#### 11th Standard Maths English Medium Free Online Test Volume 2 One Mark Questions with Answer Key 2020

11th Standard

Reg.No. :
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Maths

Time : 00:25:00 Hrs
Total Marks : 25

25 x 1 = 25
1. If $\begin{vmatrix}2a & x_1 &y_1 \\ 2b & x_2 & y_2 \\ 2c & x_3 &y_3 \end{vmatrix}={abc\over 2}\neq 0,$then the area of the triangle whose vertices are $\begin{pmatrix} {x_1\over a}, {y_1\over a} \end{pmatrix}$,$\begin{pmatrix} {x_2\over b}, {y_2\over b} \end{pmatrix}$,$\begin{pmatrix} {x_3\over c}, {y_3\over c} \end{pmatrix}$ is

(a)

${1\over 4}$

(b)

${1\over 4} abc$

(c)

${1\over 8}$

(d)

${1\over 8}abc$

2. The value of the determinant of A=$\begin{bmatrix} 0&a &-b \\ -a & 0 & c \\ b & -c & 0 \end{bmatrix}is$

(a)

-2abc

(b)

abc

(c)

0

(d)

a2+b2+c2

3. If $\overrightarrow{a}+2\overrightarrow{b}$ and $3\overrightarrow{a}+m\overrightarrow{b}$ are parallel, then the value of m is

(a)

3

(b)

$1\over3$

(c)

6

(d)

$1\over6$

4. Let f :$R \rightarrow R$ be defined by            then f is

(a)

discontinuous at x = ${1\over 2}$

(b)

continuous at  x = ${1\over 2}$

(c)

continuous everywhere

(d)

discontinuous everywhere

5. $\lim _{ x\rightarrow 1 }{ \frac { { x }^{ m }-1 }{ { x }^{ n }-1 } } is$

(a)

mn

(b)

m+n

(c)

m-n

(d)

$\frac { m }{ n }$

6. The function $f\left( x \right) =\tan { x }$ is discontinuous on the set

(a)

$\left\{ n\pi :\quad n\in z \right\}$

(b)

$\left\{ 2n\pi :\quad n\in z \right\}$

(c)

$\left\{ (2n+1)\frac { \pi }{ 2 } ,\quad n\in z \right\}$

(d)

$\left\{ n\frac { \pi }{ 2 } ,\quad n\in z \right\}$

7. A function f(x) is said to be continuous at x=a if  $\lim _{ x\rightarrow a }{ f\left( x \right) }$is equal to

(a)

$f\left( a \right)$

(b)

$f\left( -a \right)$

(c)

$2f\left( a \right)$

(d)

$f\left( \frac { 1 }{ a } \right)$

8. If the derivative of (ax - 5)e3x at x=0 is -13, then the value of a is

(a)

8

(b)

-2

(c)

5

(d)

2

9. If ,then the right hand derivative of f(x) at x = 2 is

(a)

0

(b)

2

(c)

3

(d)

4

10. Choose the correct or the most suitable answer from the given four alternatives.
$If\sin { (x+y)= } \log { (x+y) }$ then $\frac { dy }{ dx }$ is

(a)

2

(b)

-2

(c)

1

(d)

-1

11. Choose the correct or the most suitable answer from the given four alternatives.
If, $y=a+b{ x }^{ 2 }$ where a, b are arbitrary constants, then

(a)

$\frac { d^{ 2 }y }{ d{ x }^{ 2 } } =2xy$

(b)

$x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } ={ y }_{ 1 }$

(c)

$x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } -\frac { dy }{ dx } +y=0$

(d)

$x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } =2xy$

12. Assertion (A):f (x) =$\begin{cases} \begin{matrix} x+1, & x<2 \end{matrix} \\ \begin{matrix} 2x-1, & x\ge 2 \end{matrix} \end{cases}$ then f'(2) does not exist.
Reason (R) :f(x) is not continuous at 2.

(a)

Both A and it are true and R is the correct explanation of A

(b)

Both A and R are true but R is not the correct explantion of A

(c)

A is true R is false

(d)

A is false R is true

13. If $\int {3^{1\over x}\over x^2}dx=k(3^{1\over x})+c$ ,then the value of k is

(a)

log 3

(b)

-log 3

(c)

$-{1\over log3}$

(d)

${1\over log3}$

14. $\int sin^3 \ xdx$ is

(a)

${-3\over 4}cos \ x-{cos \ 3x\over 12}+c$

(b)

${3\over 4}cos \ x+{cos \ 3x\over 12}+c$

(c)

${-3\over 4}cos \ x+{cos \ 3x\over 12}+c$

(d)

${-3\over 4}sin \ x-{sin \ 3x\over 12}+c$

15. $\int{x^2+cos^2x\over x^2+1}cosec^2xdx$ is

(a)

cot x+sin -1x+c

(b)

-cot x+tan-1x+c

(c)

-tan x+cot-1x+c

(d)

-cot x-tan-1x+c

16. $\int { \frac { 1 }{ 9x^{ 2 }-4 } }$ 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)

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

17. Match List - I with List II.

 List - I List - II i $\int _{ 0 }^{ \frac { \pi }{ 2 } }{ log(tan\quad x)dx }$ a $\frac { 16 }{ 35 }$ ii $\int _{ 0 }^{ 1 }{ x{ (1-x) }^{ 10 }dx }$ b $\frac { 120 }{ 46 }$ iii $\int _{ 0 }^{ \frac { \pi }{ 2 } }{ si{ n }^{ 7 }xdx }$ c $\frac { 1 }{ 132 }$ iv $\int _{ 0 }^{ \infty }{ { x }^{ 5 }{ e }^{ -4x }dx }$ d 0

The Correct match is

(a)
 i ii iii iv d c a b
(b)
 i ii iii iv d c b a
(c)
 i ii iii iv b d c a
(d)
 i ii iii iv b c a d
18. Two items are chosen from a lot containing twelve items of which four are defective, then the probability that at least one of the item is defective

(a)

${19\over 33}$

(b)

${17\over 33}$

(c)

${23\over 33}$

(d)

${13\over 33}$

19. 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)

$\frac { 4 }{ 19 }$

20. 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

21. If A and B are two events such that P(A) = $\frac { 4 }{ 5 }$ and $P(A\cap B)=\frac { 7 }{ 10 }$ then P(B/A) =

(a)

$\frac { 1 }{ 10 }$

(b)

$\frac { 1 }{ 8 }$

(c)

$\frac { 7 }{ 8 }$

(d)

$\frac { 17 }{ 20 }$

22. If P(B)=$\frac { 3 }{ 5 }$, P(A/B)=$\frac { 1 }{ 2 }$ and P(AUB)=$\frac { 4 }{ 5 }$, then P(B/$\bar { A }$) =

(a)

$\frac { 1 }{ 5 }$

(b)

$\frac { 3 }{ 10 }$

(c)

$\frac { 1 }{ 2 }$

(d)

$\frac { 3 }{ 5 }$

23. A flash light has 8 batteries out of which 3 are dead. If 2 batteries are selected without replacement and tested, the probability that both are dead is

(a)

$\frac { 3 }{ 28 }$

(b)

$\frac { 1 }{ 14 }$

(c)

$\frac { 9 }{ 64 }$

(d)

$\frac { 33 }{ 56 }$

24. Choose the incorrect pair :

(a)

P(A) + P (B) -2P(A∩B) - Exactly one of them occur

(b)

P(A∩B) - Simultaneous occurrence of A and B

(c)

peA) + P (B) - P(A∩B) - Occurrence of either A or B or both

(d)

1 - P(A∪B) - Occurrence of only A

25. Choose the correct statement

(a)

Permutation and Combination are equal

(b)

Permutation is greater than combination

(c)

Permutation is lesser than combination

(d)

Permutation and combination are unrelated