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

12th Standard

Reg.No. :
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Maths

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

10 x 1 = 10
1. The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = has a unique solution if

(a)

k ≠ 0

(b)

-1 < k < 1

(c)

-2 < k < 2

(d)

k=0

2. The principal value of the amplitude of (1+i) is

(a)

$\frac { \pi }{ 4 }$

(b)

$\frac { \pi }{ 12 }$

(c)

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

(d)

$\pi$

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

(a)

5

(b)

$\cfrac { 1 }{ 5 }$

(c)

$\cfrac { 5 }{ 14 }$

(d)

$\cfrac { 14 }{ 5 }$

5. The director circle of the ellipse $\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 5 } =1$ is

(a)

x2 + y2 = 4

(b)

x2 +y2 = 9

(c)

x2 +y2 = 45

(d)

x2 +y2 = 14

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

7. The work done by the force $\overset { \rightarrow }{ F } =\overset { \wedge }{ i } +\overset { \wedge }{ j } +\overset { \wedge }{ k }$ acting on a particle, if the particle is displaced from A(3, 3, 3) to the point B(4, 4, 4) is _______________ units

(a)

2

(b)

3

(c)

4

(d)

7

8. The least value of a when f f(x) =x2+ax+1 is increasing on (1, 2) is

(a)

-2

(b)

2

(c)

1

(d)

-1

9. 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)

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

10. The area enclosed by the curve y = $\frac { { x }^{ 2 } }{ 2 }$ , the x - axis and the lines x = 1, x = 3 is

(a)

4

(b)

8$\frac23$

(c)

13

(d)

4$\frac{1}{3}$