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#### Model 1 Mark Book Back Questions (New Syllabus) 2020

12th Standard EM

Reg.No. :
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Maths

Time : 00:20:00 Hrs
Total Marks : 20

Part A

20 x 1 = 20
1. If (AB)-1 = $\left[ \begin{matrix} 12 & -17 \\ -19 & 27 \end{matrix} \right]$ and A-1 = $\left[ \begin{matrix} 1 & -1 \\ -2 & 3 \end{matrix} \right]$, then B-1 =

(a)

$\left[ \begin{matrix} 2 & -5 \\ -3 & 8 \end{matrix} \right]$

(b)

$\left[ \begin{matrix} 8 & 5 \\ 3 & 2 \end{matrix} \right]$

(c)

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

(d)

$\left[ \begin{matrix} 8 & -5 \\ -3 & 2 \end{matrix} \right]$

2. If 0 ≤ θ  ≤ π and the system of equations x + (sinθ)y - (cosθ)z = 0, (cosθ)x - y +z = 0, (sinθ)x + y - z = 0 has a non-trivial solution then θ is

(a)

$\frac { 2\pi }{ 3 }$

(b)

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

(c)

$\frac { 5\pi }{ 6 }$

(d)

$\frac { \pi }{ 4 }$

3. If $z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } }$ , then |z| is equal to

(a)

0

(b)

1

(c)

2

(d)

3

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

(a)

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

(b)

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

(c)

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

(d)

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

5. If α,β and γ are the roots of x3+px2+qx+r, then $\Sigma \frac { 1 }{ \alpha }$ is

(a)

-$\frac { q }{ r }$

(b)

$\frac { p }{ r }$

(c)

$\frac { q }{ r }$

(d)

-$\frac { q }{ p }$

6. ${ sin }^{ -1 }\frac { 3 }{ 5 } -{ cos }^{ -1 }\frac { 12 }{ 13 } +{ sec }^{ -1 }\frac { 5 }{ 3 } { -cosec }^{ 1- }\frac { 13 }{ 2 }$is equal to

(a)

2$\pi$

(b)

$\pi$

(c)

0

(d)

tan-1$\frac{12}{65}$

7. ${ sin }^{ -1 }\left( tan\frac { \pi }{ 4 } \right) -{ sin }^{ -1 }\left( \sqrt { \frac { 3 }{ x } } \right) =\frac { \pi }{ 6 }$.Then x is a root of the equation

(a)

x2−x−6=0

(b)

x2−x−12=0

(c)

x2+x−12=0

(d)

x2+x−6=0

8. 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)

9. The locus of a point whose distance from (-2,0) is $\frac { 2 }{ 3 }$ times its distance from the line x = $\frac { -9 }{ 2 }$ is

(a)

a parabola

(b)

a hyperbola

(c)

an ellipse

(d)

a circle

10. If $\vec { a } ,\vec { b } ,\vec { c }$ are three non-coplanar vectors such that $\vec { a } \times (\vec { b } \times \vec { c } )=\frac { \vec { b } +\vec { c } }{ \sqrt { 2 } }$, then the angle between

(a)

$\frac { \pi }{ 2 }$

(b)

$\frac { 3\pi }{ 6 }$

(c)

$\frac { \pi }{ 4 }$

(d)

${ \pi }$

11. If the length of the perpendicular from the origin to the plane 2x + 3y + λz =1, λ > 0 is $\frac{1}{5}$ then the value of λ is

(a)

$2\sqrt { 3 }$

(b)

$3\sqrt { 2 }$

(c)

0

(d)

1

12. The slope of the line normal to the curve f(x) = 2cos 4x at $x=\cfrac { \pi }{ 12 }$

(a)

$-4\sqrt { 3 }$

(b)

-4

(c)

$\cfrac { \sqrt { 3 } }{ 12 }$

(d)

$4\sqrt { 3 }$

13. The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?

(a)

$\frac{1}{31}$

(b)

$\frac15$

(c)

5

(d)

31

14. The value of $\frac { (n+2) }{ (n) } =90$ then n is

(a)

10

(b)

5

(c)

8

(d)

9

15. The order of the differential equation of all circles with centre at (h, k ) and radius ‘a’ is

(a)

2

(b)

3

(c)

4

(d)

1

16. The solution of the differential equation $\frac { dy }{ dx } =\frac { y }{ x } +\frac { \phi \left( \frac { y }{ x } \right) }{ \phi '\left( \frac { y }{ x } \right) }$is

(a)

$x\phi \left( \frac { y }{ x } \right) =k$

(b)

$\phi \left( \frac { y }{ x } \right) =kx$

(c)

$y\phi \left( \frac { y }{ x } \right) =k$

(d)

$\phi \left( \frac { y }{ x } \right) =ky$

17. A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is roUed and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is

(a)

1

(b)

2

(c)

3

(d)

4

18. Which of the following is a discrete random variable?
I. The number of cars crossing a particular signal in a day
II.The number of customers in a queue-to buy train tickets at a moment.
III.The time taken to complete a telephone call.

(a)

I and II

(b)

II only

(c)

III only

(d)

II and III

19. The operation * defined by a*b =$\frac{ab}{7}$ is not a binary operation on

(a)

Q+

(b)

Z

(c)

R

(d)

C

20. Determine the truth value of each of the following statements:
(a) 4+2=5 and 6+3=9
(b) 3+2=5 and 6+1=7
(c) 4+5=9 and1+2= 4
(d) 3+2=5 and 4+7=11

(a)
 (a) (b) (c) (d) F T T T
(b)
 (a) (b) (c) (d) T F T F
(c)
 (a) (b) (c) (d) T T F F
(d)
 (a) (b) (c) (d) F F T T