#### 12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Four

12th Standard

Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

10 x 1 = 10
1. If A = $\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right]$ and AB = I , then B =

(a)

$\left( \cos ^{ 2 }{ \frac { \theta }{ 2 } } \right) A$

(b)

$\left( \cos ^{ 2 }{ \frac { \theta }{ 2 } } \right) { A }^{ T }$

(c)

$\left( \cos ^{ 2 }{ \theta } \right) I$

(d)

(Sin2$\frac { \theta }{ 2 }$)A

2. If $\sqrt { a+ib }$ =x+iy, then possible value of $\sqrt { a-ib }$ is

(a)

x2+y2

(b)

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

(c)

x+iy

(d)

x-iy

3. 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

4. Let a > 0, b > 0, c >0. h n both th root of th quatlon ax2+b+C= 0 are

(a)

real and negative

(b)

real and positive

(c)

rational numb rs

(d)

none

5. The value of tan $\left( { cos }^{ -1 }\cfrac { 3 }{ 5 } +{ tan }^{ -1 }\cfrac { 1 }{ 4 } \right)$ is ______

(a)

$\cfrac { 19 }{ 8 }$

(b)

$\cfrac { 8 }{ 19 }$

(c)

$\cfrac { 19 }{ 12 }$

(d)

$\cfrac { 3 }{ 4 }$

6. The equation of the director circle of the hyperbola $\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } }$ = 1 is ___________

(a)

x2 + y2 = a2+ b2

(b)

x2 +y2 = a2

(c)

x2+ y2 = b2

(d)

x2+y2 = a2- b2

7. If  $\left| \overset { \rightarrow }{ a } \right| =\left| \overset { \rightarrow }{ b } \right| =1$such that $\overset { \rightarrow }{ a } +2\overset { \rightarrow }{ b }$ and $5\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b }$ are perpendicular to each other, then the angle between $\overset { \rightarrow }{ a }$ and $\overset { \rightarrow }{ b }$ is

(a)

45o

(b)

60o

(c)

cos-1 $\left( \frac { 1 }{ 3 } \right)$

(d)

cos-1 $\left( \frac { 2 }{ 7 } \right)$

8. The length of the 丄r from the origin to plane $\overset { \rightarrow }{ r } .\left( \overset { \wedge }{ 3i } +4\overset { \wedge }{ j } +12\overset { \wedge }{ k } \right)$26 is _____________

(a)

2

(b)

$\frac { 1 }{ 2 }$

(c)

26

(d)

$\frac { 26 }{ 169 }$

9. The order and degree of the differential equation $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +{ \left( \frac { dy }{ dx } \right) }^{ 1/3 }+{ x }^{ 1/4 }=0$are respectively

(a)

2, 3

(b)

3, 3

(c)

2, 6

(d)

2, 4

10. The integrating factor of the differential equation $\frac { dy }{ dx } +y=\frac { 1+y }{ \lambda }$ is

(a)

$\frac { x }{ { e }^{ \lambda } }$

(b)

$\frac { { e }^{ \lambda } }{ x }$

(c)

${ \lambda e }^{ x }$

(d)

ex