KCET-BHOOM-BHAM

The function 𝑓(𝑥)=[𝑥],𝑤ℎ𝑒𝑟𝑒 [𝑥] denotes greatest integer function is continuous at___

• 1

• 2.5

• 0

• None of these

Which one of the following is not true always?

• if 𝑓(𝑥) is not continuous at 𝑥=𝑎, then it is not differentiable at 𝑥=a

• if 𝑓(𝑥) is continuous at 𝑥=𝑎, then it is differentiable at 𝑥=𝑎

• if 𝑓(𝑥) and 𝑔(𝑥) are differentiable at 𝑥=𝑎, then 𝑓(𝑥)+𝑔(𝑥) is also differentiable 𝑥=a

• If a function 𝑓(𝑥) is continuous at 𝑥=𝑎 , then lim 𝑥→𝑎 𝑓(𝑥) exists

The function 𝑓(𝑥)=𝑒^|𝑥| is

• continuous everywhere but not differentiable at x = 0

• continuous and differentiable everywhere

• not continuous at x = 0

• none of these

If the system of homogenous equations 2𝑥−𝑦+𝑧=0,𝑥−2𝑦+𝑧=0,𝜆𝑥−𝑦+2𝑧=0 has infinitely many solutions, then

• 𝜆=5

• 𝜆=+5,-5

• 𝜆=-5

• None of these

Let 𝑓:𝑅→𝑅 be defined by 𝑓(𝑥)=1/ 𝑥 . Then f is

• one-one

• onto

• bijective

• f is not defined

The domain of 𝑠𝑖𝑛−1[(𝑙nx]

• [-1,1]

• [0,1]

• (1/e,e]

• [0,e]

𝑓:𝑅→𝑅 𝑎𝑛𝑑 𝑔:[0,∞)→𝑅 is defined by 𝑓(𝑥)=𝑥^2𝑎𝑛𝑑 𝑔(𝑥)=√𝑥.

Which one of the following is not true?

• gof(4)=4

• fog(2)=2

• fog(-4)=4

• gof(-2)=2

Which of the following functions is not continuous everywhere?

• 𝑓(𝑥) = sin(x)

• 𝑔(𝑥) = |x|

• ℎ(𝑥) = 1/x

• 𝑗(𝑥) = √x

If |𝑎| = 10,|𝑏| = 2 𝑎𝑛𝑑 𝑎 .𝑏 = 12, then value of |𝑎 × 𝑏| is

• 5

• 10

• 14

• 16

The vectors 𝜆𝑖 + 𝑗 + 2𝑘 , 𝑖 + 𝜆𝑗 − 𝑘 and 2 𝑖 - 𝑗 + 𝜆𝑘 are coplanar if

• -2

• 0

• 1

• -1