Term II Model Question Paper

10th Standard EM

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Maths

Time : 02:30:00 Hrs
Total Marks : 100
    14 x 1 = 14
  1. If n(A x B) =6 and A={1,3} then n(B) is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    6

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

    (a)

    linear

    (b)

    cubic

    (c)

    reciprocal

    (d)

    quadratic

  3. If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

    (a)

    4

    (b)

    2

    (c)

    1

    (d)

    3

  4. 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

  5. If \(\triangle\)ABC is an isosceles triangle with \(\angle\)C=90o and AC = 5 cm, then AB is

    (a)

    2.5 cm

    (b)

    5 cm

    (c)

    10 cm

    (d)

    \(5\sqrt { 2 } \)cm

  6. A tangent is perpendicular to the radius at the

    (a)

    centre

    (b)

    point of contact

    (c)

    infinity

    (d)

    chord

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

    (a)

    3

    (b)

    6

    (c)

    9

    (d)

    12

  8. tan\(\theta \)cosec2\(\theta \)-tan\(\theta \) is equal to 

    (a)

    sec\(\theta \)

    (b)

    \(cot^{ 2 }\theta \)

    (c)

    sin\( \theta \)

    (d)

    \(cot\theta \)

  9. 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 tower is 60°. The height of the tower (in metres) is equal to

    (a)

    \(\sqrt { 3 } \) b

    (b)

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

    (c)

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

    (d)

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

  10. The value of the expression [cosec(75o+θ)-sec (15o-θ)-tan(55o+θ)+cot(35o-θ] is

    (a)

    -1

    (b)

    0

    (c)

    1

    (d)

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

  11. A pole 6 m high a shadow 2\(\sqrt{3}\) m long on the ground, then the sun's elevation is

    (a)

    60o

    (b)

    45o

    (c)

    30o

    (d)

    90o

  12. 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)

    11200\(\pi\) cm3

    (c)

    56\(\pi\) cm3

    (d)

    3600\(\pi\) cm3

  13. The range of the data 8, 8, 8, 8, 8. . . 8 is

    (a)

    0

    (b)

    1

    (c)

    8

    (d)

    3

  14. A purse contains 10 notes of Rs.2000, 15 notes of Rs.500, and 25 notes of Rs.200. One note is drawn at random. What is the probability that the note is either a Rs.500 note or Rs.200 note?

    (a)

    \(\frac{1}{5}\)

    (b)

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

    (c)

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

    (d)

    \(\frac{4}{5}\)

  15. 10 x 2 = 20
  16. If A x B = {(3,2), (3,4), (5,2), (5,4)} then find A and B.

  17. Find the HCF of 396, 504, 636.

  18. Find the sum of
    12+22+...+192

  19. Solve x + 2y - z = 5; x - y + z = -2; -5x - 4y + z = -11

  20. If A = \(\left[ \begin{matrix} 1 & 2 & 0 \\ 3 & 1 & 5 \end{matrix} \right] \), B = \(\left[ \begin{matrix} 8 & 3 & 1 \\ 2 & 4 & 1 \\ 5 & 3 & 1 \end{matrix} \right] \), find AB.

  21. Show that the points P(-1.5,3), Q(6,-2) , R(-3,4) are collinear.

  22. A line makes positive intercepts on coordinate axes whose sum is 7 and it passes through (-3,8). Find its equation

  23. if cosec\(\theta \)+cot\(\theta \)=p, then prove that cos\(\theta \) = \(\frac { { p }^{ 2 }-1 }{ { p }^{ 2 }+1 } \)

  24. The radius of a conical tent is 7 m and the height is 24 m. Calculate the length of the canvas used to make the tent if the width of the rectangular canvas is 4 m?

  25. The number of televisions sold in each day of a week are 13, 8, 4, 9, 7, 12, 10. Find its standard deviation.

  26. 10 x 5 = 50
  27. Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
    (i) R1={(3,7), (4,7), (7,10), (8,1)}
    (ii) R2= {(3,1), (4,12)}
    (iii) R3= {(3,7), (4,10), (7,7), (7,8), (8,11), (8,7), (8,10)}

  28. Can the number 6n, n being a natural number end with the digit 5? Give reason for your answer.

  29. Find the sum of all natural numbers between 300 and 600 which are divisible by 7.

  30. Solve 2x2 - x - 1 = 0

  31. Find the LCM of the following
    x3 - 27, (x - 3)2, x2 - 9.

  32. In the figure, AD is the bisector of \(\angle\)A. If BD = 4 cm, DC= 3 cm and AB= 6 cm, find AC.

  33. Draw a circle of radius 4 cm. At a point L on it draw a tangent to the circle using the alternate segment.

  34. Show that the straight lines 2x + 3y - 8 = 0 and 4x + 6y + 18 = 0 are parrel.

  35. A tower stands vertically on the ground. from a point on the ground,whivh is 48m away from the foot of the tower, the angel of elevation of the top of  the tower is 30°.find the hieght of the tower.

  36. Find the volume of a cylinder whose height is 2 m and whose base area is 250 m2.

  37. 2 x 8 = 16
  38. Let A = {1,2,3,7} and B = {3,0,–1,7}, which of the following are relation from A to B ?
    (i) R1 = {(2,1), (7,1)}
    (ii) R2= {(–1,1)}
    (iii) R3 = {(2,–1), (7,7), (1,3)}
    (iv) R4= {(7,–1), (0,3), (3,3), (0,7)

  39. Using the functions f and g given below, find f o g and g o f. Check wheather f o g = g o f
     f(x)=3+x, g(x)=x-4

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