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#### Important 1 Mark Creative Questions (New Syllabus) 2020

12th Standard EM

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Maths

Time : 00:20:00 Hrs
Total Marks : 24

Part A

24 x 1 = 24
1. Which of the following is not an elementary transformation?

(a)

Ri ↔️ Rj

(b)

Ri ⟶ 2Ri + Rj

(c)

Cj ⟶ Cj + Ci

(d)

Ri ⟶ Ri + Cj

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

(a)

1

(b)

-1

(c)

i

(d)

0

3. If z = a + ib lies in quadrant then $\frac { \bar { z } }{ z }$ also lies in the III quadrant if

(a)

a > b > 0

(b)

a < b < 0

(c)

b < a < 0

(d)

b > a > 0

4. If x=cosθ + i sinθ, then xn+$\frac { 1 }{ { x }^{ n } }$ is ______

(a)

2 cos nθ

(b)

2 i sin nθ

(c)

2n cosθ

(d)

2n i sinθ

5. If ∝, β,૪ are the roots of 9x3-7x+6=0, then ∝ β ૪ is __________

(a)

$\frac{-7}{9}$

(b)

$\frac{7}{9}$

(c)

0

(d)

$\frac{-2}{3}$

6. 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

7. In a $\Delta ABC$  if C is a right angle, then  ${ tan }^{ -1 }\left( \cfrac { a }{ b+c } \right) +{ tan }^{ -1 }\left( \cfrac { b }{ c+a } \right) =$

(a)

$\cfrac { \pi }{ 3 }$

(b)

$\cfrac { \pi }{ 4 }$

(c)

$\cfrac { 5\pi }{ 2 }$

(d)

$\cfrac { \pi }{ 6 }$

8. The equation 7x2- 6$\sqrt { 3 }$ xy + 13y2 - 4$\sqrt { 3 }$ x - 4y - 12 = 0 represents

(a)

parabola

(b)

ellipse

(c)

hyperbola

(d)

rectangular hyperbola

9. Th point of curve y = 2x2 - 6x - 4 at which the targent is parallel to x - axis is

(a)

$\left( \frac { 5 }{ 2 } ,\frac { -7 }{ 12 } \right)$

(b)

$\left( \frac { -5 }{ 2 } ,\frac { -7 }{ 2 } \right)$

(c)

$\left( \frac { -5 }{ 2 } ,\frac { 17 }{ 12 } \right)$

(d)

$\left( \frac { 3 }{ 2 } ,\frac { -7 }{ 2 } \right)$

10. If θ is the angle between the vectors $\overset { \rightarrow }{ a }$ and $\overset { \rightarrow }{ b }$, then sinθ is

(a)

$\frac { \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } }{ \left| \overset { \rightarrow }{ a } \right| \left| \overset { \rightarrow }{ b } \right| }$

(b)

$\frac { \left| \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } \right| }{ \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } }$

(c)

$\sqrt { 1-{ \left( \frac { \overset { \rightarrow }{ a. } \overset { \rightarrow }{ b } }{ \left| \overset { \rightarrow }{ a } \right| \left| \overset { \rightarrow }{ b } \right| } \right) }^{ 2 } }$

(d)

0

11. For what value of $\left( \overset { \rightarrow }{ a } \right)$ will the straight lines $\frac { x+2 }{ a } =\frac { y }{ 3 } =\frac { z-1 }{ 4 }$and $\frac { x-3 }{ a } =\frac { y-1 }{ 4 } =\frac { z-7 }{ a }$be perpendicular?

(a)

1

(b)

2

(c)

3

(d)

-3

12. Let $\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,$ and $\overset { \rightarrow }{ c }$ be three vectors having magnitudes 1, 1, 2 respectively.
If $\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ c } \right) +\overset { \rightarrow }{ b } =0$ then the acute angle between $\overset { \rightarrow }{ a }$ and $\overset { \rightarrow }{ c }$ is ____________________

(a)

0

(b)

$\frac { \pi }{ 3 }$

(c)

$\frac { \pi }{ 6 }$

(d)

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

13. If a particle moves in a straight line according to s = t3-6t2-15t, the time interval during which the velocity is negative and acceleration is positive is

(a)

2 < t < 5

(b)

2 ≤ t ≤ 5

(c)

t ≥ 2

(d)

t ≤ 2

14. $\underset { x\rightarrow 0 }{ lim } \frac { x }{ tanx }$ is _________

(a)

1

(b)

-1

(c)

0

(d)

15. If u = log $\sqrt { { x }^{ 2 }+{ y }^{ 2 } }$, then $\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +\frac { { \partial }^{ 2 }u }{ { \partial y }^{ 2 } }$ is

(a)

$\sqrt { { x }^{ 2 }+{ y }^{ 2 } }$

(b)

0

(c)

u

(d)

2u

16. If u = yx then $\frac { \partial u }{ \partial y }$ = ............

(a)

xyx-1

(b)

yxy-1

(c)

0

(d)

1

17. The ratio of the volumes generated by revolving the ellipse $\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 }$ = 1 about major and minor axes is

(a)

4:9

(b)

9:4

(c)

2:3

(d)

3:2

18. $\int _{ 0 }^{ 2a }{ f(x) } dx=2\int _{ 0 }^{ 2a }{ f(x) } dx$

(a)

f(2a -x) =f(x)

(b)

f(a -x) =f(x)

(c)

f(x) = - f(-x)

(d)

f(-x) =f(x)

19. $\int _{ 0 }^{ \frac { \pi }{ 4 } }{ { cos }^{ 3 }2x \ dx= }$

(a)

$\frac { 2 }{ 3 }$

(b)

$\frac { 1 }{ 3 }$

(c)

0

(d)

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

20. The solution of $\frac{dy}{dx}+y$ cot x=sin 2x is

(a)

y sin x=$\frac{2}{3}$sin3x+c

(b)

y sec x=$\frac{x^2}{2}+c$

(c)

y sin x =c+x

(d)

2y sin x=sin x-$\frac{sin\ 3x}{3}+c$

21. 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

22. The differential equation associated with the family of concentric circles having their centres at the origin is _________.

(a)

$\frac { dy }{ dx } =\frac { -x }{ y }$

(b)

$\frac { dy }{ dx } =\frac { -y }{ x }$

(c)

$\frac { dy }{ dx } =\frac { x }{ y }$

(d)

$\frac { dy }{ dx } =\frac { y }{ x }$

23. Define * on Z by a*b = a+b+1 ∀ a,b $\in$ Z. Then the identity element of z is

(a)

1

(b)

0

(c)

1

(d)

-1

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

(a)

7

(b)

-7

(c)

0

(d)

-49