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

11th Standard

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Maths

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

    Answer all the questions

    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

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TN 11th Standard Maths free Online practice tests

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