Free Online Test Book Back 1 Mark Questions Part - Two

10th Standard

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Maths

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

    Part A

    20 x 1 = 20
  1. If f(x) = 2x2 and g(x) = \(\frac{1}{3x}\), then f o g is

    (a)

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

    (b)

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

    (c)

    \(\\ \frac { 2 }{ 9x^{ 2 } } \)

    (d)

    \(\\ \frac { 1 }{ 6x^{ 2 } } \)

  2. f(x) = (x + 1)3 - (x - 1)3 represents a function which is

    (a)

    linear

    (b)

    cubic

    (c)

    reciprocal

    (d)

    quadratic

  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. \(\frac { x }{ { x }^{ 2 }-25 } -\frac { 8 }{ { x }^{ 2 }+6x+5 } \) gives

    (a)

    \(\frac { { x }^{ 2 }-7x+40 }{ \left( x-5 \right) \left( x+5 \right) } \)

    (b)

    \(\frac { { x }^{ 2 }+7x+40 }{ \left( x-5 \right) \left( x+5 \right) \left( x+1 \right) } \)

    (c)

    \(\frac { { x }^{ 2 }-7x+40 }{ \left( { x }^{ 2 }-25 \right) \left( x+1 \right) } \)

    (d)

    \(\frac { { x }^{ 2 }+10 }{ \left( { x }^{ 2 }-25 \right) \left( x+1 \right) } \)

  6. Which of the following should be added to make x4 + 64 a perfect square

    (a)

    4x2

    (b)

    16x2

    (c)

    8x2

    (d)

    -8x2

  7. If A is a 2 x 3 matrix and B is a 3 x 4 matrix, how many columns does AB have

    (a)

    3

    (b)

    4

    (c)

    2

    (d)

    5

  8. The perimeters of two similar triangles ∆ABC and ∆PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then the length of AB is

    (a)

    \(6\frac { 2 }{ 3 } cm\)

    (b)

    \(\frac { 10\sqrt { 6 } }{ 3 } cm\)

    (c)

    \(66\frac { 2 }{ 3 } cm\)

    (d)

    15 cm

  9. The two tangents from an external points P to a circle with centre at O are PA and PB. If \(\angle APB\) = 70o then the value of \(\angle AOB\) is

    (a)

    100°

    (b)

    110°

    (c)

    120°

    (d)

    130°

  10. If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is

    (a)

    3

    (b)

    6

    (c)

    9

    (d)

    12

  11. The equation of a line passing through the origin and perpendicular to the line 7x - 3y + 4 = 0 is

    (a)

    7x - 3y + 4 = 0

    (b)

    3x - 7y + 4 = 0

    (c)

    3x + 7y = 0

    (d)

    7x - 3y = 0

  12. 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

  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. If x = a tan\(\theta \) and y = b sec\(\theta \) then

    (a)

    \(\frac { { y }^{ 2 } }{ { b }^{ 2 } } -\frac { { x }^{ 2 } }{ { a }^{ 2 } } =1\)

    (b)

    \(\frac { x^{ 2 } }{ a^{ 2 } } -\frac { y^{ 2 } }{ b^{ 2 } } =1\)

    (c)

    \(\frac { x^{ 2 } }{ a^{ 2 } } +\frac { y^{ 2 } }{ b^{ 2 } } =1\)

    (d)

    \(\frac { x^{ 2 } }{ a^{ 2 } } -\frac { y^{ 2 } }{ b^{ 2 } } =0\)

  15. A tower is 60 m height. Its shadow is x metres shorter when the sun’s altitude is 45° than when it has been 30°, then x is equal to

    (a)

    41.92 m

    (b)

    43.92 m

    (c)

    43 m

    (d)

    45.6 m

  16. If (sin α + cosec α)+ (cos α + sec α)= k + tan2α + cot2α, then the value of k is equal to

    (a)

    9

    (b)

    7

    (c)

    5

    (d)

    3

  17. If the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

    (a)

    1:2

    (b)

    1:4

    (c)

    1:6

    (d)

    1:8

  18. 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)

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

  19. The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is

    (a)

    3

    (b)

    15

    (c)

    5

    (d)

    225

  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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