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11th Standard Maths English Medium Free Online Test Volume 1 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 A={1,2,3}, B={1,4,6,9} and R is a relation from A to B defined by "x is greater than y". The range of R is

    (a)

    {1,4,6,9}

    (b)

    {4,6,9}

    (c)

    {1}

    (d)

    None of these

  2. If f(x) = |x - 2| + |x + 2|, x ∈ R, then

    (a)

    \(f(x)=\begin{cases}-2x\ if\ x∈(-∞,-2] \\4\ if \ x∈(-2,2]\\ 2x\ if\ x∈(2,∞)\end{cases}\)

    (b)

    \(f(x)=\begin{cases}2x\ if\ x∈(-∞,-2] \\4x\ if \ x∈(-2,2]\\ - 2x\ if\ x∈(2,∞)\end{cases}\)

    (c)

    \(f(x)=\begin{cases}-2x\ if\ x∈(-∞,-2] \\-4x\ if \ x∈(-2,2]\\ 2x\ if\ x∈(2,∞)\end{cases}\)

    (d)

    \(f(x)=\begin{cases}-2x\ if\ x∈(-∞,-2] \\2x\ if \ x∈(-2,2]\\ 2x\ if\ x∈(2,∞)\end{cases}\)

  3. Let S = (1, 2, 3), R be (1, 1) (1, 2) (2, 2) (1, 3) (3, 1), what are the elements to-be included to make R reflexive:

    (a)

    (3, 3)

    (b)

    (2, 3)

    (c)

    (3, 2)

    (d)

    none of these

  4. If \({ log }_{ \sqrt { x } }\) 0.25 =4 ,then the value of x is

    (a)

    0.5

    (b)

    2.5

    (c)

    1.5

    (d)

    1.25

  5. \((\sqrt { 5 } -2)(\sqrt { 5 } +2)\) is equal to

    (a)

    1

    (b)

    3

    (c)

    23

    (d)

    21

  6. Logarithm of 144 to the base 2\(\sqrt{3}\) is

    (a)

    2

    (b)

    3

    (c)

    4

    (d)

    5

  7. If cosec x+cotx=\(\frac { 11 }{ 2 } \) then tanx=

    (a)

    \(\frac { 21 }{ 22 } \)

    (b)

    \(\frac { 15 }{ 16 } \)

    (c)

    \(\frac { 44 }{ 117 } \)

    (d)

    \(\frac { 117 }{ 44 } \)

  8. If tanθ=\(\frac{-4}{3}\), then sinθ is

    (a)

    \(\frac{-4}{5}\)

    (b)

    \(\frac{4}{5}\)

    (c)

    \(\frac{-4}{5}\quad or\quad \frac{4}{5}\)

    (d)

    None

  9. If sinθ=sin\(\alpha\), then the angles θ and \(\alpha\) are related by

    (a)

    \(\theta=n\pi\pm\alpha\)

    (b)

    \(\theta=2n\pi+(-1)^n\alpha\)

    (c)

    \(\alpha=n\pi\pm(-1)^n\theta\)

    (d)

    \(\theta=(2n+1)\pi+\alpha\)

  10. Choose the incorrect pair:

    (a)

    sinx - x ∈ R

    (b)

    cos x - x ∈ R

    (c)

    log x x>0

    (d)

    e-x - x>0

  11. Find the incorrect pair

    (a)

    \(\\ \frac { a }{ sin\ A } =\frac { b }{ sin\ B } =\frac { C }{ sin\ C } \) - 2R

    (b)

    \(\frac { { b }^{ 2 }+{ c }^{ 2 }-{ a }^{ 2 } }{ 2bc } \) - cos A

    (c)

    \(\frac { a-b }{ a+b } cot\frac { c }{ 2 } \) - tan\(\frac{A-B}{2}\)

    (d)

    \(\frac { { a }^{ 2 }+{ c }^{ 2 }-{ b }^{ 2 } }{ 2ac } \) - cos C

  12. The number of five digit telephone numbers having at least one of their digits repeated is

    (a)

    90000

    (b)

    10000

    (c)

    30240

    (d)

    69760

  13. The product of r consecutive positive integers is divisible by

    (a)

    r!

    (b)

    r!+1

    (c)

    (r+1)

    (d)

    none of these

  14. There are 10 lamps in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated is

    (a)

    102

    (b)

    1023

    (c)

    210

    (d)

    10!

  15. The number of ways of disturbing 7 identical balls in 3 distinct boxes, so that no box is empty is

    (a)

    7

    (b)

    6

    (c)

    35

    (d)

    15

  16. If \(\frac { 1 }{ 7! } +\frac { 1 }{ 8! } =\frac { A }{ 9! } ,\) then the value of A is

    (a)

    72

    (b)

    82

    (c)

    9

    (d)

    92

  17. Assertion (A): Every body in a room shakes hands with everybody else. The total number of persons in the room is n. The number of hand shakes is \(\frac{n(n-1)}{2}\)
    Reason (R): The number of handshakes is nC2

    (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 explantion of A

    (c)

    A is true R is false

    (d)

    is false R is true

  18. The coefficient of x5 in the series e-2x is

    (a)

    \(\frac { 2 }{ 3 } \)

    (b)

    \(\frac { 2 }{ 3 } \)

    (c)

    \(\frac { -4 }{ 15 } \)

    (d)

    \(\frac { 4 }{ 15 } \)

  19. The series for log \(\left( \frac { 1+x }{ 1-x } \right) is\)

    (a)

    \(x+\frac { { x }^{ 3 } }{ 3 } +\frac { { x }^{ 5 } }{ 5 } +...+\infty \)

    (b)

    \(2\left[ x+\frac { { x }^{ 3 } }{ 3 } +\frac { { x }^{ 5 } }{ 5 } +...+\infty \right] \)

    (c)

    \(\frac { { x }^{ 2 } }{ 2 } +\frac { { x }^{ 4 } }{ 4 } +\frac { { x }^{ 6 } }{ 6 } +...+\infty \)

    (d)

    \(2\left[ \frac { { x }^{ 2 } }{ 2 } +\frac { { x }^{ 4 } }{ 4 } +\frac { { x }^{ 6 } }{ 6 } +...+\infty \right] \)

  20. The first and last term of an A. P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be

    (a)

    5

    (b)

    6

    (c)

    7

    (d)

    8

  21. The equation of the line with slope 2 and the length of the perpendicular from the origin equal to \(\sqrt5\) is

    (a)

    x+2y=\(\sqrt5\)

    (b)

    2x+y=\(\sqrt5\)

    (c)

    2x+y=5

    (d)

    x+2y-5=0

  22. If the lines x + q = 0, y - 2 = 0 and 3x + 2y + 5 = 0 are concurrent, then the value of q will be

    (a)

    2

    (b)

    2

    (c)

    3

    (d)

    5

  23. The lines x cos \(\alpha\)+ysin\(\alpha\)=p and xcos\(\beta\)+ysin\(\beta\)=q will be perpendicular if

    (a)

    \(\alpha =\beta\)

    (b)

    \(\alpha-\beta=\frac{\pi}{2}\)

    (c)

    \(|\alpha-\beta|=\frac{\pi}{2}\)

    (d)

    \(\alpha-\beta=0\)

  24. Separate equation of lines for a pair of lines whose equation is x2+xy-12y2=0 are

    (a)

    x+4y=0 and x+3y=0

    (b)

    2x-3y=0 and x-4y=0

    (c)

    x-6y=0 and x-3y=0

    (d)

    x+4y=0 and x-3y=0

  25. The locus of a point which is collinear with the points (a,0) and (0,b) is

    (a)

    x+y=1

    (b)

    \(\frac{x}{a}+\frac{y}{b}=1\)

    (c)

    x+y=ab

    (d)

    \(\frac{x}{a}-\frac{y}{b}=1\)

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