#### 12th Standard English Medium Maths Reduced Syllabus Creative one Mark Questions with Answer key - 2021(Public Exam )

12th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50

Multiple Choice Questions

50 x 1 = 50
1. The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = has a unique solution if

(a)

k ≠ 0

(b)

-1 < k < 1

(c)

-2 < k < 2

(d)

k=0

2. If $\rho$(A) = $\rho$([A/B]) = number of unknowns, then the system is

(a)

consistent and has infinitely many solutions

(b)

consistent

(c)

inconsistent

(d)

consistent and has unique solution

3. If $\rho$(A) = r then which of the following is correct?

(a)

all the minors of order n which do not vanish

(b)

'A' has at least one minor "of order r which does not vanish and all higher order minors vanish

(c)

'A' has at least one (r + 1) order minor which vanish

(d)

all (r + 1) and higher order minors should not vanish

4. If $\rho$(A) ≠ $\rho$([AIB]), then the system is

(a)

consistent and has infinitely many solutions

(b)

consistent and has a unique solution

(c)

consistent

(d)

inconsistent

5. If z=cos$\frac { \pi }{ 4 }$+i sin$\frac { \pi }{ 6 }$, then

(a)

|z| =1, arg(z) =$\frac { \pi }{ 4 }$

(b)

|z| =1, arg(z) =$\frac { \pi }{ 6 }$

(c)

|z|=$\frac { \sqrt { 3 } }{ 2 }$, arg(z)=$\frac { 5\pi }{ 24 }$

(d)

|z| =$\frac { \sqrt { 3 } }{ 2 }$, arg (z) =tan-1$\left( \frac { 1 }{ \sqrt { 2 } } \right)$

6. The least positive integer n such that $\left( \frac { 2i }{ 1+i } \right) ^{ n }$  is a positive integer is

(a)

16

(b)

8

(c)

4

(d)

2

7. The value of (1+i)4 + (1-i)4 is

(a)

8

(b)

4

(c)

-8

(d)

-4

8. If zn =$cos\frac { n\pi }{ 3 } +isin\frac { n\pi }{ 3 }$, then z1, z2 ..... z6 is

(a)

1

(b)

-1

(c)

i

(d)

-i

9. The points represented by 3 - 3i, 4 - 2i, 3 - i and 2 - 2i form _____ in the argand plane.

(a)

collinear points

(b)

Vertices of a parallelogram

(c)

Vertices of a rectangle

(d)

Vertices of a square

10. If a =cosα + i sinα, b= -cosβ + i sinβ then $\left( ab-\frac { 1 }{ ab } \right)$ is _________

(a)

-2i sin(α - β)

(b)

2i sin(α - β)

(c)

2 cos(α - β)

(d)

-2 cos(α - β)

11. If x=cosθ + i sinθ, then xn+$\frac { 1 }{ { x }^{ n } }$ is ______

(a)

2 cos nθ

(b)

2 i sin nθ

(c)

2n cosθ

(d)

2n i sinθ

12. If the equation ax2+ bx+c=0(a>0) has two roots ∝ and β such that ∝<- 2 and β > 2, then

(a)

b2-4ac=0

(b)

b2 - 4ac <0

(c)

b2 - 4ac >0

(d)

b2 - 4ac≥0

13. If ax2 + bx + c = 0, a, b, c E R has no real zeros, and if a + b + c < 0, then __________

(a)

c>0

(b)

c<0

(c)

c=0

(d)

c≥0

14. The value of ${ cos }^{ -1 }\left( \cfrac { cos5\pi }{ 3 } \right) +sin^{ -1 }\left( \cfrac { sin5\pi }{ 3 } \right)$ is

(a)

$\cfrac { \pi }{ 2 }$

(b)

$\cfrac { 5\pi }{ 3 }$

(c)

$\cfrac { 10\pi }{ 3 }$

(d)

0

15. $sin\left\{ 2{ cos }^{ -1 }\left( \cfrac { -3 }{ 5 } \right) \right\} =$

(a)

$\cfrac { 6 }{ 15 }$

(b)

$\cfrac { 24 }{ 25 }$

(c)

$\cfrac { 4 }{ 5 }$

(d)

$\cfrac { -24 }{ 25 }$

16. If $4{ cos }^{ -1 }x+{ sin }^{ -1 }x=\pi$ then x is

(a)

$\cfrac { 3 }{ 2 }$

(b)

$\cfrac { 1 }{ \sqrt { 2 } }$

(c)

$\cfrac { \sqrt { 3 } }{ 2 }$

(d)

$\cfrac { 2 }{ \sqrt { 3 } }$

17. $cot\left( \cfrac { \pi }{ 4 } -{ cot }^{ -1 }3 \right)$

(a)

7

(b)

6

(c)

5

(d)

none

18. If x>1,then $2{ tan }^{ -1 }x+{ sin }^{ -1 }\left( \cfrac { 2x }{ 1+{ x }^{ 2 } } \right)$ ________

(a)

4 tan-1x

(b)

0

(c)

$\cfrac { \pi }{ 2 }$

(d)

$\pi$

19. The equation of the directrix of the parabola y2+ 4y + 4x + 2 = 0 is

(a)

x = -1

(b)

x = 1

(c)

x = $\frac{-3}{2}$

(d)

x = $\frac{3}{2}$

20. If the distance between the foci is 2 and the distance between the direction is 5, then the equation of the ellipse is

(a)

6x2 + 10y2 = 5

(b)

6x2 + 10y2 = 15

(c)

x2 + 3y2 = 10

(d)

none

21. The equation 7x2- 6$\sqrt { 3 }$ xy + 13y2 - 4$\sqrt { 3 }$ x - 4y - 12 = 0 represents

(a)

parabola

(b)

ellipse

(c)

hyperbola

(d)

rectangular hyperbola

22. The director circle of the ellipse $\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 5 } =1$ is

(a)

x2 + y2 = 4

(b)

x2 +y2 = 9

(c)

x2 +y2 = 45

(d)

x2 +y2 = 14

23. The length of the diameter of a circle with centre (1, 2) and passing through (5, 5) is

(a)

5

(b)

$\sqrt{45}$

(c)

10

(d)

$\sqrt{50}$

24. If (1, -3) is the centre of the circle x+ y+ ax + by + 9 = 0 its radius is

(a)

$\sqrt{10}$

(b)

1

(c)

5

(d)

$\sqrt{19}$

25. If e1,e2 are eccentricities of the ellipse $\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } }$ = 1 and the hyperbola $\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } }$ = 1 then

(a)

${ e }_{ 1 }^{ 2 }$ - ${ e }_{ 2 }^{ 2 }$ = 1

(b)

${ e }_{ 1 }^{ 2 }$  + ${ e }_{ 2 }^{ 2 }$ = 1

(c)

${ e }_{ 1 }^{ 2 }$ - ${ e }_{ 2 }^{ 2 }$ = 2

(d)

${ e }_{ 1 }^{ 2 }$ - ${ e }_{ 2 }^{ 2 }$=2

26. If B, B1 are the ends of minor axis, F1 ,F2 are foci of the ellipse $\frac { { x }^{ 2 } }{ 8 } +\frac { { y }^{ 2 } }{ 4 }$ = 1 then area of F1BF2B1 is

(a)

16

(b)

8

(c)

16$\sqrt2$

(d)

32$\sqrt2$

27. The length of major and minor axes of 4x2 + 3y2 = 12 are ____________

(a)

4, 2$\sqrt3$

(b)

2, $\sqrt3$

(c)

2$\sqrt3$, 4

(d)

$\sqrt3$, 2

28. The number of vectors of unit length perpendicular to the vectors $\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right)$ and $\left( \overset { \wedge }{ j } +\overset { \wedge }{ k } \right)$is

(a)

1

(b)

2

(c)

3

(d)

29. The area of the parallelogram having diagonals $\overset { \rightarrow }{ a } =3\overset { \wedge }{ i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k }$ and $\overset { \rightarrow }{ b } =\overset { \wedge }{ i } -3\overset { \wedge }{ j } +\overset { \wedge }{ 4k }$ is

(a)

4

(b)

2$\sqrt { 3 }$

(c)

4$\sqrt { 3 }$

(d)

5$\sqrt { 3 }$

30. If $\overset { \rightarrow }{ a } =\left| \overset { \rightarrow }{ a } \right| \overset { \rightarrow }{ e }$ then $\overset { \rightarrow }{ e } .\overset { \rightarrow }{ e }$

(a)

0

(b)

e

(c)

1

(d)

$\overset { \rightarrow }{ 0 }$

31. The two planes 3x + 3y - 3z - 1 = 0 and x + y - z + 5 = 0 are

(a)

mutually perpendicular

(b)

parallel

(c)

inclined at 45o

(d)

inclined at 30

32. If $\lambda \overset { \wedge }{ i } +2\lambda \overset { \wedge }{ j } +2\lambda \overset { \wedge }{ k }$ is a unit vector, then the value of λ is

(a)

土 $\frac { 1 }{ 3 }$

(b)

土 $\frac { 1 }{ 4 }$

(c)

土 $\frac { 1 }{ 9 }$

(d)

$\frac { 1 }{ 2 }$

33. If the vectors $a\overset { \wedge }{ i } +\overset { \wedge }{ j } +\overset { \wedge }{ k }$$\overset { \wedge }{ i } +b\overset { \wedge }{ j } +\overset { \wedge }{ k }$ and $\overset { \wedge }{ i } +\overset { \wedge }{ j } +c\overset { \wedge }{ k }$ (a ≠ b ≠ c ≠ 1) are coplaner, then $\frac { 1 }{ 1-a } +\frac { 1 }{ 1-b } +\frac { 1 }{ 1-c } =$

(a)

0

(b)

1

(c)

2

(d)

$\frac { abc }{ (1-a)(1-b)(1-c) }$

34. If $\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c }$ are three non - coplanar vectors, then $\frac { \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } }{ \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } } +\frac { \overset { \rightarrow }{ b } .\overset { \rightarrow }{ a } \times \overset { \rightarrow }{ c } }{ \overset { \rightarrow }{ c } .\overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } }$=_____________

(a)

0

(b)

1

(c)

-1

(d)

$\frac { \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } }{ \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } .\overset { \rightarrow }{ c } }$

35. The critical points of the function f(x) = $(x-2)^{ \frac { 2 }{ 3 } }(2x+1)$ are

(a)

-1, 2

(b)

1, $\frac { 1 }{ 2 }$

(c)

1, 2

(d)

none

36. In LMV theorem, we have f'(x1) =$\frac { f(b)-f(a) }{ b-a }$ then a < x1 _________

(a)

<b

(b)

≤b

(c)

=b

(d)

≠b

37. If u = log $\sqrt { { x }^{ 2 }+{ y }^{ 2 } }$, then $\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +\frac { { \partial }^{ 2 }u }{ { \partial y }^{ 2 } }$ is

(a)

$\sqrt { { x }^{ 2 }+{ y }^{ 2 } }$

(b)

0

(c)

u

(d)

2u

38. lf u = (x-y)4+(y-z)4 +(z-x)4 then $\sum { \frac { \partial u }{ \partial x } }$ =

(a)

4

(b)

1

(c)

0

(d)

-4

39. The approximate value of (627)$\frac14$ is ................

(a)

5.002

(b)

5.003

(c)

5.005

(d)

5.004

40. The value of $\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \sqrt { \frac { 1-cos2x }{ 2x } } }$ dx is

(a)

$\frac { 1 }{ 2 }$

(b)

2

(c)

0

(d)

1

41. The area enclosed by the curve y2 = 4x, the x-axis and its latus rectum is ............ sq.units.

(a)

$\frac23$

(b)

$\frac43$

(c)

$\frac83$

(d)

$\frac{16}{3}$

42. The area of the ellipse $\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1$

(a)

(b)

36π

(c)

2

(d)

36π2

43. The volume generated by the curve y2 = 16x from x = 2 to x = 3 rotating about x - axis ......... cu. units

(a)

72π

(b)

$\frac { 256\times 19 }{ 3 }$

(c)

40ㅠ

(d)

80ㅠ

44. The solution of sec2x tan y dx+sec2y tan x dy=0 is

(a)

tan x+tan y =c

(b)

sec x+sec y=c

(c)

tan x tan y=c

(d)

sec x-sec y =c

45. The general solution of $4\frac{d^2 y}{dx^2}$+y=0 is

(a)

$y={ e }^{ \frac { x }{ 2 } }\left[ A\quad cos\frac { x }{ 2 } +B\quad sin\frac { x }{ 2 } \right]$

(b)

$y={ e }^{ \frac { x }{ 2 } }\left[ A\quad cos\frac { x }{ 2 } -B\quad sin\frac { x }{ 2 } \right]$

(c)

$y=Acos\frac { x }{ 2 } +Bsin\frac { x }{ 2 }$

(d)

$t={ Ae }^{ \frac { x }{ 2 } }+B{ e }^{ \frac { -x }{ 2 } }$

46. If $f(x)=\cfrac { 1 }{ 2 }$ ,$E\left( { x }^{ 2 } \right) =\cfrac { 1 }{ 4 }$ then var(x) is

(a)

0

(b)

$\cfrac { 1 }{ 4 }$

(c)

$\cfrac { 1 }{ 2 }$

(d)

1

47. Var (2x ± 5) is =________

(a)

5

(b)

var (2x) ± 5

(c)

4 var (X)

(d)

0

48. The sum of the mean and variance of a binomial distribution for 6 total is 2.16. Then the probability of success p=__________

(a)

0.4

(b)

0.6

(c)

0.8

(d)

0.2

49. If * is defined by a * b = a2 + b2 + ab + 1, then (2 * 3) * 2 is

(a)

20

(b)

40

(c)

400

(d)

445

50. In (N, *), x * y = max(x, y), x, y $\in$ N then 7 * (-7)

(a)

7

(b)

-7

(c)

0

(d)

-49