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

12th Standard

Reg.No. :
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Maths

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

10 x 1 = 10
1. If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT =

(a)

A

(b)

B

(c)

I

(d)

BT

2. If A, B and C are invertible matrices of some order, then which one of the following is not true?

(a)

(b)

(c)

det A-1 = (det A)-1

(d)

(ABC)-1 = C-1B-1A-1

3. If A = $\left[ \begin{matrix} \frac { 3 }{ 5 } & \frac { 4 }{ 5 } \\ x & \frac { 3 }{ 5 } \end{matrix} \right]$ and AT = A−1 , then the value of x is

(a)

$\frac { -4 }{ 5 }$

(b)

$\frac { -3 }{ 5 }$

(c)

$\frac { 3 }{ 5 }$

(d)

$\frac { 4 }{ 5 }$

4. If A = $\left[ \begin{matrix} 2 & 3 \\ 5 & -2 \end{matrix} \right]$ be such that λA−1 =A, then λ is

(a)

17

(b)

14

(c)

19

(d)

21

5. The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

(a)

$\cfrac { 1 }{ 2 } \left| z \right| ^{ 2 }$

(b)

|z|2

(c)

$\cfrac { 3 }{ 2 } \left| z \right| ^{ 2 }$

(d)

2|z|2

6. If z is a non zero complex number, such that 2iz2=$\bar { z }$ then |z| is

(a)

$\cfrac { 1 }{ 2 }$

(b)

1

(c)

2

(d)

3

7. If |z1|=1,|z2|=2|z3|=3 and |9z1z2+4z1z3+z2z3|=12, then the value of |z1+z2+z3| is

(a)

1

(b)

2

(c)

3

(d)

4

8. The principal argument of $\cfrac { 3 }{ -1+i }$

(a)

$\cfrac { -5\pi }{ 6 }$

(b)

$\cfrac { -2\pi }{ 3 }$

(c)

$\cfrac { -3\pi }{ 4 }$

(d)

$\cfrac { -\pi }{ 2 }$

9. If the coordinates at one end of a diameter of the circle x2+y2−8x−4y+c = 0 are (11,2) ,
the coordinates of the other end are

(a)

(-5,2)

(b)

(2,-5)

(c)

(5,-2)

(d)

(-2,5)

10. 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$\sqrt { 3 }$