IF `f(x) =x^(2) + alpha ` for ` x ge 0` ` and 2 sqrt(x^(2) +1) + beta ` for ` x lt 0` is continuous at ` x=0 and f((1)/(2))=2,` then `alpha ^(2) + beta ^(2)` isA. 3B. `(8)/(25)`C. `(25)/(8)`D. `(1)/(3)`

IF `f(x) =x^(2) + alpha ` for ` x ge 0` ` and 2 sqrt(x^(2) +1) + beta

1.	IF `f(x) =x^(2) + alpha ` for ` x ge 0` ` and 2 sqrt(x^(2) +1) + beta ` for ` x lt 0` is continuous at ` x=0 and f((1)/(2))=2,` then `alpha ^(2) + beta ^(2)` isA. 3B. `(8)/(25)`C. `(25)/(8)`D. `(1)/(3)`
Answer» Correct Answer - C

The sum of the first 10 terms of the series `9+99+999 +….., ` isA. `(9)/(8) (9^(10)-1)`B. `(100)/(9)(10^(9)-1)`C. `(10^(9)-1)`D. `(100)/(9)(10^(10)-1)`
A coin is tossed three times .If X denotes the absolute difference between the number of heads and the number of tails then ` P (X=1)=`A. `(1)/(2)`B. `(2)/(3)`C. `(1)/(6)`D. `(3)/(4)`
IF points `p( 4,5,x),Q (3,y,4) and R (5,8,0) ` are collinear , then the value of ` x + y` isA. `-4`B. `3`C. `5`D. `4`
`int e^(x) [(2+sin 2x)/( 1+cos 2x )]dx =`A. `e^(x) tan x+c`B. `e^(x) + tan x+c`C. `2e^(x) tan x+c `D. ` e^(x) tan 2x +c`
IF ` log _(10)""((x^(3)-y^(3))/(x^(3)+y^(3)))=2` then ` (dy)/(dx)=`A. `(x)/(y)`B. `-(y)/(x)`C. `-(x)/(y)`D. `(y)/(x)`
IF `A =[(1,2,3),(-1,1,2),( 1,2,4)]"then " (A^(2) -5A) A^(-1)=`A. `[(4,2,3),(-1,4,2),(1,2,1)]`B. `[(-4,2,3),(-1,-4,2),(1,2,-1)]`C. `[(-4,-1,1),( 2,-4,2),(3,2,-1)]`D. `[(-1,-2,1),( 4,-2,-3),(1,4,-2)]`
IF `(dx)/(sqrt(16-9x^(2)))=A sin^(-1) (bx )+c ` then `A+B=`A. `(9)/(4)`B. `(19)/(4)`C. `(3)/(4)`D. `(13)/(12)`
IF ` f :R -{2} to R ` is a function defined by ` f(x) =(x^(2)-4)/(x-2)` , then its range isA. `R`B. `R-{2}`C. `R-{4}`D. `R-{-2,2}`
IF ` y= ( tan ^(-1) x)^(2) " then " (x^(2) +1)^(2) (d^(2)y)/(dx^(2))+2x(x^(2)+1)(dy)/(dx)=`A. `4`B. `2`C. `1`D. `0`
The line ` 5x +y-1=0` coincides with one of the lines given by ` 5x^(2) +xy -kx - 2y+2=0` then the value of k isA. `-11`B. `31`C. `11`D. `-31`