Important 1mark -2

11th Standard

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Maths

Use blue pen Only

Time : 00:15:00 Hrs
Total Marks : 25

    Part A

    Answer all the questions

    25 x 1 = 25
  1. The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is

    (a)

    432

    (b)

    108

    (c)

    36

    (d)

    18

  2. In a plane there are 10 points are there out of which 4 points are collinear, then the number of triangles formed is

    (a)

    110

    (b)

    10C3

    (c)

    120

    (d)

    116

  3. In 2nC3 : nC3 = 11 : 1 then n is

    (a)

    5

    (b)

    6

    (c)

    11

    (d)

    7

  4. The product of r consecutive positive integers is divisible by

    (a)

    r!

    (b)

    r!+1

    (c)

    (r+1)

    (d)

    none of these

  5. There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is

    (a)

    45

    (b)

    40

    (c)

    39

    (d)

    38

  6. is:

    (a)

    \(\lfloor{n}(n+2)\)

    (b)

    (c)

    (d)

    none of these

  7. If 100Cr = 100C3r then r is:

    (a)

    24

    (b)

    25

    (c)

    20

    (d)

    50

  8. How many words can be formed using all the letters of the word ANAND:

    (a)

    30

    (b)

    35

    (c)

    40

    (d)

    45

  9. There are 10 lamps in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated is

    (a)

    102

    (b)

    1023

    (c)

    210

    (d)

    10!

  10. The number of positive integral solution of \(x\times y\times z=30\) is

    (a)

    3

    (b)

    1

    (c)

    9

    (d)

    27

  11. There are 15 points in a plane of which exactly 8 are collinear. The number of straight lines obtained by joining these points is

    (a)

    105

    (b)

    28

    (c)

    77

    (d)

    78

  12. If nC10 = nC6, then nC2

    (a)

    16

    (b)

    4

    (c)

    120

    (d)

    240

  13. The unit vector parallel to the resultant of the vectors \(\hat{i}+\hat{j}-\hat{k}\) and\(\hat{i}-2\hat{j}+\hat{k}\) is

    (a)

    \({\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)

    (b)

    \({2\hat{i}+\hat{j}\over\sqrt{5}}\)

    (c)

    \({2\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)

    (d)

    \({2\hat{i}-\hat{j}\over\sqrt{5}}\)

  14. If ABCD is a parallelogram, then \(\overrightarrow{AB}+\overrightarrow{AD}+\overrightarrow{CB}+\overrightarrow{CD}\) is equal to 

    (a)

    \(2(\overrightarrow{AB}+\overrightarrow{AD})\)

    (b)

    \(4\overrightarrow{AC}\)

    (c)

    \(4\overrightarrow{BD}\)

    (d)

    \(\overrightarrow{0}\)

  15. Two vertices of a triangle have position vectors \(3\hat{i}+4\hat{j}-4\hat{k}\) and\(2\hat{i}+3\hat{j}+4\hat{k}\)If the position vector of the centroid is \(\hat{i}+2\hat{j}+3\hat{k}\) ,then the position vector of the third vertex is

    (a)

    \(-2\hat{i}-\hat{j}+9\hat{k}\)

    (b)

    \(-2\hat{i}-\hat{j}-6\hat{k}\)

    (c)

    \(2\hat{i}-\hat{j}+6\hat{k}\)

    (d)

    \(-2\hat{i}+\hat{j}+6\hat{k}\)

  16. If \(\overrightarrow{a}\)  and \(\overrightarrow{b}\) having same magnitude and angle between them is 60° and their scalar product is \({1\over2}\) then \(|\overrightarrow{a}|\) is

    (a)

    2

    (b)

    3

    (c)

    7

    (d)

    1

  17. Vectors \(\overrightarrow{a}\) and \(\overrightarrow{b}\) are inclined at an angle \(\theta =120^o\) .If \(|\overrightarrow{a}|=1,|\overrightarrow{b}|=2,\) then \([(\overrightarrow{a}+3\overrightarrow{b})\times (3\overrightarrow{a}-\overrightarrow{b})]^2\) is equal to

    (a)

    225

    (b)

    275

    (c)

    325

    (d)

    300

  18. If   \(\overrightarrow{a}\)  and   \(\overrightarrow{b}\) are two vectors of magnitude 2 and inclined at an angle 60° , then the angle between   \(\overrightarrow{a}\)  and \(\overrightarrow{a}+\overrightarrow{b}\) is 

    (a)

    30°

    (b)

    60°

    (c)

    45°

    (d)

    90°

  19. If the points whose position vectors \(10\hat{i}+3\hat{j},12\hat{i}-5\hat{j}\) and \(a\hat{i}+11\hat{j}\) are collinear then a is equal to

    (a)

    6

    (b)

    3

    (c)

    5

    (d)

    8

  20. If \(y={1\over a-z}\) ,then \({dz\over dy}\) is

    (a)

    \((a-z)^2\)

    (b)

    -(z-a)2

    (c)

    (z+a)2

    (d)

    -(z+a)2

  21. If y=mx+c and f(0)=\(f'(0)=1\),then f(2) is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    -3

  22. If x=a sin \(\theta\) and y= b cos \(\theta\),then \({d^2y\over dx^2}\)is

    (a)

    \({a \over b^2}sec^2 \theta\)

    (b)

    \(-{b \over a}sec^2 \theta\)

    (c)

    \(-{b \over a^2}sec^3 \theta\)

    (d)

    \(-{b^2\over a^2}sec^3 \theta\)

  23. If f(x)=x+2, then f'(f(x)) at x= 4 is

    (a)

    8

    (b)

    1

    (c)

    4

    (d)

    5

  24. If g(x)=(x2+2x+3) f(x) and f(0)=5 and \(lim_{x \rightarrow 0}{f(x)-5\over x}=4\),then g'(0) is 

    (a)

    20

    (b)

    14

    (c)

    18

    (d)

    12

  25. The number of points in R in which the function \(f(x)=|x-1|+|x-3|+sin \ x\) is not differentiable, is

    (a)

    3

    (b)

    2

    (c)

    1

    (d)

    4

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