#### 12th Standard English Medium Maths Reduced syllabus One Mark Important Questions -2021(Public Exam )

12th Standard

Reg.No. :
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Maths

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

#### Multiple Choice Questions

50 x 1 = 50
1. If A = $\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right]$ and B = $\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right]$ then |adj (AB)| =

(a)

-40

(b)

-80

(c)

-60

(d)

-20

2. If A = $\left[ \begin{matrix} \cos { \theta } & \sin { \theta } \\ -\sin { \theta } & \cos { \theta } \end{matrix} \right]$ and A(adj A) =  $\left[ \begin{matrix} k & 0 \\ 0 & k \end{matrix} \right]$ then adj (AB) is

(a)

0

(b)

sin θ

(c)

cos θ

(d)

1

3. Which of the following is/are correct?
(i) Adjoint of a symmetric matrix is also a symmetric matrix.
(ii) Adjoint of a diagonal matrix is also a diagonal matrix.
(iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λn adj(A).

(a)

Only (i)

(b)

(ii) and (iii)

(c)

(iii) and (iv)

(d)

(i), (ii) and (iv)

4. The principal argument of (sin 40°+i cos40°)5 is

(a)

−110°

(b)

−70°

(c)

70°

(d)

110°

5. The complex number z which satisfies the condition $\left| \frac { 1+z }{ 1-z } \right|$ =1 lies on

(a)

circle x2+y2 =1

(b)

x-axis

(c)

y-axis

(d)

the lines x+y=1

6. (1+i)3 = ______

(a)

3 + 3i

(b)

1 + 3i

(c)

3 - 3i

(d)

2i - 2

7. $\frac { (cos\theta +isin\theta )^{ 6 } }{ (cos\theta -isin\theta )^{ 5 } }$ = ________

(a)

cos 11θ - isin 11θ

(b)

cos 11θ + isin 11θ

(c)

cosθ + i sinθ

(d)

$cos\frac { 6\theta }{ 5 } +isin\frac { 6\theta }{ 5 }$

8. If xr=$cos\left( \frac { \pi }{ 2^{ r } } \right) +isin\left( \frac { \pi }{ 2^{ r } } \right)$ then x1, x2 ... x is

(a)

-∞

(b)

-2

(c)

-1

(d)

0

9. According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

(a)

-1

(b)

$\frac { 5 }{ 4 }$

(c)

$\frac { 4 }{ 5 }$

(d)

5

10. For real x, the equation $\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| }$ has

(a)

one solution

(b)

two solution

(c)

at least two solution

(d)

no solution

11. If p(x) = ax2 + bx + c and Q(x) = -ax2 + dx + c where ac ≠ 0 then p(x). Q(x) = 0 has at least _______ real roots.

(a)

no

(b)

1

(c)

2

(d)

infinite

12. The number of real solutions of the equation $\sqrt { 1+cos2x } ={ 2sin }^{ -1 }\left( sinx \right) ,-\pi <x<\pi$ is

(a)

0

(b)

1

(c)

2

(d)

infinte

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

(a)

7

(b)

6

(c)

5

(d)

none

14. If tan-1(cot$\theta$) = 2$\theta$, then$\theta$ = _____________

(a)

$\pm 3$

(b)

$\pm \cfrac { \pi }{ 4 }$

(c)

$\pm \cfrac { \pi }{ 6 }$

(d)

none

15. The value of ${ sin }^{ -1 }\left( cos\cfrac { 33\pi }{ 5 } \right)$ is________

(a)

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

(b)

$\cfrac { -\pi }{ 10 }$

(c)

$\cfrac { \pi }{ 10 }$

(d)

$\cfrac { 7\pi }{ 5 }$

16. The circle x2+y2=4x+8y+5intersects the line3x−4y=m at two distinct points if

(a)

15< m < 65

(b)

35< m <85

(c)

−85<m < −35

(d)

−35<m <15

17. The equation of the circle passing through the foci of the ellipse  $\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1$ 1having centre at
(0,3) is

(a)

x2+y2−6y−7=0

(b)

x2+y2−6y+7=0

(c)

x2+y2−6y−5=0

(d)

x2+y2−6y+5=0

18. y2 - 2x - 2y + 5 = 0 is a

(a)

circle

(b)

parabola

(c)

ellipse

(d)

hyperbola

19. When the eccentricity of a ellipse becomes zero, then it becomes a

(a)

straight line

(b)

circle

(c)

point

(d)

parabola

20. If y = 2x + c is a tangent to the circle x2 + y2 = 5, then c is

(a)

土5

(b)

$\sqrt5$

(c)

土5$\sqrt2$

(d)

±2$\sqrt5$

21. The point of contact of y2 = 4ax and the tangent y = mx + c is

(a)

$\left( \frac { 2a }{ { m }^{ 2 } } ,\frac { a }{ m } \right)$

(b)

$\left( \frac { a }{ { m }^{ 2 } } ,\frac { 2a }{ m } \right)$

(c)

$\left( \frac { a }{ m} ,\frac { 2a }{ { m }^{ 2 } } \right)$

(d)

$\left( \frac {-a }{ { m }^{ 2 }} ,\frac {- 2a }{ m } \right)$

22. Th point of curve y = 2x2 - 6x - 4 at which the targent is parallel to x - axis is

(a)

$\left( \frac { 5 }{ 2 } ,\frac { -7 }{ 12 } \right)$

(b)

$\left( \frac { -5 }{ 2 } ,\frac { -7 }{ 2 } \right)$

(c)

$\left( \frac { -5 }{ 2 } ,\frac { 17 }{ 12 } \right)$

(d)

$\left( \frac { 3 }{ 2 } ,\frac { -7 }{ 2 } \right)$

23. The distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z + 7 = 0

(a)

$\frac { \sqrt { 7 } }{ 2\sqrt { 2 } }$

(b)

$\frac{7}{2}$

(c)

$\frac { \sqrt { 7 } }{ 2 }$

(d)

$\frac { 7 }{ 2\sqrt { 2 } }$

24. If $\overset { \rightarrow }{ a }$ and $\overset { \rightarrow }{ b }$ are two unit vectors, then the vectors $\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) \times \left( \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } \right)$ is parallel to the vector

(a)

$\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b }$

(b)

$\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b }$

(c)

2$\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b }$

(d)

2$\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b }$

25. The p.v, OP of a point P make angles 60o and 45with X and Y axis respectively. The angle of inclination of  $\overset { \rightarrow }{ OP }$with z-axis is

(a)

75o

(b)

60o

(c)

45o

(d)

3

26. If the work done by a force $\overset { \rightarrow }{ F } =\overset { \wedge }{ i } +m\overset { \wedge }{ j } -\overset { \wedge }{ k }$ in moving the point of application from(1, 1, 1) to (3, 3, 3) along a straight line is 12 units, then m is

(a)

5

(b)

2

(c)

3

(d)

6

27. For any three vectors $\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b }$ and $\overset { \rightarrow }{ c }$$\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) .\left( \overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right) \times \left( \overset { \rightarrow }{ c } +\overset { \rightarrow }{ a } \right)$ is

(a)

0

(b)

$\left[ \overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \right]$

(c)

2$\left[ \overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \right]$

(d)

${ \left[ \overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \right] }^{ 2 }$

28. The distance from the origin to the plane $\overset { \rightarrow }{ r } .\left( \overset { \wedge }{ 2i } -\overset { \wedge }{ j } +5\overset { \wedge }{ k } \right) =7$ is ______________

(a)

$\frac { 7 }{ \sqrt { 30 } }$

(b)

$\frac { \sqrt { 30 } }{ 7 }$

(c)

$\frac { 30 }{ 7 }$

(d)

$\frac { 7 }{ 30 }$

29. If $\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c }$ are mutually 丄r unit vectors, then $\left| \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right|$ is _______________

(a)

3

(b)

9

(c)

$\sqrt { 3 }$

(d)

$\sqrt { 3 }$

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

(a)

4

(b)

$2\sqrt { 3 }$

(c)

$4\sqrt { 3 }$

(d)

$5\sqrt { 3 }$

31. The least value of a when f f(x) =x2+ax+1 is increasing on (1, 2) is

(a)

-2

(b)

2

(c)

1

(d)

-1

32. The function/(x) = x9 + 3x7 + 64 is increasing on ________

(a)

R

(b)

(-∞, 0)

(c)

(0, ∞)

(d)

None of these

33. 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

34. 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

35. If f(x, y, z) = sin (xy) + sin (yz) + sin (zx) then fxx is

(a)

-y sin (xy) + z2 cos (xz)

(b)

y sin (xy) - z2 cos (xz)

(c)

y sin (xy) + z2 cos (xz)

(d)

-y sin (xy) - z2 cos (xz)

36. The cube root of 127 is ............

(a)

5.026

(b)

5.26

(c)

5.028

(d)

5.075

37. If is a homogeneous function of x and y of degree n, then $x\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +y\frac { { \partial }^{ 2 }u }{ \partial x\partial y }$ = .............. $\frac { { \partial }u }{ \partial { x } }$

(a)

n

(b)

0

(c)

1

(d)

n - 1

38. 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

39. $\int _{ a }^{ b }{ f(x) } dx=$ ..............

(a)

$2\int _{ 0 }^{ a }{ f(x) } dx$

(b)

$\int _{ a }^{ b }{ f(a-x) } dx$

(c)

$\int _{ b }^{ a }{ f(b-x) } dx$

(d)

$\int _{ a }^{ b }{ f(a+b-x) } dx$

40. $\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \frac { sinx }{ 2+cosx } dx= }$

(a)

0

(b)

2

(c)

log 2

(d)

log 4

41. The I.F of $\frac{dy}{dx}-y$ tan x=cos x is

(a)

sec x

(b)

cos x

(c)

etan x

(d)

cot x

42. The general solution of x $\frac{dy}{dx}$=y is _________.

(a)

y=cx

(b)

x2+y2=c

(c)

x2-y2=c

(d)

y=cx

43. Using y = vx, the differential equation $\frac { dy }{ dx } =\frac { y }{ x+\sqrt { xy } }$ is reduced to ________.

(a)

x(1+$\sqrt{v}$)dv=v$\sqrt{v}$dx

(b)

x(1-$\sqrt{v}$)dv=v$\sqrt{v}$dx

(c)

x(1+$\sqrt{v}$)dv=-v$\sqrt{v}$dx

(d)

v(1+$\sqrt{v}$)dx-v$\sqrt{v}$dv=0

44. If $f(x)={ Cx }^{ 2 }={ cx }^{ 2 },0<x<2$ is the p.d.f, of x then c is

(a)

$\cfrac { 1 }{ 3 }$

(b)

$\cfrac { 4 }{ 3 }$

(c)

$\cfrac { 8 }{ 3 }$

(d)

$\cfrac { 3 }{ 8 }$

45. Var (2x ± 5) is =________

(a)

5

(b)

var (2x) ± 5

(c)

4 var (X)

(d)

0

46. If the mean and variance of a binomial variate are 2 and 1 respectively, the probability that X takes a value greater than one is equal to__________.

(a)

$\cfrac { 5 }{ 16 }$

(b)

$\cfrac { 11 }{ 16 }$

(c)

$\cfrac { 10 }{ 16 }$

(d)

$\cfrac { 1 }{ 2 }$

47. A die is thrown 10 times. Getting a number greater than 3 is considered a success. The S.D of the number of successes is _________

(a)

2.5

(b)

1.56

(c)

5

(d)

25

48. A random variable X has the following probapality mass function?

 X -2 3 1 P(X=x) $\cfrac { \lambda }{ 6 }$ $\cfrac { \lambda }{ 4 }$ $\cfrac { \lambda }{ 12 }$
(a)

$\cfrac { \lambda }{ 6 } +\cfrac { \lambda }{ 4 } +\cfrac { \lambda }{ 12 } =1$

(b)

$\lambda =2$

(c)

$P(X=3)=\cfrac { 1 }{ 8 }$

(d)

$P(1\le X\le 3)=\cfrac { 2 }{ 3 }$

49. If a * b = a2b2 - ab then 3 * (1 * 1)

(a)

0

(b)

1

(c)

2

(d)

4

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

(a)

7

(b)

-7

(c)

0

(d)

-49