`(0, 0)`
`(0, \ frac {2\pi}{3} )`
`(\ frac {\pi}{6}, 0 )`
`(\ frac {\pi}{4}, 0\ )`
`frac {3x-x^3}{1-3x^2}`
`frac {3x+x^3}{1-3x^2}`
`frac {3x+x^3}{1+3x^2}`
`frac {3x+x^3}{1+3x^2}`
(This question may have multiple correct answers)
`\pi`
`\frac{\pi}{2}`
`4 tan^{-1}(5)`
`tan^{-1} ( \frac{65}{156} )`
`-\frac {3\pi}{4}`
`\frac {3\pi}{4}`
`-\frac {\pi}{4}`
`\frac {\pi}{4}`
` \frac{23}{25}`
`\frac{25}{23}`
`\frac{23}{24}`
`\frac{24}{23}`
`2x=3y=6z`
`6x=3y=2z`
`6x=4y=3z`
`x=y=z`
List I | List II | ||
---|---|---|---|
(P) | `[1/y^2 { (cos ( tan^-1 y) + y sin ( tan^-1 y) )/( cost ( sin^-1 y) + tan ( sin^-1 y) ) }^2 + y^4 ]^(1//2)` take value | (1) | `1/2sqrt(5/3)` |
(Q) | If ` cos x + cos y + cos z = 0 = sin x + sin y + sin z`, then possible value of `cos\ \(x -y ) /2` is | (2) | `sqrt2` |
(R) | If `cos (pi/4 -x) cos 2 x + sin x sin 2 x sec x` `= cos x sin 2x sec x + cos ( pi/4 + x ) cos 2 x`, then possible value of sec x is | (3) | `1/2` |
(S) | If `cot ( sin^-1 sqrt( 1 -x^2 ) ) = sin [ tan^-1 (x sqrt 6 ) ]`, x=0 . Then possible value of x is | (4) | 1 |
`(P) -> 3, (Q) -> 4, (R) -> 2` or `4, (S) -> 1`
`(P) -> 4, (Q) -> 3, (R) -> 2` or `4, (S) -> 1`
`(P) -> 2, (Q) -> 3, (R) -> 4` or `2, (S) -> 1`
`(P) -> 4, (Q) -> 1, (R) -> 2` or `4, (S) -> 3`
`x/(sqrt(1+x^2))`
`x`
`xsqrt(1+x^2)`
`sqrt(1+x^2)`
` 1`
`3`
`4`
`5`
`3`
`2`
`- 1/2`
`1/2`
`[−1/4,1/4]`
`[−1/2,1/4]`
`[−1/4,1/2]`
`(−1/2,1/8)`
`-1`
`-2`
`2`
`1`
`1//2`
`1`
`-1//2`
`-1`
`∞`
`2`
`0`
`1`
A
B
`− (2π)/3`
`π/3`
`(5π)/4`
`π/4`
`−7/17`
`7/17`
`−17/7`
`17/7`
`6/17`
`17/6`
`16/7`
None of these
`0`
`1`
`1/2`
`4`
`sqrt6/5`
`−(2sqrt6)/5`
`(5sqrt2)/3`
`− sqrt2/3`
`1/6`
1
1/3
-1