#### 12th Standard Maths English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - Part Three

12th Standard

Reg.No. :
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Maths

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

10 x 1 = 10
1. If A is a non-singular matrix such that A-1 = $\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right]$, then (AT)−1 =

(a)

$\left[ \begin{matrix} -5 & 3 \\ 2 & 1 \end{matrix} \right]$

(b)

$\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right]$

(c)

$\left[ \begin{matrix} -1 & -3 \\ 2 & 5 \end{matrix} \right]$

(d)

$\left[ \begin{matrix} 5 & -2 \\ 3 & -1 \end{matrix} \right]$

2. If (1+i)(1+2i)(1+3i)...(1+ni)=x+iy, then $2\cdot 5\cdot 10...\left( 1+{ n }^{ 2 } \right)$ is

(a)

1

(b)

i

(c)

x2+y2

(d)

1+n2

3. According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

(a)

-1

(b)

$\frac { 5 }{ 4 }$

(c)

$\frac { 4 }{ 5 }$

(d)

5

4. If |x|$\le$1, then 2tan-1 x-sin-1 $\frac{2x}{1+x^2}$ is equal to

(a)

tan-1x

(b)

sin-1x

(c)

0

(d)

$\pi$

5. If P(x, y) be any point on 16x2+25y2=400 with foci F1 (3,0) and F2 (-3,0) then PF1 PF2 +
is

(a)

8

(b)

6

(c)

10

(d)

12

6. If the two tangents drawn from a point P to the parabolay2 = 4x are at right angles then the locus of P is

(a)

2x+1=0

(b)

x = −1

(c)

2x−1=0

(d)

x =1

7. Distance from the origin to the plane 3x - 6y + 2z 7 = 0 is

(a)

0

(b)

1

(c)

2

(d)

3

8. The maximum value of the function x2 e-2x,

(a)

$\cfrac { 1 }{ e }$

(b)

$\cfrac { 1 }{ 2e }$

(c)

$\cfrac { 1 }{ { e }^{ 2 } }$

(d)

$\cfrac { 4 }{ { e }^{ 4 } }$

9. If w (x, y, z) = x2 (v - z) + y2 (z - x) + z2(x - y), then $\frac { { \partial }w }{ \partial x } +\frac { \partial w }{ \partial y } +\frac { \partial w }{ \partial z }$ is

(a)

xy + yz + zx

(b)

x(y + z)

(c)

y(z + x)

(d)

0

10. The value of $\int _{ 0 }^{ a }{ { (\sqrt { { a }^{ 2 }-{ x }^{ 2 } } ) }^{ 2 } } dx$

(a)

$\frac { { \pi a }^{ 2 } }{ 16 }$

(b)

$\frac { 3\pi { a }^{ 4 } }{ 16 }$

(c)

$\frac { 3\pi { a }^{2 } }{ 8}$

(d)

$\frac { 3\pi { a }^{ 4 } }{ 8}$