Term 1 Model Question Paper

10th Standard EM

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Maths

Time : 02:00:00 Hrs
Total Marks : 60
    6 x 1 = 6
  1. Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

    (a)

    0, 1, 8

    (b)

    1, 4, 8

    (c)

    0, 1, 3

    (d)

    0, 1, 3

  2. If (x - 6) is the HCF of x2 - 2x - 24 and x2 - kx - 6 then the value of k is

    (a)

    3

    (b)

    5

    (c)

    6

    (d)

    8

  3. Graph of a linear polynomial is a

    (a)

    straight line

    (b)

    circle

    (c)

    parabola

    (d)

    hyperbola

  4. 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

  5. The point of intersection of 3x − y = 4 and x + y = 8 is

    (a)

    (5, 3)

    (b)

    (2, 4)

    (c)

    (3, 5)

    (d)

    (4, 4)

  6. if sin\(\theta \)=cos\(\theta \)=a and sec\(\theta \)+cosec\(\theta \)=b, then the value of b (a2-1) is equal to 

    (a)

    2a

    (b)

    3a

    (c)

    0

    (d)

    2ab

  7. 9 x 2 = 18
  8. Let X={1,2,3,4} and Y={2,4,6,8,10} and R={(1,2),(2,4),(3,6),(4,8)} Show that R is a function and find its domain, co-domain and range?

  9. Find k if f o g(k) = 5 where f(k)=2k-1.

  10. Write an A.P. whose first term is 20 and common difference is 8.

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

  12. If A = \(\left[ \begin{matrix} 2 & 1 \\ 1 & 3 \end{matrix} \right] \), B = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 3 \end{matrix} \right] \) find AB and BA. Check if AB = BA

  13. Prove that tan2\(\theta \)-sin2 \(\theta \) = tan\(\theta \) sin\(\theta \)

  14. Simplify (1+tan2θ)(1-sinθ)(1+sinθ)

  15. Find the depth of a cylindrical tank of radius 28 m, if its capacity is equal to that of a rectangular tank of size 28 m x 16 m x 11 m.

  16. Find the standard deviation of 30, 80, 60, 70, 20, 40, 50 using the direct method.

  17. 4 x 5 = 20
  18. The arrow diagram shows a relationship between the sets P and Q. Write the relation in (i) Set builder form (ii) Roster form (iii) What is the domain and range of R.

  19. The 13th term of an A.P is 3 and the sum of the first 13 terms is 234.Find the common difference and the sum of first 21 terms.

  20. If A = \(\left[ \begin{matrix} 1 & 3 & -2 \\ 5 & -4 & 6 \\ -3 & 2 & 9 \end{matrix} \right] \), B = \(\left[ \begin{matrix} 1 & 8 \\ 3 & 4 \\ 9 & 6 \end{matrix} \right] \), find A + B.

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

  22. 2 x 8 = 16
  23. Let f: A ⟶ B be a function defined by f(x) = \(\frac{x}{2}\)-1, where A={2,4,6,10,12}, B={0,1,2,4,5,9}, Represent f by
    (i) set of ordered pairs
    (ii) a table
    (iii) an arrow diagram
    (iv) a graph

  24. The sum of three consecutive terms that are in A.P. is 27 and their product is 288. Find the three terms.

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