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

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