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Sample 1 Mark Creative Questions (New Syllabus) 2020

12th Standard EM

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Maths

Time : 00:20:00 Hrs
Total Marks : 23

Part A

23 x 1 = 23
1. If $\rho$(A) = r then which of the following is correct?

(a)

all the minors of order n which do not vanish

(b)

'A' has at least one minor "of order r which does not vanish and all higher order minors vanish

(c)

'A' has at least one (r + 1) order minor which vanish

(d)

all (r + 1) and higher order minors should not vanish

2. In the non - homogeneous system of equations with 3 unknowns if $\rho$(A) = $\rho$([AIB]) = 2, then the system has _______

(a)

unique solution

(b)

one parameter family of solution

(c)

two parameter family of solutions

(d)

in consistent

3. 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$\frac { \theta }{ 2 }$

4. The modular of $\frac { (-1+i)(1-i) }{ 1+i\sqrt { 3 } }$ is ______

(a)

$\sqrt{2}$

(b)

2

(c)

1

(d)

$\frac{1}{2}$

5. 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

6. The number of solutions of the equation ${ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\cfrac { \pi }{ 4 }$

(a)

2

(b)

3

(c)

1

(d)

none

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

(a)

5

(b)

$\cfrac { 1 }{ 5 }$

(c)

$\cfrac { 5 }{ 14 }$

(d)

$\cfrac { 14 }{ 5 }$

8. If x>1,then $2{ tan }^{ -1 }x+{ sin }^{ -1 }\left( \cfrac { 2x }{ 1+{ x }^{ 2 } } \right)$ ________

(a)

4 tan-1x

(b)

0

(c)

$\cfrac { \pi }{ 2 }$

(d)

$\pi$

9. The length of the latus rectum of the ellipse $\frac { { x }^{ 2 } }{ 36 } +\frac { { y }^{ 2 } }{ 49 }$ = 1 is

(a)

$\frac { 98 }{ 6 }$

(b)

$\frac { 72 }{ 7 }$

(c)

$\frac { 72 }{ 14 }$

(d)

$\frac { 98 }{ 12 }$

10. If (1, -3) is the centre of the circle x+ y+ ax + by + 9 = 0 its radius is

(a)

$\sqrt{10}$

(b)

1

(c)

5

(d)

$\sqrt{19}$

11. The tangent at any point P on the ellipse $\frac { { x }^{ 2 } }{ 6 } +\frac { { y }^{ 2 } }{ 3 }$ = 1 whose centre C meets the major axis at T and PN is the perpendicular to the major axis; The CN CT = ______________

(a)

$\sqrt6$

(b)

3

(c)

$\sqrt3$

(d)

6

12. If $\overset { \rightarrow }{ a }$ and $\overset { \rightarrow }{ b }$ are two unit vectors, then the vectors $\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) \times \left( \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } \right)$ is parallel to the vector

(a)

$\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b }$

(b)

$\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b }$

(c)

2$\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b }$

(d)

2$\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b }$

13. If $\overset { \rightarrow }{ p } \times \overset { \rightarrow }{ q } =2\overset { \wedge }{ i } +3\overset { \wedge }{ j }$$\overset { \rightarrow }{ r } \times \overset { \rightarrow }{ s } =3\overset { \wedge }{ i } +2\overset { \wedge }{ k }$ then $\overset { \rightarrow }{ p } .\left( \overset { \rightarrow }{ q } \left( \overset { \rightarrow }{ r } \times \overset { \rightarrow }{ s } \right) \right)$ is

(a)

9

(b)

6

(c)

2

(d)

5

14. If the rate of increase of s =x3-5x2+5x+8 is twice the rate of increase of x, then one value of x is

(a)

$\frac{3}{5}$

(b)

$\frac{10}{3}$

(c)

$\frac{3}{10}$

(d)

$\frac{1}{3}$

15. The curve y = ex is ________

(a)

convex

(b)

concave

(c)

convex upwards

(d)

concave upwards

16. If u = xy + yx then ux + uy at x = y = 1 is

(a)

0

(b)

2

(c)

1

(d)

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

(a)

xyx-1

(b)

yxy-1

(c)

0

(d)

1

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

(a)

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

(b)

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

(c)

f(x) is odd

(d)

f(x) is even

19. $\int _{ a }^{ b }{ f(x) } dx=$ ..............

(a)

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

(b)

$\int _{ a }^{ b }{ f(a-x) } dx$

(c)

$\int _{ b }^{ a }{ f(b-x) } dx$

(d)

$\int _{ a }^{ b }{ f(a+b-x) } dx$

20. The I.F of y log y$\frac{dx}{dy}+x-log\ y=0$ is

(a)

log(log y)

(b)

log y

(c)

$\frac{1}{log\ y}$

(d)

$\frac{1}{log(log\ y)}$

21. The I.F. of (1+y2)dx=(tan-1-t-x)dy is ________.

(a)

etan-1 y

(b)

etan-1 x

(c)

tan-1 y

(d)

tan-1x

22. The Identity element of $\left\{ \left( \begin{matrix} x & x \\ x & x \end{matrix} \right) \right\}$ |x$\in$R, x≠0} under matrix multiplication is

(a)

$\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right)$

(b)

$\left( \begin{matrix} \frac { 1 }{ 4x } & \frac { 1 }{ 4x } \\ \frac { 1 }{ 4x } & \frac { 1 }{ 4x } \end{matrix} \right)$

(c)

$\left( \begin{matrix} \frac { 1 }{ 2 } & \frac { 1 }{ 2 } \\ \frac { 1 }{ 2 } & \frac { 1 }{ 2 } \end{matrix} \right)$

(d)

$\left( \begin{matrix} \frac { 1 }{ 2x } & \frac { 1 }{ 2x } \\ \frac { 1 }{ 2x } & \frac { 1 }{ 2x } \end{matrix} \right)$

23. 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