Free Online Test 1 Mark Questions with Answer Key 2020 - 2021 Part - 6

10th Standard

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Maths

Time : 00:25:00 Hrs
Total Marks : 25

    Part A

    25 x 1 = 25
  1. Let f and g be two functions given by
    f = {(0,1), (2,0), (3,-4), (4,2), (5,7)}
    g = {(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

    (a)

    {0,2,3,4,5}

    (b)

    {–4,1,0,2,7}

    (c)

    {1,2,3,4,5}

    (d)

    {0,1,2}

  2. The function t which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C \(t(C)=\frac { 9c }{ 5 } +32\) is ___________

    (a)

    37

    (b)

    39

    (c)

    35

    (d)

    36

  3. An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is

    (a)

    16 m

    (b)

    62 m

    (c)

    31 m

    (d)

    \(\frac { 31 }{ 2 } \) m

  4. The difference between the remainders when 6002 and 601 are divided by 6 is ____________

    (a)

    2

    (b)

    1

    (c)

    0

    (d)

    3

  5. Sum of first n terms of the series \(\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +...\) is ____________

    (a)

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

    (b)

    \(\sqrt { n } \)

    (c)

    \(\frac { n\left( n+1 \right) }{ \sqrt { 2 } } \)

    (d)

    1

  6. The square root of \(\frac { 256{ x }^{ 8 }{ y }^{ 4 }{ z }^{ 10 } }{ 25{ x }^{ 6 }{ y }^{ 6 }{ z }^{ 6 } } \) is equal to

    (a)

    \(\frac { 16 }{ 5 } \left| \frac { { x }^{ 2 }{ z }^{ 4 } }{ { y }^{ 2 } } \right| \)

    (b)

    \(16\left| \frac { { y }^{ 2 } }{ { x }^{ 2 }{ z }^{ 4 } } \right| \)

    (c)

    \(\frac { 16 }{ 5 } \left| \frac { y }{ x{ z }^{ 2 } } \right| \)

    (d)

    \(\frac { 16 }{ 5 } \left| \frac { x{ z }^{ 2 } }{ y } \right| \)

  7. 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

  8. If \(\frac { p }{ q } =a\) then \(\frac { { p }^{ 2 }+{ q }^{ 2 } }{ { p }^{ 2 }-{ q }^{ 2 } } \) ___________

    (a)

    \(\frac { { a }^{ 2 }+1 }{ { a }^{ 2 }-1 } \)

    (b)

    \(\frac { 1+{ a }^{ 2 } }{ 1-{ a }^{ 2 } } \)

    (c)

    \(\frac { 1-{ a }^{ 2 } }{ 1-{ +a }^{ 2 } } \)

    (d)

    \(\frac { { a }^{ 2 }-1 }{ { a }^{ 2 }+1 } \)

  9. If P and Q are matrices, then which of the following is true?

    (a)

    PQ ≠ QP

    (b)

    (PT)≠ P

    (c)

    P + Q ≠ Q + P

    (d)

    All are true

  10. In figure if PR is tangent to the circle at P and O is the centre of the circle, then \(\angle PQR\) is

    (a)

    120o

    (b)

    100°

    (c)

    110°

    (d)

    90°

  11. In the given figure if OC = 9 cm and OB = 15 cm then OB + BD is equal to ____________

    (a)

    23 cm

    (b)

    24 cm

    (c)

    27 cm

    (d)

    30 cm

  12. If A is a point on the Y axis whose ordinate is 8 and B is a point on the X axis whose abscissae is 5 then the equation of the line AB is

    (a)

    8x + 5y = 40

    (b)

    8x - 5y = 40

    (c)

    x = 8

    (d)

    y = 5

  13. The four vertices of a quardrilateral are (1, 2), (5, -6), (7, -4) and (k, -2) taken in order. If the area of quadrilateral is zero then find the value of k.

    (a)

    4

    (b)

    -2

    (c)

    6

    (d)

    3

  14. The y-intercept of the line 3x - 4y + 8 = 0 is ___________

    (a)

    \(-\frac { 8 }{ 3 } \)

    (b)

    \(\frac { 8 }{ 3 } \)

    (c)

    2

    (d)

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

  15. (1 + tan \(\theta \) + sec\(\theta \)) (1 + cot\(\theta \) - cosec\(\theta \)) is equal to 

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    -1

  16. If cos9∝ = sin∝ and 9∝ < 90o, then the value of tan t∝ is

    (a)

    \(\frac{1}{\sqrt{3}}\)

    (b)

    \({\sqrt{3}}\)

    (c)

    1

    (d)

    0

  17. The maximum value of sin θ is ___________

    (a)

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

    (b)

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

    (c)

    1

    (d)

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

  18. (sec A + tan A)(1 - sin A) is equal to ___________

    (a)

    sec A

    (b)

    sin A

    (c)

    cosec A

    (d)

    cos A

  19. A ladder of length 14m just reaches the top of a wall. If the ladder makes an angle of 60o with the horizontal, then the height of the wall is ____________

    (a)

    \(14\sqrt { 3 } \)

    (b)

    \(28\sqrt { 3 } \)

    (c)

    \(7\sqrt { 3 } \)

    (d)

    \(35\sqrt { 3 } \)

  20. The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be

    (a)

    12 cm

    (b)

    10 cm

    (c)

    13 cm

    (d)

    5 cm

  21. 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)

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

  22. The radius of a wire is decreased to one-third of the original. If volume the same, then the length will be increased _______of the original.

    (a)

    3 times

    (b)

    6 times

    (c)

    9 times

    (d)

    27 times

  23. Which of the following is incorrect?

    (a)

    P(A) > 1

    (b)

    0 ≤ P(A) ≤ 1

    (c)

    P(ф) = 0

    (d)

    P(A) + P(\(\bar { A } \)) = 1

  24. The mean of a observation x1, x2, x3, ......... xn is \(\bar { x } \). If each observation is multiplied by p, there the mean of the new observations is ___________

    (a)

    \(\frac { \bar { x } }{ p } \)

    (b)

    p\(\bar { x } \)

    (c)

    \(\bar { x } \)

    (d)

    P+\(\bar { x } \)

  25. In a competition containing two events A and B, the probability of winning the events A and B are \(\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 4 } \) respectively and the probability if winning both events is ___________

    (a)

    \(\frac { 1 }{ 12 } \)

    (b)

    \(\frac { 5 }{ 12 } \)

    (c)

    \(\frac { 1 }{ 12 } \)

    (d)

    \(\frac { 7 }{ 12 } \)

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