11th Second Revision Test 2019

11th Standard

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Maths

Time : 02:30:00 Hrs
Total Marks : 90
    20 x 1 = 20
  1. For real numbers x and y, define xRy if x-y+√2 is an irrational number. Then the relation R is

    (a)

    reflexive

    (b)

    symmetric

    (c)

    transitive

    (d)

    none of these

  2. The number of students who take both the subjects Mathematics and Chemistry is 70. This represents 10% of the enrollment in Mathematics and 14% of the enrollment in Chemistry. The number of students take at least one of these two subjects, is

    (a)

    1120

    (b)

    1130

    (c)

    1100

    (d)

    insufficient data

  3. If \(\frac { |x-2| }{ x-2 } \ge 0\), then x belongs to

    (a)

    \([2,\infty]\)

    (b)

    \((2,\infty )\)

    (c)

    \((-\infty,2)\)

    (d)

    \((-2,\infty )\)

  4. If sin(45 ° + 10°) - sin(45° -10°) =\(\sqrt{2}\)sin x then x is

    (a)

    0o

    (b)

    (c)

    10°

    (d)

    15°

  5. If \(\alpha\) and \(\beta\) are two values of θ obtained from the equation a cosθ+b sinθ=c then the value of \(tan(\frac{\alpha+\beta}{2})\) is

    (a)

    \(\frac{a}{b}\)

    (b)

    \(\frac{b}{a}\)

    (c)

    \(\frac{c}{a}\)

    (d)

    \(\frac{c}{b}\)

  6. The number of ways to average the letters of the word CHEESE are

    (a)

    120

    (b)

    240

    (c)

    720

    (d)

    6

  7. If nPr = 720, nCr =120 then r is:

    (a)

    2

    (b)

    4

    (c)

    3

    (d)

    5

  8. The nth term of the sequence \(\frac { 1 }{ 2 } ,\frac { 3 }{ 4 } ,\frac { 7 }{ 8 } ,\frac { 15 }{ 6 } \).+.....is

    (a)

    2n-n-1

    (b)

    1-2n

    (c)

    2-n+n-1

    (d)

    2n-1

  9. If 7x2 - 8xy +A = 0 represents a pair of perpendicular lines, the A is

    (a)

    7

    (b)

    -7

    (c)

    -8

    (d)

    8

  10. If the points (2k,k)(k,2k) and (k,k)enclose a triangle of area 18 sq units, then the centroid of the triangle is

    (a)

    (8,8)

    (b)

    (4,4)

    (c)

    (3,3)

    (d)

    (2,2)

  11. If the square of the matrix \(\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}\) is the unit matrix of order 2, then\(\alpha ,\beta \) and \(\gamma\) should satisfy the relation.

    (a)

    1+\(\alpha ^2+\beta \gamma=0\)

    (b)

    1-\(\alpha ^2-\beta \gamma=0\)

    (c)

    1-\(\alpha ^2+\beta \gamma=0\)

    (d)

    1+\(\alpha ^2-\beta \gamma=0\)

  12. If A is a square matrix of order 3, then the number of minors in determinant of A are

    (a)

    3

    (b)

    21

    (c)

    9

    (d)

    27

  13. If \(\overrightarrow{a},\overrightarrow{b}\) are the position vectors A and B, then which one of the following points whose position vector lies on AB, is

    (a)

    \(\overrightarrow{a}+\overrightarrow{b}\)

    (b)

    \({2\overrightarrow{a}-\overrightarrow{b}\over 2}\)

    (c)

    \({2\overrightarrow{a}+\overrightarrow{b}\over 2}\)

    (d)

    \({\overrightarrow{a}-\overrightarrow{b}\over 3}\)

  14. \(lim_{\alpha \rightarrow {\pi/4}}{sin \alpha -cos \alpha \over \alpha -{\pi\over 4}}\) is

    (a)

    \(\sqrt{2}\)

    (b)

    \(1\over \sqrt{2}\)

    (c)

    1

    (d)

    2

  15. For what values of x is the rate of increase of x3 - 2x2 + 3x + 8 is twice the rate of increase of x?

    (a)

    \(\left( -\frac { 1 }{ 3 } ,-3 \right) \)

    (b)

    \(\left( \frac { 1 }{ 3 } ,3 \right) \)

    (c)

    \(\left( -\frac { 1 }{ 3 } ,3 \right) \)

    (d)

    \(\left( \frac { 1 }{ 3 } ,1 \right) \)

  16. If y=\({1\over4}u^4,u={2\over 3}x^3+5,\) then \({dy\over dx}\) is

    (a)

    \({1\over 27}x^2(2 x^3+15)^3\)

    (b)

    \({2\over 27}x(2 x^3+5)^3\)

    (c)

    \({2\over 27}x^2(2 x^3+15)^3\)

    (d)

    \(-{2\over 27}x(2 x^3+5)^3\)

  17. \(\int{x^2+cos^2x\over x^2+1}cosec^2xdx\) is

    (a)

    cot x+sin -1x+c

    (b)

    -cot x+tan-1x+c

    (c)

    -tan x+cot-1x+c

    (d)

    -cot x-tan-1x+c

  18. \(\int { x } \) sin x dx = -x cos x + a, then a =  

    (a)

    sin x + c

    (b)

    cos x + c

    (c)

    c

    (d)

    none of these

  19. A number x is chosen at random from the first 100 natural numbers. Let A be the event of numbers which satisfies\({(x-10)(x-50)\over x-30}\ge0\), then P(A) is

    (a)

    0.20

    (b)

    0.51

    (c)

    0.71

    (d)

    0.70

  20. If P(A\(\cup \)B) = 0.8 and P(A\(\cap \)B) = 0.3 then \(P(\bar { A } )+P(\bar { B } )\) =

    (a)

    0.3

    (b)

    0.5

    (c)

    0.7

    (d)

    0.9

  21. 7 x 2 = 14
  22. If X = {1, 2, 3, .. 10} and A = {1, 2, 3, 4, 5}, find the number of sets \(B\subseteq X\) such that A - B = {4}.

  23. Find the value of \(cot(\frac{-15\pi}{4})\).

  24. Write down all the permutations of the vowels A, E, I, O, U in English alphabets taking there at a time starting with A.

  25. Find the general term in the expansion of \({ \left( \frac { 4x }{ 5 } -\frac { 5 }{ 2x } \right) }^{ 9 }\)

  26. The sum of the distance of a moving point from the points (4,0) and (-4, 0) is always 10 units. Find the equation to the locus of the moving point.

  27. Find a direction ratio and direction cosines of the following vectors \(3\hat{i}+4\hat{j}-6\hat{k}\)
     

  28. Evaluate \(\lim _{ x\rightarrow 2 }{ \frac { { x }^{ 2 }-3x+2 }{ { x }^{ 2 }-x-2 } } \)

  29. Find the derivatives of the following functions using first principle.f(x)=-x2+2

  30. Integrate the following with respect to x:\({1\over \sqrt{1-25 x^2}}\)

  31. The ratio of the number of boys to the number of girls in a class is 1:2. It is known that the probability of a girl and a boy getting a first class are 0.25 and 0.28 respectively. Find the probability that a student chosen  at random will get first class?

  32. 7 x 3 = 21
  33. Consider the functions:(i) y = ex; (ii) y = logeX.

  34. Evaluate log \({{(\sqrt{\sqrt{625}+11})(\sqrt{64})}\over{\sqrt{\sqrt [ 5 ]{ 3125 }+\sqrt{\sqrt [ 3 ]{ 343 } } }}}\)

  35. What is the length of the arc intercepted by a central angle of measure 410 in a circle radius 10 ft ?

  36. Write the first six terms of the sequences given by a1 = a2 = 1,an = an-1+ an-2 (n≥3)

  37. If the angle between two lines is \(\frac{\pi}{4}\) and slope of one of the line is \(\frac{1}{2}\) find the slope of the other line

  38. Give your own examples of matrices satisfying the following conditions in each case
    A and B such that AB=O=BA, A\(\neq\) O, and B \(\neq\) O.

  39. Calculate \(lim_{x \rightarrow \infty}{1-x^3\over 3x+2}\)

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

  41. Evaluate the following :\(\int \sqrt{(x-3)(5-x)}dx\)

  42. A town has 2 fire engines operating independently. The probability that a fire engine is available when needed is 0.96.
    (i) What is the probability that a fire engine is available when needed?
    (ii) What is the probability that neither is available when needed?

  43. 7 x 5 = 35
    1. Check the following functions for one-to-oneness and ontoness.
      \(f:N\rightarrow N\) defined by f(n)=n2.

    2. Find the values of k so that the equation x2 =-2x(1+3k)+7(3+2k)=0 has real and equal roots.

    1. The Government plans to have a circular zoological park of diameter 8 km. A separate area in the form of a segment formed by a chord of length 4 km is to be allotted exclusively for a veterinary hospital in the park. Find the area of the segment to be allotted for the veterinary hospital.

    2. By the principle of mathematical induction, prove that, for all integers n \(\ge\)1,1+2+3+....+n=\({n(n+1)\over2}\) .

    1. Compute the sum of first n terms of the following series 8 + 88 + 888 + .......

    2. Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y - 15 = 0 are paralle llines.

    1. Find the equation of the line passing through the point of intersection 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x +4y = 7.

    2. Find the value of the product \(\begin{vmatrix} log_364 &log_43 \\ log_38 & log_49 \end{vmatrix}\times \begin{vmatrix} log_23 & log_83 \\ log_34 & log_34 \end{vmatrix}\)

    1. Let A, Band C represent the angles of a \(\triangle\)ABC and a, band c represent the lengths of the sides opposite to them, then prove that a2 = b2 + c2 - 2bc cos A (Law of cosines)

    2. Evaluate the following limits :\(lim_{x\rightarrow0}{e^x-e^{-x}\over sin x}\)

    1. Differentiate \({ \left( \sin { x } \right) }^{ { \cos { ^{ -1x } } } }\) with respect to 'x'.

    2. Integrate the following functions with respect to x:\({1\over \sqrt{1-81x^2}}\)

    1. Evaluate \(\int { \frac { { x }^{ 2 }{ tan }^{ -1 }\left( { x }^{ 3 } \right) }{ 1+{ x }^{ 6 } } } \)dx

    2. for a loaded die, the probabilities of outcomes are given as under
      P(1) = P(2) = \(\frac { 2 }{ 10 } \), P(3) = P(5) = P(6) = \(\frac { 1 }{ 10 } \) and P(4) = \(\frac { 3 }{ 10 } \)
      The die is thrown 2 times. Let A and B be the events as defined below
      A: Getting same number each time
      B: Getting a total score of 10 or more
      Discuss the independency of the events A and B

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