11th Standard Maths English Medium Free Online Test Volume 2 One Mark Questions 2020

Download Tamil Nadu 11th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

Questions:

Multiple Choice Question

25 x 1 = 25

Assertion (A) : nP_r > nC_r
Reason (R) : nP_r = nC_r x r!

(a)

Both A and (R) are true and (R) is the correct explanation of (A)

(b)

Both A and R are true but (R) is not the correct explanation of A

(c)

A is true R is false

(d)

A is false R is true

Find the odd one of out of the following

(a)

tan x

(b)

$\frac{1}{x}$

(c)

$\\ \\ \\ \\ \\ \\ \\ \frac { { x }^{ 2 }+5x+4 }{ { x }^{ 2 }+4x+4 } $

(d)

cos x

$\int { \frac { 1 }{ 9x^{ 2 }-4 } } $ dx = ________+c.

(a)

log$\left| \frac { 3x-2 }{ 3x+2 } \right| $

(b)

$\frac { 1 }{ 12 } $log$\left| \frac { 3x-2 }{ 3x+2 } \right| $

(c)

12log$\left| \frac { 3x-2 }{ 3x+2 } \right| $

(d)

$\frac { 1 }{ 12 } log\left| \frac { 3x+2 }{ 3x-2 } \right| $

$\int { \frac { 4\left( sin^{ -1 }x \right) ^{ 3 } }{ \sqrt { 1-{ x }^{ 2 } } } } $ dx = ________+c.

(a)

log (sin ^-1x)

(b)

(sin ^-1 x)⁴

(c)

4 (sin^-1 x)⁴

(d)

$\frac { \left( { sin }^{ -1 }x \right) ^{ 4 } }{ 4 } $

$\int { \frac { 1 }{ 2 } } { sec }^{ 2 }$ x dx is _____ + c.

(a)

$\frac { 1 }{ 2 } $ tan x

(b)

tan x

(c)

2 tan x

(d)

none of these

Two dice are thrown. It is known that the sum of the numbers on the dice was less than 6, the probability of getting a sum 3 is

(a)

$\frac { 1 }{ 18 } $

(b)

$\frac { 5 }{ 18 } $

(c)

$\frac { 1 }{ 5 } $

(d)

$\frac { 2 }{ 5 } $

If P(A$\cup $B) = 0.8 and P(A$\cap $B) = 0.3 then $P(\bar { A } )+P(\bar { B } )$ =

(a)

0.3

(b)

0.5

(c)

0.7

(d)

0.9

Three integers are chosen at random from the first 20 integers. The probability that their product is even is

(a)

$\frac { 2 }{ 19 } $

(b)

$\frac { 3 }{ 19 } $

(c)

$\frac { 17 }{ 19 } $

(d)

$\frac { 4 }{ 19 } $

The rate of change of area A of a circle of radius r is

(a)

$2\pi r$

(b)

$2\pi r\frac { dr }{ dt } $

(c)

$\pi { r }^{ 2 }\frac { dr }{ dt } $

(d)

$\pi \frac { dr }{ dt } $

10.

$\lim _{ x\rightarrow 2 }{ \frac { 2{ x }^{ 2 }+x+1 }{ x+2 } } $ is equal to

(a)

$\frac { 1 }{ 2 } $

(b)

(c)

$\frac { 11 }{ 4 } $

(d)

11.

Choose the correct or the most suitable answer from the given four alternatives.
If $y=\sin ^{-1}\left(\frac{1-x^2}{1+x^2}\right)$ then $\frac{dy}{dx}$ is ______

(a)

$\frac { -2 }{ 1+{ x }^{ 2 } } $

(b)

$\frac { 2 }{ 1+{ x }^{ 2 } } $

(c)

$\frac { 1 }{ 2-{ x }^{ 2 } } $

(d)

$\frac { 2 }{ 2-{ x }^{ 2 } } $

12.

Choose the correct or the most suitable answer from the given four alternatives.
If $y=\log \left(\frac{1-x^2}{1+x^2}\right)$ then $\frac{dy}{dx}$ is ______

(a)

$\frac { 4{ x }^{ 3 } }{ 1-{ x }^{ 4 } } $

(b)

$-\frac { 4x }{ 1-{ x }^{ 4 } } $

(c)

$\frac { 1 }{ 4-{ x }^{ 4 } } $

(d)

$\frac { -4{ x }^{ 3 } }{ 1-{ x }^{ 4 } } $

13.

If A and B are square matrices of order 3 and |A| = 5, |B| = 3 then |3 AB| is _____________

(a)

(b)

(c)

135

(d)

405

14.

A letter is taken at random from the letters of the word ‘ASSISTANT’ and another letter is taken at random from the letters of the word ‘STATISTICS’. The probability that the selected letters are the same is

(a)

${7\over 45}$

(b)

${17\over 90}$

(c)

${29\over 90}$

(d)

${19\over 90}$

15.

$\int \frac{x+2}{\sqrt{x^2-1}} d x$ is

(a)

$\sqrt{x^2-1}-2 log|x+\sqrt{x^2-1}|+c$

(b)

$sin^{-1}x-2 log|x+\sqrt{x^2-1}|+c$

(c)

$2 log|x+\sqrt{x^2-1}|-sin^{-1}x+c$

(d)

$\sqrt{x^2-1}+2log|x+\sqrt{x^2-1}|+c$

16.

$\int \frac{\sin ^8 x-\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x} d x$ is

(a)

${1\over2}sin 2x+c$

(b)

$-{1\over2}sin 2x+c$

(c)

${1\over2}cos 2x+c$

(d)

$-{1\over2}cos 2x+c$

17.

$\text { If } f(x)=\left\{\begin{array}{ll} a x^2-b, & -1<x<1 \\ \frac{1}{|x|}, & \text { elsewhere } \end{array} \ \text { is differentiable at } x=1\right. \text {, then }$

(a)

$a={1\over2},b={-3\over 2}$

(b)

$a={-1\over2},b={3\over 2}$

(c)

$a=-{1\over2},b=-{3\over 2}$

(d)

$a={1\over2},b={3\over 2}$

18.

If y = mx + c and f(0) =$f '(0)=1$, then f(2) is

(a)

(b)

(c)

(d)

-3

19.

The value of $lim_{x\rightarrow k^-}x-\left\lfloor x \right\rfloor $ , where k is an integer is

(a)

-1

(b)

(c)

(d)

20.

$lim_{x \rightarrow 0}{a^x-b^x\over x}=$

(a)

log ab

(b)

log$({a\over b})$

(c)

log$({b\over a})$

(d)

${a\over b}$

21.

Vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are inclined at an angle $\theta =120^o$. If $|\overrightarrow{a}|=1,|\overrightarrow{b}|=2,$ then $[(\overrightarrow{a}+3\overrightarrow{b})\times (3\overrightarrow{a}-\overrightarrow{b})]^2$ is equal to

(a)

225

(b)

275

(c)

325

(d)

300

22.

One of the diagonals of parallelogram ABCD with $\overrightarrow{a}$ and $\overrightarrow{b}$ as adjacent sides is $\overrightarrow{a}+\overrightarrow{b}$ The other diagonal $\overrightarrow{BD}$ is

(a)

$\overrightarrow{a}-\overrightarrow{b}$

(b)

$\overrightarrow{b}-\overrightarrow{a}$

(c)

$\overrightarrow{a}+\overrightarrow{b}$

(d)

$\overrightarrow{a}+\overrightarrow{b}\over 2$

23.

If A + I =$\begin{bmatrix} 3& -2 \\ 4 & 1 \end{bmatrix}$, then (A + I )(A - I) is equal to

(a)

$\begin{bmatrix} -5& -4 \\ 8 & -9 \end{bmatrix}$

(b)

$\begin{bmatrix} -5& 4 \\ -8 & 9 \end{bmatrix}$

(c)

$\begin{bmatrix} 5& 4 \\ 8 & 9 \end{bmatrix}$

(d)

$\begin{bmatrix} -5& -4 \\ -8 & -9 \end{bmatrix}$

24.

If the square of the matrix $\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}$ is the unit matrix of order 2, then $\alpha ,\beta $ and $\gamma$ should satisfy the relation.

(a)

1 + $\alpha ^2+\beta \gamma=0$

(b)

1 - $\alpha ^2-\beta \gamma=0$

(c)

1 - $\alpha ^2+\beta \gamma=0$

(d)

1 + $\alpha ^2-\beta \gamma=0$

25.

If A and B are two matrices such that A + B and AB are both defined, then

(a)

A and B are two matrices not necessarily of same order

(b)

A and B are square matrices of same order

(c)

Number of columns of A is equal to the number of rows of B

(d)

A = B.

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Answers Key:

Multiple Choice Question

25 x 1 = 25

(a)
Both A and (R) are true and (R) is the correct explanation of (A)

(d)
cos x

(b)
$\frac { 1 }{ 12 } $log$\left| \frac { 3x-2 }{ 3x+2 } \right| $

(b)
(sin ^-1 x)⁴

(a)
$\frac { 1 }{ 2 } $ tan x

(d)
0.9

(b)
$2\pi r\frac { dr }{ dt } $

10.

11.

(a)
$\frac { -2 }{ 1+{ x }^{ 2 } } $

12.

(b)
$-\frac { 4x }{ 1-{ x }^{ 4 } } $

13.

(d)
405

14.

Assistant Statistics
$\begin{array}{ll} A=2 & S=3 \\ S=3 & T=3 \\ T=2 & A=1 \\ I=1 & I=2 \\ N=1 & C=1 \end{array}$
$\mathrm{n}(\mathrm{S})=9 \mathrm{C}_{1} \times 10 \mathrm{C}_{1}=90$
One letter in I word and another letter (same) in II word the combinations are
$\begin{array}{ll} \mathrm{AA} & \mathrm{A} \\ \mathrm{SSS} & \mathrm{SSS} \\ \mathrm{TT} & \mathrm{TTT} \\ \mathrm{I} & \mathrm{II} \end{array}$
No. of doublets are
AA, AA, SS, SS, SS, SS, SS, SS, S$ SS, SS, TT TT,
TT, TT, TT, TT, II, II
n(A) = 19
$P(A) =\frac{n(A)}{n(S)} $
$=\frac{19}{90} $

15.

$\int \frac{x+2}{\sqrt{x^{2}-1}} d x =\int\left(\frac{x}{\sqrt{x^{2}-1}} d x+\frac{2}{\sqrt{x^{2}-1}}\right) d x $
$=\sqrt{x^{2}-1}+2 \log \left|x+\sqrt{x^{2}-1}\right|+c $

16.

$\sin ^{8} x-\cos ^{8} x =\left(\sin ^{4} x-\cos ^{4} x\right)\left(\sin ^{4} x+\cos ^{4} x\right) $
$=\left(\sin ^{2} x+\cos ^{2} x\right)\left(\sin ^{2} x-\cos ^{2} x\right) $
$\times \left[\left(\sin ^{2} x+\cos ^{2} x\right)^{2}-2 \sin ^{2} x \cos ^{2} x\right] $
$=(1)(-\cos 2 x)\left(1-2 \sin ^{2} x \cos ^{2} x\right) $
$ \therefore \frac{\sin ^{8} x-\cos ^{8} x}{1-2 \sin ^{2} x \cos ^{2} x}=-\cos 2 x $
$ \therefore \int \frac{\sin ^{8} x-\cos ^{8} x}{1-2 \sin ^{2} x \cos ^{2} x} d x=\frac{-\sin 2 x}{2}+c $

17.

Given f is differentiable
$\therefore f^{\prime}\left(1^{-}\right)=f^{\prime}\left(1^{+}\right)=1 $
$f^{\prime}\left(1^{-}\right) =\lim _{x \rightarrow 1^{-}} \frac{f(x)-f(1)}{x+1}=\lim _{x \rightarrow 1^{-}} \frac{\left(a x^{2}-b\right)-(a-b)}{x+1} $
$=\lim _{x \rightarrow 1^{-}} \frac{a x^{2}-b-a+b}{x+1}=\lim _{x \rightarrow 1^{-}} \frac{a\left(x^{2}-1\right)}{x+1} $
$=\lim _{x \rightarrow 1^{-}}-a(x+1) $
$=a(1+1)=2 a $
$\therefore f^{\prime}\left(1^{+}\right) =\lim _{x \rightarrow 1^{+}} \frac{f(x)-f(1)}{x-1}=\lim _{x \rightarrow 1^{+}} \frac{\frac{1}{x}-1}{x-1} $
$=\lim _{x \rightarrow 1^{+}} \frac{1-x}{x(x-1)}=\lim _{x \rightarrow 1^{+}} \frac{-1}{x}=-1$
$\therefore 2 a =-1 $
$a =\frac{-1}{2} $
$\text { and } f(1)=1$
$a-b=1 $
$-1 / 2-1=b $
$b=-3 / 2 $

18.

$y =m x+c $
$f(x) =m x+c \Rightarrow f(0)=c=1 $
$\therefore c =1 $
$f^{\prime}(x) =m $
$f^{\prime}(0) =1=m $
$\therefore m =1 $
$\therefore f(x) =x+1 $
$f(2) =2+1=3 $

19.

$\text { WKT }\left\lfloor k^{-}\right\rfloor=k-1 \text { and }\left\lfloor k^{+}\right\rfloor=k \text { where } k \text { is an integer }$
$\therefore \lim _{x \rightarrow k^{-}} x-\lfloor x\rfloor=k-(k-1)=1$

20.

$\lim _{x \rightarrow \infty} \frac{a^{x}-b^{x}}{x}=\log \frac{a}{b} \cdot(\text { standard result })$

21.

$(\vec{a}+3 \vec{b}) \times(3 \vec{a}-\vec{b}) =3(\vec{a} \times \vec{a})-\vec{a} \times \vec{b}+9 \vec{b} \times \vec{a}-3 \vec{b} \times \vec{b} $
$=\overrightarrow{0}+\vec{b} \times \vec{a}+9(\vec{b} \times \vec{a})-\overrightarrow{0} $
$=10 \vec{b} \times \vec{a} $
$\frac{\sqrt{3}}{2} \times 2 =|\vec{a} \times \vec{b}| $
$|\vec{a} \times \vec{b}| =\sqrt{3} $
$[(\vec{a}+3 \vec{b}) \times(3 \vec{a}-\vec{b})]^{2} =100(\vec{b} \times \vec{a})^{2} $
$=100(\vec{a} \times \vec{b})^{2}=100(\sqrt{3})^{2} $
$=100 \times 3=300 $

22.

$\text { In } \Delta \mathrm{BCD}, \overrightarrow{\mathrm{BD}}=\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CD}}$
$=\overrightarrow{\mathrm{b}}-\overrightarrow{\mathrm{a}}$

23.

$A+I =\left[\begin{array}{cc} 3 & -2 \\ 4 & 1 \end{array}\right] $
$A =\left[\begin{array}{cc} 3 & -2 \\ 4 & 1 \end{array}\right]-\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]=\left[\begin{array}{cc} 2 & -2 \\ 4 & 0 \end{array}\right] $
$A-I =\left[\begin{array}{cc} 2 & -2 \\ 4 & 0 \end{array}\right]-\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]=\left[\begin{array}{ll} 1 & -2 \\ 4 & -1 \end{array}\right] $
$(A+I)(A-I) =\left[\begin{array}{ll} 3 & -2 \\ 4 & 1 \end{array}\right]\left[\begin{array}{ll} 1 & -2 \\ 4 & -1 \end{array}\right] $
$=\left[\begin{array}{ll} 3-8 & -6+2 \\ 4+4 & -8-1 \end{array}\right] $
$=\left[\begin{array}{cc} -5 & -4 \\ 8 & -9 \end{array}\right] $

24.

$\text { Given } \text {matrix } A=\left[\begin{array}{cc} \alpha & \beta \\ \gamma & -\alpha \end{array}\right] \text { is unit matrix }$
$|A|=1 $
$-\alpha^{2}-\beta \gamma=1 $
$1+\alpha^{2}+\beta \gamma=0 $

25.

If A + B and AB are both defined means A & B are square matrices of same order