List of top Mathematics Questions asked in KEAM

∫\dfrac{x+5}{x^{2}+1}dx=

$∫sin^2 πx dx =$ ?

\int\frac{1}{x^2-2x+2}dx=

\lim_{x\to0}\dfrac{ln(1+(ln5)x)}{5^{x}}-1

If

y=x^{e^x}+x^{e} for x>0

,the

\dfrac{dy}{dx}

is equal to ?

Let $f:R→R$ be defined by $f(x)=$ { $2x+3,x≤5 3x+α,x>5$ .Then the value of $α$ so that f is continuous on $R$ is

Let

f(x)=αsin^23x

.If

f ′(\dfrac{π}{12})

=

−3

,then the value of

α

is

The equation of the line passing through origin which is parallel to the tangent of the curve

y=\dfrac{x-2}{x-3}

at

x=4

is

The minimum of $f(x)=\sqrt{(10-x^2)}$ in the interval $[-3,2]$ is

Let

f:R→R

be a function defined by

f(x) =   \begin{cases}     3e^x       & \quad \text {if}\  {x<0}\\     x^2+3x+3  & \quad \text {if}\  0≤x<1   \\ x^2-3x-3 & \quad \text {if} \ x≥1\end{cases}

Let

f(x)=(1-1/x)2,x>0

. Then

Let [.]denote the greatest integer function and f(x)=[x]+[2-x],-1≤x≤4.Then

Let

f(x)

={-

5,x≤0 x-5,x>0

and

g(x)=If(x)+2f(IxI)

.Then

g(-2)

will be

The projection of the vector $a=2i-3j+4k$ on the vector $b=i+2j+2k$ is ?

The value of λ for which the vectors

2i-3j+4k

and

-4i+λj-8k

are collinear is

Let x be a real number and a be any non-zero vector such

|(4-x)a|<|3a|

.Then which of the following options is correct?

Let

a

and

b

be perpendicular vectors such that

IaI=√104

and

IbI=6

.Then the value of

Ia-bI

is ?

The position vectors of two points P and Q are given by

OP=2a-b

and

OQ=a+3b

,respectively.If a point R divides the line joining P and Q internally in the ratio

1:2

,then the position vector of the point R is ?

The value of

λ

for which the vectors

i+j-k

and

λi+3j+k

are perpendicular is ?

The direction cosines of the vector

\vec{a} = -2\hat{i} + \hat{j} - \hat{k}

are

Let $a=i+j+2k$ and $b=i-2j+3k$ be two vectors. Then the unit vector in the direction of $a-b$ is

Let, $a=i-j+2k$ . Then the vector in the direction of a with magnitude $5$ units is ?

The value of

\tan^{-1}(√3)-\sec^{-1}(\dfrac{2}{√3})

is ?

The value of

\tan^{-1}(\dfrac{1}{2})+\tan^{-1}(\dfrac{2}{5})

is ?

The value of

cos^{-1}(cos(\dfrac{7\pi}{4}))

is