#### +1 Public Exam March 2019 Important One Mark Questions

11th Standard

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Time : 00:30:00 Hrs
Total Marks : 50
50 x 1 = 50
1. The value of x, if $\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0$ is

(a)

0, - 1

(b)

0, 1

(c)

- 1, 1

(d)

- 1, - 1

2. If $\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}$ then $\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}$ is

(a)

$\triangle$

(b)

-$\triangle$

(c)

3$\triangle$

(d)

-3$\triangle$

3. The value of the determinant ${\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}$is

(a)

abc

(b)

0

(c)

a2b2c2

(d)

-abc

4. If A is a square matrix of order 3, then |kA| is

(a)

k|A|

(b)

-k|A|

(c)

k3|A|

(d)

-k3|A|

5. adj (AB) is equal to

(a)

(b)

(c)

(d)

6. If A = $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$such that ad - bc $\neq$ 0 then A-1 is

(a)

${{1}\over{ad-bc}}\begin{pmatrix} d & b \\-c & a\end{pmatrix}$

(b)

${{1}\over{ad-bc}}\begin{pmatrix} d & b \\c & a\end{pmatrix}$

(c)

${{1}\over{ad-bc}}\begin{pmatrix} d & -b \\-c & a\end{pmatrix}$

(d)

${{1}\over{ad-bc}}\begin{pmatrix} d & -b \\c & a\end{pmatrix}$

7. The number of Hawkins-Simon conditions for the viability of an input - output analysis is

(a)

1

(b)

3

(c)

4

(d)

2

8. The inventor of input-output analysis is

(a)

Sir Francis Galton

(b)

Fisher

(c)

Prof. Wassily W. Leontief

(d)

Arthur Caylay

9. If A and B are non-singular matrices then, which of the following is incorrect?

(a)

A2 = Iimplies A-1 = A

(b)

I-1 = I

(c)

If AX = B, then X = B-1 A

(d)

If A is square matrix of order 3 then |adj A|= |A|2

10. If $\triangle=\begin{vmatrix} {a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23} \\ {a}_{31} & {a}_{32} & {a}_{33} \end{vmatrix}$ and Aij is cofactor of aij, then value of $\triangle$ is given by

(a)

a11 A31 + a12 A32 + a13 A33

(b)

a11 A11 + a12 A21 + a13 A31

(c)

a21 A11 + a22 A12 + a23 A13

(d)

a11 A11 + a21 A21 + a31 A31

11. The value of n, when nP2 = 20 is

(a)

3

(b)

6

(c)

5

(d)

4

12. The number of ways selecting 4 players out of 5 is

(a)

4!

(b)

20

(c)

25

(d)

5

13. If nPr = 720 (nCr), then r is equal to

(a)

4

(b)

5

(c)

6

(d)

7

14. The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n $\in$ N is

(a)

2

(b)

6

(c)

20

(d)

24

15. If n is a positive integer, then the number of terms in the expansion (x + a)n is

(a)

n

(b)

n + 1

(c)

n-1

(d)

2n

16. For all n > 0, nC1 + nC2 + nC3 + ... +nCn is equal to

(a)

2n

(b)

2n- 1

(c)

n2

(d)

n2 - 1

17. The last term in the expansion of (3 +$\sqrt{2}$ )8 is

(a)

81

(b)

16

(c)

8$\sqrt{2}$

(d)

27$\sqrt{3}$

18. There are 10 true or false questions in an examination. Then these questions can be answered in

(a)

240 ways

(b)

120 ways

(c)

1024 ways

(d)

100 ways

19. The value of (5Co + 5C1) + (5C1 + 5C2) + (5C2 + 5C3) + (5C3 + 5C4) + (5C4 + 5C5 ) is

(a)

26-2

(b)

25-1

(c)

28

(d)

27

20. 13 guests have participated in a dinner. The number of handshakes happened in the dinner is

(a)

715

(b)

78

(c)

286

(d)

13

21. The angle between the pair of straight lines x2 - 7xy + 4y2 = 0

(a)

$tan^{-1}\left(1\over 3\right)$

(b)

$tan^{-1}\left(1\over 2\right)$

(c)

$tan^{-1}\left(\sqrt{33}\over 5\right)$

(d)

$tan^{-1}\left(5\over\sqrt{33}\right)$

22. The x - intercept of the straight line 3x + 2y - 1 = 0 is

(a)

3

(b)

2

(c)

1/3

(d)

1/2

23. If kx2 + 3xy - 2y2 = 0 represent a pair of lines which are perpendicular then k is equal to

(a)

1/2

(b)

-1/2

(c)

2

(d)

-2

24. The centre of the circle x2 + y - 2x + 2y - 9 = 0 is

(a)

(1,1)

(b)

(-1,-1)

(c)

(-1,1)

(d)

(1, -1)

25. The equation of the circle with centre on the x axis and passing through the origin is

(a)

x2 - 2ax + y = 0

(b)

y2 - 2ay + x2 = 0

(c)

x2+y2=a2

(d)

x2 - 2ay + y = 0

26. In the equation of the circle x2 +y2 = 16 then y-intercept is (are)

(a)

4

(b)

16

(c)

±4

(d)

±16

27. If the perimeter of the circle is 8π units and centre is (2,2) then the equation of the circle is

(a)

(x - 2)2 + (y - 2)2 = 4

(b)

(x - 2)2 + (y - 2)2 = 16

(c)

(x - 4)2 + (y - 4)2 = 2

(d)

x2 + y2 =4

28. The equation of the circle with centre (3,-4) and touches the x - axis

(a)

(x - 3)2 +(y - 4)2 = 4

(b)

(x - 3)2 +(y + 4)2 =16

(c)

(x-3)2+(y- 4)2=16

(d)

x2+y2=16

29. If the circle touches x axis, y axis and the line x = 6 then the length of the diameter of the circle is

(a)

6

(b)

3

(c)

12

(d)

4

30. The double ordinate passing through the focus is

(a)

focal chord

(b)

latus rectum

(c)

directrix

(d)

axis

31. The degree measure of $\frac{\pi}{8}$ is

(a)

20o60'

(b)

22o30'

(c)

20o60'

(d)

20o30'

32. The radian measure of 37o30' is

(a)

$\frac{5\pi}{24}$

(b)

$\frac{3\pi}{24}$

(c)

$\frac{7\pi}{24}$

(d)

$\frac{9\pi}{24}$

33. The value of $\cos(-480^o)$ is

(a)

$\sqrt3$

(b)

$-\frac{\sqrt3}{2}$

(c)

$\frac{1}{2}$

(d)

$\frac{-1}{2}$

34. The value of $\sin 28^o\cos 17^o+\cos 28^o\sin 17^o$ is

(a)

$\frac{1}{\sqrt2}$

(b)

1

(c)

$\frac{-1}{\sqrt2}$

(d)

0

35. The value of cos245o-sin245o is

(a)

$\frac{\sqrt3}{2}$

(b)

$\frac{1}{2}$

(c)

0

(d)

$\frac{1}{\sqrt{2}}$

36. The value of $\frac{2\tan30^o}{1+tan^230}$ is

(a)

$\frac12$

(b)

$\frac{1}{\sqrt3}$

(c)

$\frac{\sqrt{3}}{2}$

(d)

$\sqrt3$

37. If $\tan A=\frac{1}{2}$ and $\tan B=\frac{1}{3}$ then tan(2A+B) is equal to

(a)

1

(b)

2

(c)

3

(d)

4

38. $\sin\left(\cos^{-1}\frac{3}{5}\right)$ is

(a)

$\frac{3}{5}$

(b)

$\frac{5}{3}$

(c)

$\frac{4}{5}$

(d)

$\frac{5}{4}$

39. The value of $\frac{1}{cosec(-45^o)}$ is

(a)

$\frac{-1}{\sqrt2}$

(b)

$\frac{1}{\sqrt2}$

(c)

$\sqrt2$

(d)

$-\sqrt2$

40. $\left(\frac{\cos x}{cosec x}\right)-\sqrt{1-\sin^2x}\sqrt{1-\cos^2x}$ is

(a)

cos2x-sin2x

(b)

sin2x-cos2x

(c)

1

(d)

0

41. For $f\left( x \right) =\begin{cases} { x }^{ 2 }-4x\quad ifx\ge 2 \\ x+2\quad ifx<2 \end{cases}$ then f(0) is

(a)

2

(b)

5

(c)

-1

(d)

0

42. If f(x) = $\frac{1-x}{1+x}$ then f(-x) is equal to

(a)

-f(x)

(b)

$\frac{1}{f(x)}$

(c)

$\frac{-1}{f(x)}$

(d)

f(x)

43. If f(x) = 2x and get g(x) = $\frac{1}{2^x}$ then (fg)(x) is

(a)

1

(b)

0

(c)

4x

(d)

$\frac{1}{4^x}$

44. Which of the following function is neither even nor odd?

(a)

f(x) = x3 + 5

(b)

f(x) = x5

(c)

f(x) = x10

(d)

f(x) = x2

45. f(x) = - 5 , for all $x\epsilon R$, is a

(a)

an identity function

(b)

modulus function

(c)

exponential function

(d)

constant function

46. The range of f(x) = |x|, for all $x\epsilon R$, is

(a)

(0, $\infty$)

(b)

(0, $\infty$)

(c)

(-$\infty$$\infty$)

(d)

(1, $\infty$)

47. If f(x) = x2 and g(x) = 2x + 1 then (fg)(0) is

(a)

0

(b)

2

(c)

1

(d)

4

48. $\lim _{ x\rightarrow \infty }{ \frac { \tan { \theta } }{ \theta } } =$

(a)

1

(b)

$\infty$

(c)

$-\infty$

(d)

$\theta$

49. For what value of x, f(x) = $\frac{x+2}{x-1}$ is not continuous?

(a)

-2

(b)

1

(c)

2

(d)

-1

50. If y = x and z = $\frac{1}{x}$ then $\frac{dy}{dz}=$

(a)

x2

(b)

1

(c)

-x2

(d)

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