#### 11th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Eight

11th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

Answer all the questions

10 x 1 = 10
1. 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

2. The value of log108+log105-log10=

(a)

${ log }_{ 10 }^{ 9 }$

(b)

${ log }_{ 10 }^{ 36 }$

(c)

1

(d)

-1

3. For x≥2, |x-2|=

(a)

2-x

(b)

2+x

(c)

x-2

(d)

x

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

(a)

1

(b)

2

(c)

e

(d)

2e

5. 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)

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

(a)

parallel

(b)

perpendicular

(c)

coincident

(d)

None

7. 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)

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

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

9. 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

10.  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)

$\frac { 1 }{ \log _{ a }{ x } }$