Free Online Test Book Back 1 Mark Questions with Answer Key Part - 1

10th Standard

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Maths

Time : 00:20:00 Hrs
Total Marks : 20

    Part A

    20 x 1 = 20
  1. A = {a,b,p}, B = {2,3}, C = {p,q,r,s} then n[(A U C) x B] is

    (a)

    8

    (b)

    20

    (c)

    12

    (d)

    16

  2. Let f(x) = \(\sqrt { 1+x^{ 2 } } \) then

    (a)

    f(xy) = f(x).f(y)

    (b)

    f(xy) ≥ f(x).f(y)

    (c)

    f(xy) ≤ f(x).f(y)

    (d)

    None of these

  3. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

    (a)

    2025

    (b)

    5220

    (c)

    5025

    (d)

    2520

  4. The next term of the sequence \(\frac { 3 }{ 16 } ,\frac { 1 }{ 8 } ,\frac { 1 }{ 12 } ,\frac { 1 }{ 18 } \), ..... is

    (a)

    \(\frac { 1 }{ 24 } \)

    (b)

    \(\frac { 1 }{ 27 } \)

    (c)

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

    (d)

    \(\frac { 1 }{ 81 } \)

  5. A system of three linear equations in three variables is inconsistent if their planes

    (a)

    intersect only at a point

    (b)

    intersect in a line

    (c)

    coincides with each other

    (d)

    do not intersect

  6. y2 + \(\frac {1}{y^{2}}\) is not equal to

    (a)

    \(\frac {y^{2} + 1}{y^{2}}\)

    (b)

    \({ \left( y+\frac { 1 }{ y } \right) }^{ 2 }\)

    (c)

    \({ \left( y-\frac { 1 }{ y } \right) }^{ 2 }+2\)

    (d)

    \({ \left( y+\frac { 1 }{ y } \right) }^{ 2 }-2\)

  7. Graph of a linear equation is a ____________

    (a)

    straight line

    (b)

    circle

    (c)

    parabola

    (d)

    hyperbola

  8. Find the matrix X if 2X + \(\left( \begin{matrix} 1 & 3 \\ 5 & 7 \end{matrix} \right) =\left( \begin{matrix} 5 & 7 \\ 9 & 5 \end{matrix} \right) \)

    (a)

    \(\left(\begin{array}{cc} -2 & -2 \\ 2 & -1 \end{array}\right)\)

    (b)

    \(\left(\begin{array}{cc} 2 & 2 \\ 2 & -1 \end{array}\right)\)

    (c)

    \(\left(\begin{array}{ll} 1 & 2 \\ 2 & 2 \end{array}\right)\)

    (d)

    \(\left(\begin{array}{ll} 2 & 1 \\ 2 & 2 \end{array}\right)\)

  9. In a \(\triangle\)ABC, AD is the bisector \(\angle\)BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. The length of the side AC is

    (a)

    6 cm

    (b)

    4 cm

    (c)

    3 cm

    (d)

    8 cm

  10. In figure CP and CQ are tangents to a circle with centre at O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then the length of BR is

    (a)

    6 cm

    (b)

    5 cm

    (c)

    8 cm

    (d)

    4 cm

  11. The slope of the line joining (12, 3), (4, a) is \(\frac 18\)The value of ‘a’ is

    (a)

    1

    (b)

    4

    (c)

    -5

    (d)

    2

  12. (2, 1) is the point of intersection of two lines.

    (a)

    x - y - 3 = 0; 3x - y - 7 = 0

    (b)

    x + y = 3; 3x + y = 7

    (c)

    3x + y = 3; x + y = 7

    (d)

    x + 3y - 3 = 0; x - y - 7 = 0

  13. If sin \(\theta \) + cos\(\theta \) = a and sec \(\theta \) + cosec \(\theta \) = b, then the value of b(a- 1) is equal to 

    (a)

    2a

    (b)

    3a

    (c)

    0

    (d)

    2ab

  14. The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point ‘b’ metres above the first, the depression of the foot of the pole is 60°. The height of the pole (in metres) is equal to

    (a)

    \(\sqrt { 3 } \) b

    (b)

    \(\frac { b }{ 3 } \)

    (c)

    \(\frac { b }{ 2 } \)

    (d)

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

  15. The total surface area of a cylinder whose radius is \(\frac{1}{3}\)of its height is

    (a)

    \(\frac { 9\pi { h }^{ 2 } }{ 8 } \) sq.units

    (b)

    24\(\pi\)h2 sq.units

    (c)

    \(\frac { 8\pi { h }^{ 2 } }{ 9 } \) sq.units

    (d)

    \(\frac { 56\pi { h }^{ 2 } }{ 9 } \) sq.units

  16. The total surface area of a hemi-sphere is how much times the square of its radius.

    (a)

    \(\pi\)

    (b)

    4\(\pi\)

    (c)

    3\(\pi\)

    (d)

    2\(\pi\)

  17. The volume (in cm3) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

    (a)

    \(\frac{4}{3}\pi\)

    (b)

    \(\frac{10}{3}\pi\)

    (c)

    \(5\pi\)

    (d)

    \(\frac{20}{3}\pi\)

  18. If the standard deviation of x, y, z is p then the standard deviation of 3x + 5, 3y + 5, 3z + 5 is

    (a)

    3p + 5

    (b)

    3p

    (c)

    p + 5

    (d)

    9p + 15

  19. The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is

    (a)

    \(\frac { q }{ p+q+r } \)

    (b)

    \(\frac { p }{ p+q+r } \)

    (c)

    \(\frac { p+q }{ p+q+r } \)

    (d)

    \(\frac { p+r }{ p+q+r } \)

  20. If a letter is chosen at random from the English alphabets {a, b,...,z}, then the probability that the letter chosen precedes x

    (a)

    \(\frac{12}{13}\)

    (b)

    \(\frac{1}{13}\)

    (c)

    \(\frac{23}{26}\)

    (d)

    \(\frac{3}{26}\)

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