Full Portion - Important One Mark Question Paper

11th Standard

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Business Mathematics

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

    Multiple  Choice Question

    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. The value of the determinant \({\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}\)is

    (a)

    abc

    (b)

    0

    (c)

    a2b2c2

    (d)

    -abc

  3. 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

  4. The number of Hawkins-Simon conditions for the viability of an input - output analysis is

    (a)

    1

    (b)

    3

    (c)

    4

    (d)

    2

  5. 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)

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

  6. If A \(=\begin{pmatrix} -1 & 2 \\ 1 & -4 \end{pmatrix}\) then A (adj A) is 

    (a)

    \(\begin{pmatrix} -4 & -2 \\ -1 & -1 \end{pmatrix}\)

    (b)

    \(\begin{pmatrix} 4 & -2 \\ -1 & 1 \end{pmatrix}\)

    (c)

    \(\begin{pmatrix} 2 & 0 \\ 0 & 2 \end{pmatrix}\)

    (d)

    \(\begin{pmatrix} 0 & 2 \\ 2 & 0 \end{pmatrix}\)

  7. If A is an invertible matrix of order 2, then det (A-1) be equal to

    (a)

    det (A)

    (b)

    \({{1}\over{det(A)}}\)

    (c)

    1

    (d)

    0

  8. If A is 3 x 3 matrix and |A|= 4, then |A-1| is equal to

    (a)

    \({{1}\over{4}}\)

    (b)

    \({{1}\over{16}}\)

    (c)

    2

    (d)

    4

  9. If \(\begin{vmatrix} x & 2 \\ 8 &5 \end{vmatrix}=0\) then the value of x is

    (a)

    \({{-5}\over{6}}\)

    (b)

    \({{5}\over{6}}\)

    (c)

    \({{-16}\over{5}}\)

    (d)

    \({{16}\over{5}}\)

  10. 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

  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 number of diagonals in a polygon of n seates is equal to

    (a)

    nC2

    (b)

    nC2 - 2

    (c)

    nC2 - n

    (d)

    nC2 - 1

  14. The term containing x3 in the expansion of (x - 2y)7 is

    (a)

    3rd

    (b)

    4th

    (c)

    5th

    (d)

    6th

  15. 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

  16. 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

  17. There are 10 true or false questions in an examination. Then these questions can be answered in

    (a)

    240 ways 

    (b)

    120 ways 

    (c)

    1024 ways 

    (d)

    100 ways 

  18. 13 guests have participated in a dinner. The number of handshakes happened in the dinner is

    (a)

    715

    (b)

    78

    (c)

    286

    (d)

    13

  19. Number of words with or without meaning that can be formed using letters of the word "EQUATION" , with no repetition of letters is

    (a)

    7!

    (b)

    3!

    (c)

    8!

    (d)

    5!

  20. Sum of the binomial co-efficients is

    (a)

    2n

    (b)

    n2

    (c)

    2n

    (d)

    n + 17

  21. The angle between the pair of straight lines x2 - 7xy + 4y2 = 0

    (a)

    \(tan^{-1}\left(1\over 3\right)\)

    (b)

    \(tan^{-1}\left(1\over 2\right)\)

    (c)

    \(tan^{-1}\left(\sqrt{33}\over 5\right)\)

    (d)

    \(tan^{-1}\left(5\over\sqrt{33}\right)\)

  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 x - intercept of the straight line 3x + 2y - 1 = 0 is

    (a)

    3

    (b)

    2

    (c)

    1/3

    (d)

    1/2

  24. 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)

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

  25. The length of the tangent from (4,5) to the  circle x2 +y2 = 16 is

    (a)

    4

    (b)

    5

    (c)

    16

    (d)

    25

  26. The centre of the circle x2 + y - 2x + 2y - 9 = 0 is

    (a)

    (1,1)

    (b)

    (-1,-1)

    (c)

    (-1,1)

    (d)

    (1, -1)

  27. ax2 + 4xy + 2y2 = 0 represents a pair of parallel lines then 'a' is

    (a)

    2

    (b)

    -2

    (c)

    4

    (d)

    -4

  28. If the perimeter of the circle is 8π units and centre is (2,2) then the equation of the circle is

    (a)

    (x - 2)2 + (y - 2)2 = 4

    (b)

    (x - 2)2 + (y - 2)2 = 16

    (c)

    (x - 4)2 + (y - 4)2 = 2

    (d)

    x2 + y2 =4

  29. The equation of the circle with centre (3,-4) and touches the x - axis

    (a)

    (x - 3)2 +(y - 4)2 = 4

    (b)

    (x - 3)2 +(y + 4)2 =16

    (c)

    (x-3)2+(y- 4)2=16

    (d)

    x2+y2=16

  30. The equation of directrix of the parabola y2 = - x is

    (a)

    4x+ 1 =0

    (b)

    4x - 1 = 0

    (c)

    x - 4=0

    (d)

    x + 4 = 0

  31. The degree measure of \(\frac{\pi}{8}\) is

    (a)

    20o60'

    (b)

    22o30'

    (c)

    20o60'

    (d)

    20o30'

  32. 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

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

    (a)

    -1

    (b)

    cos2 A

    (c)

    sec2 A

    (d)

    1

  34. The value of cos245o-sin245o is

    (a)

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

    (b)

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

    (c)

    0

    (d)

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

  35. The value 4cos340o-3cos40o is

    (a)

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

    (b)

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

    (c)

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

    (d)

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

  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. 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)

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

  38. The value of \(cosec^{-1}\left(\frac{2}{\sqrt{3}}\right)\) is

    (a)

    \(\frac{\pi}{4}\)

    (b)

    \(\frac{\pi}{2}\)

    (c)

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

    (d)

    \(\frac{\pi}{6}\)

  39. \(\tan\left(\frac{\pi}{4}-x\right)\) is

    (a)

    \(\left(\frac{1+\tan x}{1-\tan x}\right)\)

    (b)

    \(\left(\frac{1-\tan x}{1+\tan x}\right)\)

    (c)

    1-tan x

    (d)

    1+tan x

  40. If p sec 50o=tan 50o then p is

    (a)

    cos 50o

    (b)

    sin 50o

    (c)

    tan 50o

    (d)

    sec 50o

  41. Let \(f\left( x \right) =\begin{cases} { x }^{ 2 }-4x\quad ifx\ge 2 \\ x+2\quad ifx<2 \end{cases}\), then f(5) is

    (a)

    -1

    (b)

    2

    (c)

    5

    (d)

    7

  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 minimum value of the function f(x)= Ixl is

    (a)

    0

    (b)

    -1

    (c)

    +1

    (d)

    \(-\infty \)

  45. Which of the following function is neither even nor odd?

    (a)

    f(x) = x3 + 5

    (b)

    f(x) = x5

    (c)

    f(x) = x10

    (d)

    f(x) = x2

  46. f(x) = - 5 , for all \(x\epsilon R\), is a

    (a)

    an identity function

    (b)

    modulus function

    (c)

    exponential function

    (d)

    constant function

  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. If y = x and z = \(\frac{1}{x}\) then \(\frac{dy}{dz}=\)

    (a)

    x2

    (b)

    1

    (c)

    -x2

    (d)

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

  49. If y = e2x then \(\frac{d^2y}{dx^2}\) at x = 0 is

    (a)

    4

    (b)

    9

    (c)

    2

    (d)

    0

  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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