#### Term 1 Model Question Paper

11th Standard

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Maths

Time : 02:00:00 Hrs
Total Marks : 60
9 x 1 = 9
1. Let f:R➝R be defined by f(x)=1-|x|. Then the range of f is

(a)

R

(b)

(1,∞)

(c)

(-1,∞)

(d)

(-∞,1]

2. The number of roots of (x+3)4+(x+5)4=16 is

(a)

4

(b)

2

(c)

3

(d)

0

3. If tan400=λ, then $\frac { tan{ 140 }^{ 0 }-tan{ 130 }^{ 0 } }{ 1+tan{ 140 }^{ 0 }.tan{ 130 }^{ 0 } }$=

(a)

$\frac { 1-\lambda ^{ 2 } }{ \lambda }$

(b)

$\frac { 1+{ \lambda }^{ 2 } }{ \lambda }$

(c)

$\frac { 1+{ \lambda }^{ 2 } }{ 2\lambda }$

(d)

$\frac { 1-{ \lambda }^{ 2 } }{ 2\lambda }$

4. In a $\triangle$ ABC, C = 90° then the value of sin A + sin B-2$\sqrt{2} cos{A\over2}cos {B\over 2}is$

(a)

-1

(b)

1

(c)

0

(d)

${1\over 2}$

5. If Pr stands for r Pr then the sum of the series 1+ P1 + 2P2 + 3P3 +...+ nPn is

(a)

Pn+1

(b)

Pn+1-1

(c)

Pn-1+1

(d)

(n+1)P(n-1)

6. The HM of two positive numbers whose AM and GM are 16,8 respectively is

(a)

10

(b)

6

(c)

5

(d)

4

7. 1 - 2x + 3x2 - 4x3 + ..., Ixl< 1 is:

(a)

(1-x)-2

(b)

(1+x)-2

(c)

(1-x)2

(d)

(1+x)2

8. If a vertex of a square is at the origin and its one side lies along the line 4x + 3y - 20 = 0, then the area of the square is

(a)

20 sq. units

(b)

16 sq. units

(c)

25 sq. units

(d)

4 sq.units

9. If(1, 3) (2,1) (9, 4) are collinear then a is:

(a)

$\frac{1}{2}$

(b)

2

(c)

0

(d)

-$\frac{1}{2}$

10. 10 x 2 = 20
11. State whether the following sets are finite or infinite.
{x $\in$ N:x is an even prime number}

12. Solve (2x+1)2-(3x+2)2=0

13. Show that $\frac { (cos\theta -cos3\theta )(sin8\theta +sin2\theta ) }{ (sin5\theta -sin\theta )(cos4\theta -cos6\theta ) } =1$

14. Prove that $\sin { 4\alpha } =4\tan { \alpha } .\frac { 1-\tan ^{ 2 }{ \alpha } }{ { \left( 1+\tan ^{ 2 }{ \alpha } \right) }^{ 2 } }$

15. Find sin15°, cos15° and tan15°. Hence evaluate cot75° + tan75°.

16. Find the values of $sin(-\frac{11\pi}{3})$.

17. How many two-digit numbers can be formed using 1, 2, 3, 4, 5 without repetition of digits?

18. Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?

19. A Mathematics club has 15 members. In that 8 are girls: 6 of the members are to be selected for a competition and half of them should be girls. How many ways of these selections are possible?

20. In the binomial expansion of (a+b)n the coefficients of the 4th and 13th terms are equal to each other, find n.

21. 7 x 3 = 21
22. By taking suitable sets A, B, C, verify the following results:
(A$\times$ B)$\cap$(B$\times$A) = (A$\cap$B) $\times$ (B$\cap$A)

23. Compare and contrast the graph y = x2 - 1, y = 4(x2 - 1) and y = (4x)2 = 1.

24. Find the real roots of x4=16

25. Find the principal value of sec-1$\left( -\sqrt { 2 } \right)$​​​​​​​

26. Show that sin 12o sin 48o sin 54o = $\frac{1}{8}$

27. A polygon has 90 diagonals. Find the number of its sides?

28. Write the first 4 terms of the logarithmic series of log (1 + 4x)

29. 2 x 5 = 10
30. Check the following functions for one-to-oneness and ontoness.
$f:N\rightarrow N$ defined by f(n)=n2.

31. Express each of the following as a product.
sin 50o + sin 40o