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

12th Standard

Reg.No. :
•
•
•
•
•
•

Maths

Time : 00:10:00 Hrs
Total Marks : 10
25 x 1 = 25
1. Let A be a 3 x 3 matrix and B its adjoint matrix If |B|=64, then |A|=

(a)

±2

(b)

±4

(c)

±8

(d)

±12

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. If A is a non-singular matrix then IA-1|= ______

(a)

$\left| \frac { 1 }{ { A }^{ 2 } } \right|$

(b)

$\frac { 1 }{ |A^{ 2 }| }$

(c)

$\left| \frac { 1 }{ A } \right|$

(d)

$\frac { 1 }{ |A| }$

4. 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

5. If $\omega \neq 1$ is a cubic root of unity and $\left| \begin{matrix} 1 & 1 & 1 \\ 1 & { -\omega }^{ 2 } & { \omega }^{ 2 } \\ 1 & { \omega }^{ 2 } & { \omega }^{ 2 } \end{matrix} \right|$ =3k, then k is equal to

(a)

1

(b)

-1

(c)

$\sqrt { 3i }$

(d)

$-\sqrt { 3i }$

6. If z=$\frac { 1 }{ 1-cos\theta -isin\theta }$, the Re(z) =

(a)

0

(b)

$\frac{1}{2}$

(c)

cot$\frac { \theta }{ 2 }$

(d)

$\frac{1}{2}$cot$\frac { \theta }{ 2 }$

7. The conjugate of $\frac { 1+2i }{ 1-(1-i)^{ 2 } }$ is _______

(a)

$\frac { 1+2i }{ 1-(1-i)^{ 2 } }$

(b)

$\frac { 5 }{ 1-(1-i)^{ 2 } }$

(c)

$\frac { 1-2i }{ 1+(1+i)^{ 2 } }$

(d)

$\frac { 1+2i }{ 1+(1-i)^{ 2 } }$

8. The polynomial x3+2x+3 has

(a)

one negative and two real roots

(b)

one positive and two imaginary roots

(c)

three real roots

(d)

no solution

9. Ifj(x) = 0 has n roots, thenf'(x) = 0 has __________ roots

(a)

n

(b)

n -1

(c)

n+1

(d)

(n-r)

10. If (2+√3)x2-2x+1+(2-√3)x2-2x-1=$\frac { 2 }{ 2-\sqrt { 3 } }$ then x=

(a)

0,2

(b)

0,1

(c)

0,3

(d)

0, √3

11. If cot-1 2 and cot-1 3 are two angles of a triangle, then the third angle is

(a)

$\frac{\pi}{4}$

(b)

$\frac{3\pi}{4}$

(c)

$\frac{\pi}{6}$

(d)

$\frac{\pi}{3}$

12. If sin-1 $\frac{x}{5}+ cosec^{-1}\frac{5}{4}=\frac{\pi}{2}$, then the value of x is

(a)

4

(b)

5

(c)

2

(d)

3

13. ·If $\alpha ={ tan }^{ -1 }\left( \cfrac { \sqrt { 3 } }{ 2y-x } \right) ,\beta ={ tan }^{ -1 }\left( \cfrac { 2x-y }{ \sqrt { 3y } } \right)$ then $\alpha -\beta$

(a)

$\cfrac { \pi }{ 6 }$

(b)

$\cfrac { \pi }{ 3 }$

(c)

$\cfrac { \pi }{ 2 }$

(d)

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

14. The value of sin(2(tan-1 0.75) is___________

(a)

0.75

(b)

1.5

(c)

0.96

(d)

sin-1(1.5)

15. The centre of the circle inscribed in a square formed by the lines x2−8x−12=0 and y2−14y+45 = 0 is

(a)

(4,7)

(b)

(7,4)

(c)

(9,4)

(d)

(4,9)

16. The ellipse E1$\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1$ is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point(0,4) circumscribes the rectangle R . The eccentricity of the ellipse is

(a)

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

(b)

$\frac { \sqrt { 3 } }{ 2 }$

(c)

$\frac { 1 }{ 2 }$

(d)

$\frac { 3 }{ 4 }$

17. Area of the greatest rectangle inscribed in the ellipse $\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1.$ is

(a)

2ab

(b)

ab

(c)

$\sqrt{ ab}$

(d)

$\frac { a }{ b }$

18. The equation of tangent at (1, 2) to the circle x+ y2 = 5 is

(a)

x+y=3

(b)

x + 2y = 3

(c)

x- y= 5

(d)

x - 2y = 5

19. The number of normals to the hyperbola $\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } }$ = 1 from an external point is

(a)

2

(b)

4

(c)

6

(d)

5

20. The locus of the foot of perpendicular from the focus on any tangent to y2 = 4ax is

(a)

x2 + y2 = a2 - b2

(b)

x2 + y2 = a2

(c)

x2 + y2 = a2 - b2

(d)

x = 0

21. 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)

$\frac { \pi }{ 2 }$

22. If $\overset { \rightarrow }{ d } =\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) +\overset { \rightarrow }{ b } \times \left( \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \right) +\overset { \rightarrow }{ c } \times \left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right)$, then

(a)

$\left| \overset { \rightarrow }{ d } \right|$

(b)

$\overset { \rightarrow }{ d } =\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c }$

(c)

$\overset { \rightarrow }{ d } =\overset { \rightarrow }{ 0 }$

(d)

a, b, c are coplanar

23. 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

24. 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)

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

25. 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)

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