Important One Mark Question Paper

11th Standard

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Business Mathematics

Time : 01:00:00 Hrs
Total Marks : 50

    Answer ALL Questions

    50 x 1 = 50
  1. The value of x if \(\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0\) is

    (a)

    0, -1

    (b)

    0, 1

    (c)

    -1, 1

    (d)

    -1, -1

  2. adj (AB) is equal to

    (a)

    adj A adj B

    (b)

    adj AT adj BT

    (c)

    adj B adj A

    (d)

    adj BT adj AT

  3. If A = \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\)such that ad - bc \(\neq\) 0 then A-1 is

    (a)

    \({{1}\over{ad-bc}}\begin{pmatrix} d & b \\-c & a\end{pmatrix}\)

    (b)

    \({{1}\over{ad-bc}}\begin{pmatrix} d & b \\c & a\end{pmatrix}\)

    (c)

    \({{1}\over{ad-bc}}\begin{pmatrix} d & -b \\-c & a\end{pmatrix}\)

    (d)

    \({{1}\over{ad-bc}}\begin{pmatrix} d & -b \\c & a\end{pmatrix}\)

  4. The Inverse of matrix of\(\begin{pmatrix} 3 & 1 \\ 5 & 2\end{pmatrix}\) is

    (a)

    \(\begin{pmatrix} 2 & -1 \\-5 & 3 \end{pmatrix}\)

    (b)

    \(\begin{pmatrix} -2 & 5 \\1 & -3 \end{pmatrix}\)

    (c)

    \(\begin{pmatrix} 3 & -1 \\-5 & -3 \end{pmatrix}\)

    (d)

    \(\begin{pmatrix} -3 & 5 \\1 & -2 \end{pmatrix}\)

  5. If A and B are non-singular matrices then, which of the following is incorrect?

    (a)

    A2 = Iimplies A-1 = A

    (b)

    I-1 = I

    (c)

    If AX = B, then X = B-1 A

    (d)

    If A is square matrix of order 3 then |adj A|= |A|2

  6. The value of \(\begin{vmatrix} x & x^2 & -yz & 1 \\ y & y^2 & -zx & 1 \\ z & z^2 & -xy &1 \end{vmatrix}\) is

    (a)

    1

    (b)

    0

    (c)

    -1

    (d)

    -xyz

  7. If A = \(\begin{vmatrix}cos \theta & sin \theta \\ -sin \theta&cons\theta \end{vmatrix}\) then |2A| is equal to

    (a)

    4 cos 2 \(\theta\)

    (b)

    4

    (c)

    2

    (d)

    1

  8. If \(\triangle=\begin{vmatrix} {a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23} \\ {a}_{31} & {a}_{32} & {a}_{33} \end{vmatrix}\) and Aij is cofactor of aij, then value of \(\triangle\) is given by

    (a)

    a11 A31 + a12 A32 + a13 A33

    (b)

    a11 A11 + a12 A21 + a13 A31

    (c)

    a21 A11 + a22 A12 + a23 A13

    (d)

    a11 A11 + a21 A21 + a31 A31

  9. If \(\begin{vmatrix} 4 & 3 \\ 3 & 1 \end{vmatrix}=-5\) then value of \(\begin{vmatrix} 20 & 15 \\ 15 & 5 \end{vmatrix}\) is

    (a)

    -5

    (b)

    -125

    (c)

    -25

    (d)

    0

  10. If nC3 = nC2, then the value of nC4 is

    (a)

    2

    (b)

    3

    (c)

    4

    (d)

    5

  11. The number of ways selecting 4 players out of 5 is

    (a)

    4!

    (b)

    20

    (c)

    25

    (d)

    5

  12. If nPr = 720 (nCr), then r is equal to

    (a)

    4

    (b)

    5

    (c)

    6

    (d)

    7

  13. The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n \(\in\) N is

    (a)

    2

    (b)

    6

    (c)

    20

    (d)

    24

  14. If n is a positive integer, then the number of terms in the expansion (x + a)n is

    (a)

    n

    (b)

    n + 1

    (c)

    n-1

    (d)

    2n

  15. The middle term in the expansion of \({ \left( x+\frac { 1 }{ x } \right) }^{ 10 }\)

    (a)

    10C4\(\left( \frac { 1 }{ x } \right) \)

    (b)

    10C5

    (c)

    10C6

    (d)

    10C7x4

  16. If \(\frac { kx }{ (x+4)(2x-1) } =\frac { 4 }{ x+4 } +\frac { 1 }{ 2x-1 } \) then k is equal to 

    (a)

    9

    (b)

    11

    (c)

    5

    (d)

    7

  17. The number of 3 letter words that can be formed from the letters of the word number when the repetition is allowed are

    (a)

    206

    (b)

    133

    (c)

    216

    (d)

    300

  18. The number of parallelograms that can be formed from the set of four parallel lines intersecting another set of three parallel lines is

    (a)

    18

    (b)

    12

    (c)

    9

    (d)

    6

  19. The value of (5Co + 5C1) + (5C1 + 5C2) + (5C2 + 5C3) + (5C3 + 5C4) + (5C4 + 5C5 ) is

    (a)

    26-2

    (b)

    25-1

    (c)

    28

    (d)

    27

  20. Sum of Binomial co-efficient in a particular expansion is 256, then number of terms in the expansion is

    (a)

    8

    (b)

    7

    (c)

    6

    (d)

    9

  21. Sum of the binomial co-efficients is

    (a)

    2n

    (b)

    n2

    (c)

    2n

    (d)

    n + 17

  22. If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is

    (a)

    (-1, 1)

    (b)

    (1,1)

    (c)

    (1, -1 )

    (d)

    (-1, -1)

  23. The locus of the point P which moves such that P is at equidistance from their coordinate axes is

    (a)

    \(y={1\over x}\)

    (b)

    y=-x

    (c)

    y=x

    (d)

    \(y=-{1\over x}\)

  24. The locus of the point P which moves such that P is always at equidistance from the line x + 2y+ 7 = 0 is

    (a)

    x+2y+2=0

    (b)

    x - 2y + 1 = 0

    (c)

    2x - y + 2 = 0

    (d)

    3x + y + 1=0

  25. Length of the latus rectum of the parabola y2 = - 25x is

    (a)

    25

    (b)

    -5

    (c)

    5

    (d)

    -25

  26. If the centre of the circle is (-a, -b) and radius \(\sqrt{a^2-b^2}\)then the equation of circle is

    (a)

    x2+y2+2ax+2by+2b2=0

    (b)

    x2+y2+2ax +2by-2b2=0

    (c)

    x2 +y2 - 2ax - 2by - 2b2 = 0

    (d)

    x2 + y - 2ax - 2by + 2b2 = 0

  27. Combined equation of co-ordinate axes is

    (a)

    x2-y2=0

    (b)

    x2+y2=0

    (c)

    xy=c

    (d)

    xy=0

  28. If the circle touches x axis, y axis and the line x = 6 then the length of the diameter of the circle is

    (a)

    6

    (b)

    3

    (c)

    12

    (d)

    4

  29. The distance between directrix and focus of a parabola y2 = 4ax is

    (a)

    a

    (b)

    2a

    (c)

    4a

    (d)

    3a

  30. The radian measure of 37o30' is

    (a)

    \(\frac{5\pi}{24}\)

    (b)

    \(\frac{3\pi}{24}\)

    (c)

    \(\frac{7\pi}{24}\)

    (d)

    \(\frac{9\pi}{24}\)

  31. If \(\tan\theta=\frac{1}{\sqrt5}\) and \(\theta\) lies in the first quadrant, then \(\cos\theta\) is

    (a)

    \(\frac{1}{\sqrt6}\)

    (b)

    \(\frac{-1}{\sqrt6}\)

    (c)

    \(\frac{\sqrt5}{\sqrt6}\)

    (d)

    \(\frac{-\sqrt5}{\sqrt6}\)

  32. The value of \(\sin(-420^o)\) is

    (a)

    \(\frac{\sqrt3}{2}\)

    (b)

    \(-\frac{\sqrt3}{2}\)

    (c)

    \(\frac{1}{2}\)

    (d)

    \(\frac{-1}{2}\)

  33. The value of \(\sin 28^o\cos 17^o+\cos 28^o\sin 17^o\) is

    (a)

    \(\frac{1}{\sqrt2}\)

    (b)

    1

    (c)

    \(\frac{-1}{\sqrt2}\)

    (d)

    0

  34. The value of sec A sin(270o+A) is

    (a)

    -1

    (b)

    cos2 A

    (c)

    sec2 A

    (d)

    1

  35. The value of 1-2sin245o is

    (a)

    1

    (b)

    \(\frac{1}{2}\)

    (c)

    \(\frac14\)

    (d)

    0

  36. The value of \(\frac{2\tan30^o}{1+tan^230}\) is

    (a)

    \(\frac12\)

    (b)

    \(\frac{1}{\sqrt3}\)

    (c)

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

    (d)

    \(\sqrt3\)

  37. If \(\sin A=\frac{1}{2}\) then \(4\cos^3A-3\cos A\) is

    (a)

    1

    (b)

    0

    (c)

    \(\frac{\sqrt3}{2}\)

    (d)

    \(\frac{1}{\sqrt{2}}\)

  38. The value of \(\frac{3\tan10^o-\tan^310}{1-3\tan^210}\) is

    (a)

    \(\frac{1}{\sqrt3}\)

    (b)

    \(\frac{1}{2}\)

    (c)

    \(\frac{\sqrt3}2\)

    (d)

    \(\frac{1}{\sqrt2}\)

  39. If \(\alpha\) and \(\beta\) be between 0 and \(\frac{\pi}{2}\) and if \(\cos(\alpha+\beta)=\frac{12}{13}\) and \(\sin(\alpha-\beta)=\frac{3}{5}\) then \(\sin2\alpha\) is 

    (a)

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

    (b)

    0

    (c)

    \(\frac{56}{65}\)

    (d)

    \(\frac{64}{65}\)

  40. The value of \(\frac{1}{cosec(-45^o)}\) is

    (a)

    \(\frac{-1}{\sqrt2}\)

    (b)

    \(\frac{1}{\sqrt2}\)

    (c)

    \(\sqrt2\)

    (d)

    \(-\sqrt2\)

  41. If f(x) = x2 - x + 1, then f (x + 1) is

    (a)

    x2

    (b)

    x

    (c)

    1

    (d)

    x2 + x + 1

  42. For \(f\left( x \right) =\begin{cases} { x }^{ 2 }-4x\quad ifx\ge 2 \\ x+2\quad ifx<2 \end{cases}\) then f(0) is

    (a)

    2

    (b)

    5

    (c)

    -1

    (d)

    0

  43. The graph of the line y = 3 is

    (a)

    Parallel to x-axis

    (b)

    Parallel to y-axis

    (c)

    Passing through the origin

    (d)

    Perpendicular to x-axis

  44. The graph of y = 2x2 is passing through

    (a)

    (0,0)

    (b)

    (2,1)

    (c)

    (2,0)

    (d)

    (0,2)

  45. Which one of the following functions has the property f (x) = \(f\left( \frac { 1 }{ x } \right) \)

    (a)

    \(f\left( x \right) =\frac { { x }^{ 2 }-1 }{ x } \)

    (b)

    \(f\left( x \right) =\frac { 1-{ x }^{ 2 } }{ x } \)

    (c)

    f(x) = x

    (d)

    \(f\left( x \right) =\frac { { x }^{ 2 }+1 }{ x } \)

  46. The range of f(x) = |x|, for all \(x\epsilon R\), is

    (a)

    (0, \(\infty \))

    (b)

    (0, \(\infty \))

    (c)

    (-\(\infty \)\(\infty \))

    (d)

    (1, \(\infty \))

  47. The graph of f(x) = ex is identical to that of

    (a)

    f(x) = ax, a > 1

    (b)

    f(x) = ax, a < 1

    (c)

    f(x) = ax, 0 < a < 1

    (d)

    y = ax +b, a \(\ne\) 0

  48. For what value of x, f(x) = \(\frac{x+2}{x-1}\) is not continuous?

    (a)

    -2

    (b)

    1

    (c)

    2

    (d)

    -1

  49. \(\frac{d}{dx}(\frac{1}{x})\) is equal to

    (a)

    \(-\frac{1}{x^2}\)

    (b)

    \(-\frac{1}{x}\)

    (c)

    log x

    (d)

    \(\frac{1}{x^2}\)

  50. If y = log x then y2 =

    (a)

    \(\frac{1}{x}\)

    (b)

    \(-\frac{1}{x^2}\)

    (c)

    \(-\frac{2}{x^2}\)

    (d)

    e2

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