The function f(x) = log (x + \(\sqrt{x^2+1}\)) is ___________

(a)

an even function

(b)

an odd function

(c)

a periodic function

(d)

neither an even nor an odd function

The value of log₁₀⁸ + log₁₀⁵- log₁₀⁴ = ___________

(a)

\({ log }_{ 10 }^{ 9 }\)

(b)

\({ log }_{ 10 }^{ 36 }\)

(c)

1

(d)

-1

For x≥2, |x-2|=

(a)

2-x

(b)

2+x

(c)

x-2

(d)

x

\(\left(1+\frac{1}{\lfloor2}+\frac{1}{\lfloor4}+\frac{1}{\lfloor6}+...\right)^2-\left(1+\frac{1}{\lfloor3}+\frac{1}{\lfloor5}+\frac{1}{\lfloor7}+...\right)^2=\)______________

(a)

1

(b)

2

(c)

e

(d)

2e

Find the nearest point on the line 3x + y = 10 from the origin is ______________

(a)

(2, 1)

(b)

(1, 2)

(c)

(3, 1)

(d)

(1,3)

If h² = ab, then the lines represented by ax²+ 2hx + by² = 0 are ______________

(a)

parallel

(b)

perpendicular

(c)

coincident

(d)

None

On using elementary row operation R₁⟶R₁-3R₂ in the following matrix equation \(\begin{pmatrix} 4 & 2 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)________.

(a)

\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & -7 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

(b)

\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} -1 & -3 \\ 1 & 1 \end{pmatrix}\)

(c)

\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 1 & -7 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

(d)

\(\begin{pmatrix} 4 & 2 \\ -5 & -7 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ -3 & -3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

The vector in the direction of the vector\(\hat{i}-2\hat{j}+2\hat{k}\) that has magnitude 9 is _________ .

(a)

\(\hat{i}-2\hat{j}+2\hat{k}\)

(b)

\(\frac { \hat { i } -2\hat { j } +2\hat { k } }{ 3 } \)

(c)

3(\(\hat{i}-2\hat{j}+2\hat{k}\))

(d)

9(\(\hat{i}-2\hat{j}+2\hat{k}\))

The slope of the graph of \(f\left( x \right) =\frac { \left| x \right| }{ x } ,x>0\quad is\)

(a)

1

(b)

0

(c)

-1

(d)

undefined

 Choose the correct or the most suitable answer from the given four alternatives.
If \(y=\log _{ a }{ x } \) then \(\frac { dy }{ dx } \) is ______

(a)

\(\frac { 1 }{ x } \)

(b)

\(\frac { 1 }{ x\log _{ e }{ a } } \)

(c)

\(\log { _{ e }^{ a } } \)

(d)

\(\frac { 1 }{ \log _{ a }{ x } } \)