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11th Standard English Medium Maths Subject Creative 3 Mark Questions with Solution Part - I

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 75

    3 Marks

    25 x 3 = 75
  1. Find the quotient of the identity function by the modulus function

  2. Show that the function f : R ⟶ R given by f(x) = cos x for all x ∈ R is neither one-one nor onto.

  3. Which of the following sets are finite and which are infinite?
    Set of concentric circles in a plane.

  4. Write a description of each shaded area. Use symbols U, A, B, C, U, ∩, ' and \ as necessary.

  5. Draw venn diagram of three sets A, B and C which illustrates the following:
    A ∩ B ∩ C

  6. Solve the equation x2/3 + x1/3 - 2 = 0.

  7. Solve \(\sqrt [ 8 ]{{{x}\over{x+3}} } -\sqrt{{{x+3}\over{x}}}=2.\)

  8. Find the value of log2 \(\left({{\sqrt [ 3 ]{4 } }\over{4^2\sqrt{8}}} \right).\)

  9. Simplify: \(\frac{cos(90°+\theta)sec(-\theta)tan(180°-\theta)}{sec(360°-\theta)sin(180°+\theta)cot(90°+\theta)}\)

  10. Prove that sin (A+B) sin (A - B) = cos2B - cos2A.

  11. If \(tan\alpha=\frac{1}{3}\ and\ tan \beta=\frac{1}{7}\) show that \(2\alpha+\beta=\frac{\pi}{4}.\)

  12. Prove that n!(n + 2) = n! + (n + 1)!

  13. How many 3-digit numbers more than 600 can be formed using the digits 2, 3, 4, 6, 7?

  14. If 9P+ 5.9P= 10Pr , find r.

  15. If the letter of the word 'RACHIT' are arranged in all possible ways as listed in dictionary, then what is the rank of the word 'RACHIT'?

  16. How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7 if no digit is repeated?

  17. Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the points.

  18. if n is an odd positive integer, prove that the Co-efficients of the middle terms in the expansion equal

  19. Prove that in the expansion of (1+x)n, the Co-efficient of terms equidistant from the beginning and from the end are equal

  20. Find 3 numbers in AP where sum is 15 and sum of their reciprocals is \(\frac{71}{105}.\)

  21. Find \(\sum_{1}^{\infty}{\frac{1}{(k+1)(k+2)}}\).

  22. Sum up to n terms the series: 
    7 + 77 + 777 + 7777 + ...

  23. The line 2x - y = 5 turns about the point on it, whose ordinate and abscissae are equal, through an angle of 45° in the anti-clockwise direction. find the equation of the line in the new position.

  24. Find matrix C if \(A=\left[ \begin{matrix} 3 & 7 \\ 2 & 5 \end{matrix} \right] ,B=\left[ \begin{matrix} -3 & 2 \\ 4 & -1 \end{matrix} \right] \) and 5C + 2B = A.

  25. If x = \(a\sec ^{ 3 }{ \theta }\) and \(y=a\tan ^{ 3 }{ \theta }\) find \(\frac { dy }{ dx }\) at \(\theta =\frac { \pi }{ 3 }\)

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