#### 12th Standard Maths English Medium Free Online Test Volume 1 One Mark Questions 2020

12th Standard

Reg.No. :
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Maths

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

25 x 1 = 25
1. If A is a non-singular matrix such that A-1 = $\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right]$, then (AT)−1 =

(a)

$\left[ \begin{matrix} -5 & 3 \\ 2 & 1 \end{matrix} \right]$

(b)

$\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right]$

(c)

$\left[ \begin{matrix} -1 & -3 \\ 2 & 5 \end{matrix} \right]$

(d)

$\left[ \begin{matrix} 5 & -2 \\ 3 & -1 \end{matrix} \right]$

2. If A =$\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right)$ and A(adj A) =$\lambda$ $\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right)$ then $\lambda$ is

(a)

sinx cosx

(b)

1

(c)

2

(d)

none

3. In the non - homogeneous system of equations with 3 unknowns if $\rho$(A) = $\rho$([AIB]) = 2, then the system has _______

(a)

unique solution

(b)

one parameter family of solution

(c)

two parameter family of solutions

(d)

in consistent

4. If A = [2 0 1] then the rank of AAT is ______

(a)

1

(b)

2

(c)

3

(d)

0

5. The conjugate of a complex number is $\cfrac { 1 }{ i-2 }$/Then the complex number is

(a)

$\cfrac { 1 }{ i+2 }$

(b)

$\cfrac { -1 }{ i+2 }$

(c)

$\cfrac { -1 }{ i-2 }$

(d)

$\cfrac { 1 }{ i-2 }$

6. 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$\left( \frac { 1 }{ \sqrt { 2 } } \right)$

7. If z = $\frac { 1 }{ (2+3i)^{ 2 } }$ then |z| =

(a)

$\frac { 1 }{ 13 }$

(b)

$\frac { 1 }{ 5}$

(c)

$\frac { 1 }{ 12 }$

(d)

none of these

8. 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)

9. If x3+12x2+10ax+1999 definitely has a positive zero, if and only if

(a)

a≥0

(b)

a>0

(c)

a<0

(d)

a≤0

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 x2 - hx - 21 = 0 and x2 - 3hx + 35 = 0 (h > 0) have a common root, then h = ___________

(a)

0

(b)

1

(c)

4

(d)

3

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. If tan-1(3)+tan-1(x)=tan-1(8)then x=

(a)

5

(b)

$\cfrac { 1 }{ 5 }$

(c)

$\cfrac { 5 }{ 14 }$

(d)

$\cfrac { 14 }{ 5 }$

14. 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)

$\cfrac { 3 }{ 4 }$

15. The equation of the normal to the circle x2+y2−2x−2y+1=0 which is parallel to the line
2x+4y=3 is

(a)

x+2y=3

(b)

x+2y+3= 0

(c)

2x+4y+3=0

(d)

x−2y+3= 0

16. Equation of tangent at (-4, -4) on x2 = -4y is

(a)

2x - y + 4 = 0

(b)

2x + y - 4 = 0

(c)

2x - y - 12 = 0

(d)

2x + y + 4 = 0

17. The area of the circle (x - 2)2 + (y - k)2 = 25 is

(a)

25ㅠ

(b)

5ㅠ

(c)

10ㅠ

(d)

25

18. If t1 and t2 are the extremities of any focal chord of y2 = 4ax then t1tis ______________

(a)

-1

(b)

0

(c)

±1

(d)

$\frac12$

19. If $\vec { a }$ and $\vec { b }$ are unit vectors such that $[\vec { a } ,\vec { b },\vec { a } \times \vec { b } ]=\frac { \pi }{ 4 }$, then the angle between $\vec { a }$ and $\vec { b }$ is

(a)

$\frac { \pi }{ 6 }$

(b)

$\frac { \pi }{ 4 }$

(c)

$\frac { \pi }{ 3 }$

(d)

$\frac { \pi }{ 2 }$

20. The angle between the vector $3\overset { \wedge }{ i } +4\overset { \wedge }{ j } +\overset { \wedge }{ 5k }$ and the z-axis is

(a)

30o

(b)

60o

(c)

45o

(d)

90o

21. If $\overset { \rightarrow }{ a } =\overset { \wedge }{ i } +\overset { \wedge }{ 2j } +\overset { \wedge }{ 3k }$$\overset { \rightarrow }{ b } =-\overset { \wedge }{ i } +\overset { \wedge }{ 2j } +\overset { \wedge }{ k }$$\overset { \rightarrow }{ c } =3\overset { \wedge }{ i } +\overset { \wedge }{ j }$ then $\overset { \rightarrow }{ a } +\left( -\overset { \rightarrow }{ b } \right)$will be perpendiculur to $\overset { \rightarrow }{ c }$ only when t =

(a)

5

(b)

4

(c)

3

(d)

$\frac { 7 }{ 3 }$

22. The value of ${ \left| \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \right| }^{ 2 }$ is

(a)

$2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right)$

(b)

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

(c)

$2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }-{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right)$

(d)

${ \left| \overset { \rightarrow }{ a } \right| }^{ 2 }{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 }$

23. 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)

$\frac { 1 }{ 2 }$

24. The unit normal vectors to the plane 2x - y + 2z = 5 are ________________

(a)

$\overset { \wedge }{ 2i } -\overset { \wedge }{ j } +2\overset { \wedge }{ k }$

(b)

$\frac { 1 }{ 3 } \left( \overset { \wedge }{ 2i } -\overset { \wedge }{ j } +2\overset { \wedge }{ k } \right)$

(c)

$-\frac { 1 }{ 3 } \left( \overset { \wedge }{ 2i } -\overset { \wedge }{ j } +2\overset { \wedge }{ k } \right)$

(d)

$\pm \frac { 1 }{ 3 } \left( \overset { \wedge }{ 2i } -\overset { \wedge }{ j } +2\overset { \wedge }{ k } \right)$

25. 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)

$5\sqrt { 3 }$