the vertices of a parallelogram
the vertices of a rectangle
the vertices of a square
collinear
2
3
4
6
`0`
`8`
`16`
`24`
odd
even
both even and odd
neither even nor odd
`(-1)^k (k -1) pi`
`(-1)^(k-1) (k -1) pi`
`(-1)^k k pi`
`(-1)^(k-1) k pi`
`1` square unit
`2 sqrt2` square unit
`2` square unit
`2 sqrt3` square unit
Column I(Function) | Column I(Maximum value) | ||
---|---|---|---|
(A) | `sin x + cos x` | (P) | `sqrt(10)` |
(B) | `3 sin x + 4 cos x` | (Q) | `sqrt2` |
(C) | `2 sin x + cos x` | (R) | `5` |
(D) | `sin x + 3 cos x` | (S) | `sqrt5` |
2 3 1 4
2 3 4 1
3 2 1 4
3 2 4 1
`[(a^(-1), 0, 0),(0, b^(-1), 0),(0,0,c^(-1))]`
`1/(abc)[(a^(-1), 0, 0),(0, b^(-1), 0),(0,0,c^(-1))]`
`1/(abc)[(1, 0, 0),(0, 1, 0),(0,0,1)]`
`1/(abc)[(a, 0, 0),(0, b, 0),(0,0,c)]`
None of the above
0
`pi/4`
`pi/3`
`pi/2`
`(3 pi)/2 < A < (5 pi)/2` only
`pi/2 < A < (3pi )/2 ` only
`(3 pi)/2 < A < (7 pi)/2`
`0 < A < (3 pi)/2`
`(-pi/2 , pi/2)`
`[-pi/2, pi/2]`
`[0,pi/2]`
`[0,pi]`
1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and
`alpha = beta`
`alpha > beta`
`alpha < beta`
`alpha = 2 beta`
`sqrt3` unit
`2 sqrt3` unit
`sqrt3/2` unit
`1/sqrt3` unit
`P+Q`
`2P+3Q`
`2Q`
`Q`
`(r-p)//(q-r),1//2`
`(p-q)//(q-r),1`
`(q-r)//(p-q),1`
`(r-p)//(p-q),1//2`
`B' uu C'`
`B uu C`
`B' nn C'`
` B nn C`
A
B
C
{ `x : x` is a multiple of 100 }
`1/27`
`1/64`
`1/81`
1
`|vec a|^2`
`2| vec a|^2`
`3| vec a |^2`
`4|vec a|^2`
`5/sqrt13` units
`3/sqrt17` units
`sqrt17` units
`sqrt17/2` units
The local maximum value in large than local maximum value
The local maximum value in smaller than local maximum value
The function has no local maximum
The function has no local minimum
-1
0
1
4
4
2
1
-4
`((p+q) sin alpha)/(p-q)`
`(p sin alpha )/(p + q)`
`(p sin alpha) /( p-q)`
`((p -q) sin alpha ) / ( p +q)`
`2,-3`
`2` only
`1`
`3`
8 and 3
3 and 4
3 and 8
8 and 8
A
B
C
{ `x : x` is a multiple of 100 }
`[(2 +3i, 5 ), ( 7 ,2 -3 i)]`
`[(2 -3i, 5 ), ( 7 , 2 +3 i)]`
`[(2- 3 i, 7 ), ( 5 , 2 + 3 i )]`
`[(2 + 3 i, 5 ) , ( 7 , 2 + 3 i)]`
`|vec a|^2`
`2| vec a|^2`
`3| vec a |^2`
`4|vec a|^2`
`y + sqrt3x + 5 = 0`
`y - sqrt 3 x + 5 = 0`
`y + sqrt 3 x - 5 = 0`
`y - sqrt 3x - 5 = 0`
`21x + 46y - 180 = 0`
`21 x - 46 y + 96 = 0`
`46 x + 21y - 155 = 0`
`46 x - 21 y -29 = 0`
`1`
`cos theta`
`sin theta`
`cos 2 theta`
A
`2 |A| I` , where I is the identity matrix
null matrix whose order is same a that of A
Unit matrix whose order is same as that of A
`(hat a - hat b)`
`( hat a + hat b)`
`(2 hat a - hat b )`
`(2 hat a + hat b)`
`tan [f(x) ]` where `[.]` is the greatest integer function , and ` 1/(f(x))` are both continuous
`tan [f(x) ]` where `[.]` is the greatest integer function , and ` f^(-1) (x)` are both continuous
`tan [f(x) ]` where `[.]` is the greatest integer function , and ` 1/(f(x))` are both discontinuous
`tan [f(x) ]` where `[.]` is the greatest integer function is discontinous but ` 1/(f(x))` is continuous
`0`
`1`
`a +b + c`
`abc`
`(7/3, -8/3 , 0 )`
`(-7/3 , -8/3 , 0)`
`(-7/3, 8/3, 0 )`
`(7/3 , 8/3 , 0 )`
outside the ellipse
inside the ellipse but not at the focus
on the ellipse
at the focus
`4 x^2 + 4 y^2 + 142 x + 47 y + 140 = 0`
`4 x^2 + 4 y^2 - 142 x - 47 y + 138 = 0`
`4x^2 + 4y^2 -142 x + 47 y + 138 = 0`
`4x^2 + 4 y^2 + 150 x - 49y + 138 = 0`
`x/a + y/b + z /c = 1`
`a/x + b / y +c/z = 1`
`a/x + b/y + c/z = 1`
`a/x + b/y + c/z = 2`
`x +2 y + 3z - 6 = 0`
`x +2 y + 3z + 6 = 0`
`3x +4 y + 5 y + 5 z - 8 = 0`
`3x + 4 y + 5 z + 8 = 0`
`52`
`4`
`2`
`1`
`202`
`101`
`51`
`50`
`2^26`
`2^49`
`2^50`
`2^51`
`2^26`
`2^49`
`2^50`
`2^51`
`1`
`4`
`8`
`16`
symmetric only
symmetric and transitive only
equivalane relation
reflexive only
`x= y/(1+y)`
`x=y/(1-y)`
`x= (1+y)/y`
`x= (1-y)/y`
`3x^2+8x+16=0`
`3x^2-8x-16=0`
`3x^2+8x-16=0`
`x^2+8x+16=0`
`0`
`1`
`-1`
`-2`
`n,2`
`n,3`
`n+1,2`
`n+1,3`
`a+b+c`
`b=c+a`
`c=a+b`
`b-c`
`1+ sqrt 3`
`1+ sqrt 5`
`1- sqrt 5`
`sqrt 5-1`
all integers
all integers except `0` and `1`
all integers except `0`
all integers except `1`
`y''+(sin x+ cos x) y'=1`
`y''= (sin x+ cos x)y'`
`y''=(y')^2 + sin x cos x`
`y''+y=0`
Both Statement `I` and Statement `II` are true and Statement `II` is the correct explanation of Statement `I`
Both Statement `I` and Statement `II` are true and Statement `II` is not the correct explanation of Statement `I`
Statement `I` is the true but Statement `II` is false
Statement `I` is the False but Statement `II` is true
`24` minutes
`34` minute
`125` minutes
`135` minutes
`24` minutes
`34` minute
`125` minutes
`135` minutes
`y= x/(phi(x)+c)`
`y= (phi (x))/x+ c`
`y= (phi(x)+ c)/x`
`y= (phi(x))/(x+c)`
`2`
`1`
`0`
`1/2`
`( alpha- beta)(beta- gamma)(alpha- gamma)`
`(alpha- beta)(beta- gamma)(gamma- alpha)`
`(alpha- beta)(beta- gamma)(gamma- alpha)(alpha+ beta+ gamma)`
`0`
`[(-1,6,2),(-2,1,-4),(6,3,1)]`
`[(1,6,-2),(-2,1,4),(6,-3,1)]`
`[(6,1,2),(4,-1,2),(6,3,-1)]`
`[(-6,2,1),(4,-2,1),(3,1,-6)]`
`A^2=-2A`
`A^2=-4A`
`A^2=-3A`
`A^2=4A`
Circle
ellipse
rectangular hyperbola
parabola
`0`
`1`
`pa+qb=rc`
`pa+qb+rc+a+b+c`
`1/6`
`2/3`
`1/3`
`1/2`
`1/3`
`2/3`
`4/9`
`5/9`
`1` only
`2` only
Both `1` and `2`
neither `1` nor `2`
`1/6`
`1/4`
`1/3`
`1/2`
`1` and `2` only
`2` and `3` only
`1` and `3` only
`1 , 2 ` and `3`
` x = y^(1/(log 5)) , y> 0`
` x = y^(log 5) , y> 0`
` x = y^(1/(log 5)) , y < 0`
` x = 5 In , y , y> 0`
`f(x) ` is continuous at ` x = 0` but not differentiable at ` x = 0 `
`f(x) ` is continuous at as well as differentiable at ` x = 0 `
`f(x) ` is discontinuous at ` x = 0`
None of the above
` - (y^2 tan x) /(1 - y log ( cos x))`
` (y^2 tan x) /(1 + y log ( cos x))`
` (y^2 tan x) /(1 - y log ( sin x))`
` (y^2 sin x) /(1 + y log ( sin x))`
`1` and `2` only
`2` and `3` only
`1` and `3` only
`1 , 2` and `3`
` 1` and `2` only
`2` only
`1` only
`1 , 2 ` and `3`
`0`
`1`
` (x - 1)/(x +1)`
` (x + 1)/(x -1)`
`(pix)/4 + x^2/4 +c`
`(pix)/2 + x^2/4 +c`
`(pi)/4 + (pix^2)/4 +c`
`(pix)/4 - x^2/4 +c`
`f'(x) = 2x ` for ` 0 < x <= 1`
`f'(x) = -2x ` for ` 0 < x <= 1`
`f'(x) = -2x ` for ` 0 < x < 1`
`f'(x) = 0 ` for ` 0 < x < oo`
`1` and `2` only
`2` and `3` only
`1` and `3` only
`1 , 2 ` and `3`
`e`
`1/e`
`2/e`
`1`
` a = b = 0`
` a = - b != 0`
` a = b != 0 , h = k`
` a = b != 0`
`l = 1 , m = 1`
`l = 2/pi , m = oo`
`l = 2/pi , m = 0`
`l = 1 , m = oo`
`(1,1)`
`(-1,1)`
`(-1/2,2)`
`(1/3 , 10/3)`
`1/5`
`1/7`
`1/8`
`1/10`
`5/(36)`
`(25)/(36)`
`(25)/(216)`
`(25)/(54)`
`1/(243)`
`(10)/(243)`
`(11)/(243)`
`(13)/(243)`
`(33)/(144)`
`(17)/(72)`
`1/(144)`
`2/9`
` Y = 3 .2X + 58`
` X = 3 .2Y + 58`
` X = -8 + 0 .2 y`
` Y = - 8 + 0.2 X`
`1/(12)`
`3/4`
`1/(15)`
`1/9`
`1:1`
`10 : 9`
` 100 : 91`
`5 : 4`
` 2n`
`n + 1`
`n`
`n/2`
`(mp)/( 1 + mp) `
`(mp)/( 1 + (m -1) p)`
` ((m-1)p)/(1 + ( m -1) p)`
`((m-1) p)/( 1 + mp)`
` x_1 + x_2 > 2 sqrt (x_1 x_2)`
` sqrt (x_1 ) + sqrt (x_2) > sqrt2`
`| sqrt (x_1 ) - sqrt (x_2) | > sqrt2`
` x_1 + x_2 < 2 (sqrt (x_1 x_2) +1)`
`1` only
`2` only
Both `1 ` and `2`
Neither `1` nor `2`
`0.5`
`0.4`
`0.3`
`0`
`0.36`
`0.2`
`0.6`
`0.9`
`8`
`4`
`2`
`0`
`(0 ,1)`
`( 0 , 1/2]`
`( 0 , 1/2)`
None of these
`3` and `2`
`2` and `2`
`2` and `3`
`1` and `3`
` - (2)/(1 + x^2)` for all ` |x | < 1`
` - (2)/(1 + x^2)` for all ` |x | > 1`
` (2)/(1 + x^2)` for all ` |x | < 1`
None of the above
1 and 3 only
2 and 3 only
1 and 2 only
1,2 and 3
`(0 ,oo)`
`( -oo ,oo)`
`( -oo , 0) cup ( 0 , oo)`
`(-1 , oo)`
continuous but not differentiable at ` x = 0`
differentiable at ` x = 0`
not continuous at ` x = 0`
None of the above
` x (In x)^(-1) + c`
` x (In x)^(-2) + c`
` x (In x) + c`
` x (In x)^(2) + c`
`1`
`2`
`3`
`4`
`pi/4`
`pi/2`
`pi/(2 sqrt2)`
`pi/sqrt2`
`25` m
`25 sqrt3 ` m
`50` m
`50 sqrt3` m
1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3
`19958400`
`19954800`
`19952400`
`39916800`