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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 : 28

Pat A

28 x 1 = 28
1. 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

2. If $\rho$(A) = $\rho$([A/B]) = number of unknowns, then the system is

(a)

consistent and has infinitely many solutions

(b)

consistent

(c)

inconsistent

(d)

consistent and has unique solution

3. If $\rho$(A) ≠ $\rho$([AIB]), then the system is

(a)

consistent and has infinitely many solutions

(b)

consistent and has a unique solution

(c)

consistent

(d)

inconsistent

4. If, i2 = -1, then i1 + i2 + i3 + ....+ up to 1000 terms is equal to

(a)

1

(b)

-1

(c)

i

(d)

0

5. 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

6. If x =cosθ + i sinθ, then the value of xn+$\frac { 1 }{ { x }^{ n } }$ is

(a)

2 cosθ

(b)

2i sin nθ

(c)

2i sin nθ

(d)

2i cos nθ

7. If x is real and $\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 }$ then

(a)

$\frac{1}{3}$ ≤k≤

(b)

k≥5

(c)

k≤0

(d)

none

8. lf the root of the equation x3 +bx2+cx-1=0 form an lncreasing G.P, then

(a)

one of the roots is 2

(b)

one of the rots is 1

(c)

one of the rots is -1

(d)

one of the rots is -2

9. If ax2 + bx + c = 0, a, b, c E R has no real zeros, and if a + b + c < 0, then __________

(a)

c>0

(b)

c<0

(c)

c=0

(d)

c≥0

10. ·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)

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

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

(a)

5

(b)

$\cfrac { 1 }{ 5 }$

(c)

$\cfrac { 5 }{ 14 }$

(d)

$\cfrac { 14 }{ 5 }$

12. If $4{ cos }^{ -1 }x+{ sin }^{ -1 }x=\pi$ then x is

(a)

$\cfrac { 3 }{ 2 }$

(b)

$\cfrac { 1 }{ \sqrt { 2 } }$

(c)

$\cfrac { \sqrt { 3 } }{ 2 }$

(d)

$\cfrac { 2 }{ \sqrt { 3 } }$

13. y2 - 2x - 2y + 5 = 0 is a

(a)

circle

(b)

parabola

(c)

ellipse

(d)

hyperbola

14. If the distance between the foci is 2 and the distance between the direction is 5, then the equation of the ellipse is

(a)

6x2 + 10y2 = 5

(b)

6x2 + 10y2 = 15

(c)

x2 + 3y2 = 10

(d)

none

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

(a)

25ㅠ

(b)

5ㅠ

(c)

10ㅠ

(d)

25

16. 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

17. 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$\sqrt { 3 }$

18. 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)

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

19. Equation of the normal to the curve y=2x2+3 sin x at x=0 is

(a)

x + y = 0

(b)

3y = 0

(c)

x + 3y = 7

(d)

x + 3y = 0

20. The curve y = ex is ________

(a)

convex

(b)

concave

(c)

convex upwards

(d)

concave upwards

21. If f(x,y) = 2x2 - 3xy + 5y + 7 then f(0, 0) and f(1, 1) is

(a)

7,11

(b)

11,7

(c)

0,7

(d)

1,0

22. If u = sin-1 $\left( \frac { { x }^{ 4 }+{ y }^{ 4 } }{ { x }^{ 2 }+{ y }^{ 2 } } \right)$ and f= sin u then f is a homogeneous function of degree ..................

(a)

0

(b)

1

(c)

2

(d)

4

23. $\int _{ 0 }^{ \infty }{ { e }^{ -mx } } { x }^{ 7 }$ dx is

(a)

(b)

(c)

(d)

24. $\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { sin \ x-cos \ x }{ 1+sin \ x cos \ x } dx= }$ ............

(a)

$\frac { \pi }{ 2 }$

(b)

0

(c)

$\frac { \pi }{ 4 }$

(d)

$\pi$

25. The I.F of $\frac{dy}{dx}-y$ tan x=cos x is

(a)

sec x

(b)

cos x

(c)

etan x

(d)

cot x

26. The number of binary operations that can be defined on a set of 3 elements is

(a)

32

(b)

33

(c)

39

(d)

31

27. If p is true and q is unknown, then _________

(a)

~ p is true

(b)

p v (~p) is false

(c)

p ∧ (~p) is true

(d)

p v q is true

28. In (N, *), x * y = max(x, y), x, y $\in$ N then 7 * (-7)

(a)

7

(b)

-7

(c)

0

(d)

-49