Free Online Test Book Back 1 Mark Questions with Answer Key Part - 2

10th Standard

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Maths

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

    Part A

    20 x 1 = 20
  1. If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

    (a)

    3

    (b)

    2

    (c)

    4

    (d)

    8

  2. If g = {(1,1), (2,3), (3,5), (4,7)} is a function given by g(x) = αx + β then the values of α and β are

    (a)

    (-1,2)

    (b)

    (2,-1)

    (c)

    (-1,-2)

    (d)

    (1,2)

  3. The sum of the exponents of the prime factors in the prime factorization of 1729 is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  4. If 6 times of 6th term of an A.P. is equal to 7 times the 7th term, then the 13th term of the A.P. is

    (a)

    0

    (b)

    6

    (c)

    7

    (d)

    13

  5. The value of (1+ 2+ 3+...+153) - (1 + 2 + 3 +...+ 15)is 

    (a)

    14400

    (b)

    14200

    (c)

    14280

    (d)

    14520

  6. \(\frac {3y - 3}{y} \div \frac {7y - 7}{3y^{2}}\) is

    (a)

    \(\frac {9y}{7}\)

    (b)

    \(\frac {9y^{2}}{(21y - 21)}\)

    (c)

    \(\frac {21y^2 - 42y + 21}{3y^{2}}\)

    (d)

    \(\frac {7(y^{2} - 2y + 1)}{y^{2}}\)

  7. The solution of (2x - 1)2 = 9 is equal to

    (a)

    -1

    (b)

    2

    (c)

    -1, 2

    (d)

    None of these

  8. The number of points of intersection of the quadratic polynomial x2 + 4x + 4 with the X axis is

    (a)

    0

    (b)

    1

    (c)

    0 or 1

    (d)

    2

  9. If A = \(\left( \begin{matrix} 1 & 2 & 3 \\ 3 & 2 & 1 \end{matrix} \right) \), B = \(\left( \begin{matrix} 1 & 0 \\ 2 & -1 \\ 0 & 2 \end{matrix} \right) \) and C = \(\left( \begin{matrix} 0 & 1 \\ -2 & 5 \end{matrix} \right) \), Which of the following statements are correct?
    (i) AB + C =  \(\left( \begin{matrix} 5 & 5 \\ 5 & 5 \end{matrix} \right) \)
    (ii) BC = \(\left( \begin{matrix} 0 & 1 \\ 2 & -3 \\ -4 & 10 \end{matrix} \right) \)
    (iii) BA + C = \(\left( \begin{matrix} 2 & 5 \\ 3 & 0 \end{matrix} \right) \)
    (iv) (AB)C = \(\left( \begin{matrix} -8 & 20 \\ -8 & 13 \end{matrix} \right) \) 

    (a)

    (i) and (ii) only

    (b)

    (ii) and (iii) only

    (c)

    (iii) and (iv) only

    (d)

    all of these

  10. In the adjacent figure \(\angle BAC\) = 90o and AD\(\bot \)BC then 

    (a)

    BD.CD = BC2

    (b)

    AB.AC = BC2

    (c)

    BD.CD = AD2

    (d)

    AB.AC = AD2

  11. The area of triangle formed by the points (−5, 0), (0, −5) and (5, 0) is

    (a)

    0 sq.units

    (b)

    25 sq.units

    (c)

    5 sq.units

    (d)

    none of these

  12. The slope of the line which is perpendicular to a line joining the points (0, 0) and (– 8, 8) is

    (a)

    –1

    (b)

    1

    (c)

    \(\frac13\)

    (d)

    -8

  13. A straight line has equation 8y = 4x + 21. Which of the following is true

    (a)

    The slope is 0.5 and the y intercept is 2.6

    (b)

    The slope is 5 and the y intercept is 1.6

    (c)

    The slope is 0.5 and the y intercept is 1.6

    (d)

    The slope is 5 and the y intercept is 2.6

  14. (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

  15. If sin \(\theta \) = cos \(\theta \), then 2 tan\(\theta \) + sin\(\theta \) -1 is equal to 

    (a)

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

    (b)

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

    (c)

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

    (d)

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

  16. 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)

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

  17. If two solid hemispheres of same base radius r units are joined together along their bases, then curved surface area of this new solid is

    (a)

    4\(\pi\)r2 sq.units

    (b)

    6\(\pi\)r2 sq.units

    (c)

    3\(\pi\)r2 sq.units

    (d)

    8\(\pi\)r2 sq.units

  18. In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If its height is 20 cm, the volume of the material in it is

    (a)

    5600\(\pi\) cm3

    (b)

    1120\(\pi\) cm3

    (c)

    56\(\pi\) cm3

    (d)

    3600\(\pi\) cm3

  19. The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is

    (a)

    1:2:3

    (b)

    2:1:3

    (c)

    1:3:2

    (d)

    3:1:2

  20. If the mean and coefficient of variation of a data are 4 and 87.5% then the standard deviation is

    (a)

    3.5

    (b)

    3

    (c)

    4.5

    (d)

    2.5

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