#### 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,,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 fig AD is the bisector ofÐA. 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.