
`60^0`
None of these
`135^0`
`90^0`
`75^0`
`60^0`
`2-sqrt3`
`2+sqrt3`
`sqrt2-sqrt3`
`sqrt3-sqrt2`
`0`
`sqrt3/2`
`1/2`
`1/sqrt2`
`1`
`2`
`4`
`10`
`1/2`
`1/sqrt2`
`sqrt3/2`
`1/3`
`8/17`
`8/15`
`15/17`
`23/32`
`1/3`
`2/3`
`1`
`-1`
`pi/6`
`pi/3`
`pi/4`
`pi/8`
`-1`
`0`
`1`
`2`
`0`
`1/2`
`1`
`2`
`0`
`1`
`2`
`2(sinA+sinB)`
`0`
`1`
`2`
`-1`
Only I
Only II
Both I and II
Neither I nor II
-1
`0`
`1`
Infinity
`1`
`0`
`cos^2 theta`
`2 sintheta`
`7-4sqrt3`
`7+4 sqrt3`
`7+2sqrt3`
`7+6sqrt3`
`2 tan x`
`2 cosec x`
`2 cos x`
`2 sin x`
`1`
`2`
`3`
`4`
`-1`
`0`
`1`
`2`
`-1`
`0`
`1`
`3`
`1`
`2`
`3`
`4`
`|a| le 4`
`|a| le 2`
`|a| le sqrt3`
None of these
`1/y-1/x`
`1/x-1/y`
`1/x+1/y`
`-1/x-1/y`
`1`
`2`
`3`
`4`
`0`
`1`
`2`
None of these
`30^0`
`45^0`
`60^0`
`90^0`
`3sin alpha`
`(2 sin alpha)/3`
`(sin alpha)/3`
`2 sin alpha`
`(sintheta+costheta-1)/(sintheta+costheta+1)`
`(sintheta+costheta+1)/(sintheta+costheta-1)`
`(sintheta-costheta-1)/(sintheta+costheta+1)`
`(sintheta-costheta+1)/(sintheta+costheta-1)`
`sec 18^0`
`cosec 18^0`
`-sec 18^0`
`-cosec 18^0`
`0`
`1`
`2`
`3`
`1`
`1/sqrt2`
`sqrt3/2`
`0`
`(mn)/(m^2+n^2)`
`(2mn)/(m^2+n^2)`
`(m^2+n^2)/(2mn)`
`(mn)/(m+n)`
`1/4`
`1/8`
`1/16`
`1`
`0`
`1`
`-1`
None of these
`sin 1^0 > sin 1`
`sin 1^0 < sin 1`
`sin 1^0 =sin 1`
`sin 1^0 = pi/180 sin1`
`0`
`pi/4`
`pi/2`
`pi`
`-cot(x/2)`
`cot(x/2)`
`tan(x/2)`
`-tan(x/2)`
`1`
`1/sqrt2`
`1/sqrt3`
`sqrt3`
`1/4`
`4`
`2`
`1`
`sqrt6 + sqrt3 - sqrt2 + 2`
`sqrt6 + sqrt3 + sqrt2 + 2`
`sqrt6 - sqrt3 + sqrt2 - 2`
`sqrt6 + sqrt3 + sqrt2 - 2`
`1/4`
`1/2`
`1/3`
None of these
`1/4`
`sqrt3/2`
`-1/4`
`-3/4`
`225^0`
`240^0`
`210^0`
None of these
`sqrt3`
`2sqrt3`
`4`
`2`
`0`
`1`
`-1`
`tan A tan B tan C`
`8`
`7`
`4`
`3`
`-1`
`1`
`1/3`
`3`
Only I
Only II
Both I and II
Neither I nor II
`(5pi)/6`
`(2pi)/3`
`(3pi)/4`
`(11pi)/12`
`-4`
`-p^2` tor some odd prime `p`
`(-q/p)` where `p` is an odd prime and `q` is a positive integer with `(q/p)` not an integer
`-p` for some odd prime `p`
`1`
`-1`
`-1/2`
`1/2`
`4`
`3`
`2`
`1`
Column I | Column II | ||
---|---|---|---|
(A) | `tan15^0` | (1) | `-2-sqrt3` |
(B) | `tan75^0` | (2) | `2+sqrt3` |
(C) | `tan105^0` | (3) | `-2+sqrt3` |
(4) | `2-sqrt3` |
`A -> 4 , B -> 1 , C -> 2`
`A -> 4 , B -> 2 , C -> 1`
`A -> 3 , B -> 2 , C -> 1`
`A -> 2 , B -> 1 , C -> 4`
P is finite and positive
P is finite and negative
P = 0
P is not defined
`(5pi)/12`
`pi/3`
`pi/6`
`pi/4`
`cos(2theta) = cos(2phi)-1`
`cos(2theta) = cos(2phi)+1`
`cos(2theta) = [(cos(2phi)-1)/2]`
`cos(2theta) = [(cos(2phi)+1)/2]`
`45^0, 30^0`
`30^0 , 45^0`
`15^0 , 60^0`
`45^0 , 15^0`
`pi/6`
`pi/4`
`pi/3`
`pi/2`
`-1`
`0`
`1`
`2`
`cosA`
`cos(2A)`
`2cos(A/2)`
`sqrt(2cosA)`
`1`
`1/2`
`1/sqrt2`
`sqrt3/2`
identity for only one value of `phi`
not an identity
identity for all values of `phi`
None of the above
`1/2(sqrt(2-sqrt3))`
`1/2(sqrt(2+sqrt3))`
`sqrt2+sqrt3`
`sqrt2-sqrt3`
`1`
`2`
`4`
Many
Assertion : Let `X= {theta = [0, 2pi] sintheta = cos theta}` (A) The number of elements in `X` is `2`.
Reason : (R) `sin theta` and `cos theta` are both negative both in second are fourth quadrants
1 rad
2 rad
3 rad
4 rad
an irrational number and is greater than 1
a rational number but not an integer
an integer
an irrational number and is less than 1
`1`
`-1`
`1/2`
`2`
`tan35^0`
`tan10^0`
`1/sqrt2`
`1`
`pi/6`
`pi/4`
`pi/3`
`pi/2`
`sin2pi : sin(-pi)`
`tan45^0 : tan(-315^0)`
`cot(tan^(-1) 0.5) : tan(cot^(-1) 0.5)`
`tan420^0 : tan(-60^0)`
`(sqrt3+1)/2`
`(sqrt6+sqrt2)/4`
`(sqrt3+sqrt2)/4`
`(sqrt6+1)/2`
Ill > II > I
I > II > Ill
I > Ill > II
Ill > I > II
`1`
`2sin(alpha-beta)`
`sin(alpha-beta)`
`3sin(alpha-beta)`
`1`
`-1`
`0`
`2`
`sin^2 theta + cos^6 theta = sin^6 theta + cos^2 theta`
`cosec^2 theta + cot^6 theta = cosec^6 theta + cot^2 theta`
`sin^2 theta - cos^4 theta = sin^4 theta + cos^2 theta`
`cosec^2 theta + cot^4 theta = cosec^4 theta + cot^2 theta`
`B = npi + A`
`A = 2npi - B`
`A = 2npi + B`
`B = npi - A`
`0`
`1/4`
`8`
`4`
`0`
`1`
`2`
`3`
`0`
`1`
`-1`
`oo`
`0`
`sin A + sin B + sin C`
`cos A + cos B + cos C`
`1`
`0`
`pi/4`
`pi/6`
`pi/3`
`sqrt6+sqrt2`
`-sqrt6+sqrt2`
`sqrt6-sqrt2`
`-sqrt6-sqrt2`
`2 tan beta+tangamma = tanalpha`
`tanbeta+2tangamma = tanalpha`
`tanbeta+tangamma = tanalpha`
`2(tanbeta+tangamma) = tanalpha`