#### 12th Standard Maths English Medium Free Online Test Creative 1 Mark Questions - Part Five

12th Standard

Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

10 x 1 = 10
1. 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

2. If z = $\frac { 1 }{ (2+3i)^{ 2 } }$ then |z| =

(a)

$\frac { 1 }{ 13 }$

(b)

$\frac { 1 }{ 5}$

(c)

$\frac { 1 }{ 12 }$

(d)

none of these

3. The equation $\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 }$ has

(a)

no solution

(b)

one solution

(c)

two solution

(d)

more than one solution

4. ${ tan }^{ -1 }\left( \cfrac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \cfrac { 2 }{ 11 } \right)$ =

(a)

0

(b)

$\cfrac { 1 }{ 2 }$

(c)

-1

(d)

none

5. The eccentricity of the ellipse 9x2+ 5y2 - 30y= 0 is

(a)

$\frac13$

(b)

$\frac23$

(c)

$\frac34$

(d)

none of these

6. If $\overset { \rightarrow }{ a }$,$\overset { \rightarrow }{ b }$ and $\overset { \rightarrow }{ c }$ are any three vectors, then $\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) =\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right)$ if and only if

(a)

$\overset { \rightarrow }{ b }$$\overset { \rightarrow }{ c }$ are collinear

(b)

$\overset { \rightarrow }{ a }$ and $\overset { \rightarrow }{ c }$ are collinear

(c)

$\overset { \rightarrow }{ a }$ and $\overset { \rightarrow }{ b }$ are collinear

(d)

none

7. In LMV theorem, we have f'(x1) =$\frac { f(b)-f(a) }{ b-a }$ then a < x1 _________

(a)

<b

(b)

≤b

(c)

=b

(d)

≠b

8. If u = log (x3 + y3 + z3 - 3xyz) then $\frac { { \partial }u }{ \partial { x } } +\frac { { \partial }u }{ { \partial y } }+ \frac { { \partial }u }{ \partial z }$ =

(a)

$\frac { 3 }{ x+y+z }$

(b)

x+y+z

(c)

$\frac { -9 }{ { (x+y+z) }^{ 2 } }$

(d)

$\frac { -9 }{ { (x+y+z) }^{ 2 } }$

9. The transformation y=vx reduces $\\ \\ \\ \frac { dy }{ dx } =\frac { x+y }{ 3x }$

(a)

$\frac { 3av }{ 4v+1 } =\frac { dx }{ x }$

(b)

$\frac { 3dv }{ v+1 } =\frac { dx }{ x }$

(c)

$2x\frac { dv }{ dx } =v$

(d)

$\frac { 3dv }{ 1-2v } ==\frac { dx }{ x }$

10. If a random variable X has the p.d.f.$f(x)=\cfrac { k }{ { x }^{ 2 }+1 } ,0<x<\infty$ then k is

(a)

$\pi$

(b)

$\cfrac { 1 }{ \pi }$

(c)

1

(d)

$\cfrac { 2 }{ \pi }$