#### 12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020

12th Standard

Reg.No. :
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Maths

Time : 00:25:00 Hrs
Total Marks : 25

25 x 1 = 25
1. If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT =

(a)

A

(b)

B

(c)

I

(d)

BT

2. If the system of equations x = cy + bz, y = az + cx and z = bx + ay has a non - trivial solution then

(a)

a2 + b2 + c2 = 1

(b)

abc ≠ 1

(c)

a + b + c =0

(d)

a2 + b2 + c2 + 2abc =1

3. If A is a non-singular matrix then IA-1|= ______

(a)

$\left| \frac { 1 }{ { A }^{ 2 } } \right|$

(b)

$\frac { 1 }{ |A^{ 2 }| }$

(c)

$\left| \frac { 1 }{ A } \right|$

(d)

$\frac { 1 }{ |A| }$

4. The value of $\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) }$ is

(a)

1+ i

(b)

i

(c)

1

(d)

0

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

(a)

$\frac { \pi }{ 4 }$

(b)

$\frac { \pi }{ 12 }$

(c)

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

(d)

$\pi$

6. The amplitude of $\frac{1}{i}$ is equal to

(a)

0

(b)

$\frac { \pi }{ 2 }$

(c)

-$\frac { \pi }{ 2 }$

(d)

$\pi$

7. If f and g are polynomials of degrees m and n respectively, and if h(x) =(f 0 g)(x), then the degree of h is

(a)

mn

(b)

m+n

(c)

mn

(d)

nm

8. 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

9. sin−1(cos x)$=\frac{\pi}{2}-x$ is valid for

(a)

$-\pi \le x\le 0$

(b)

$0\pi \le x\le 0$

(c)

$-\frac { \pi }{ 2 } \le x\le \frac { \pi }{ 2 }$

(d)

$-\frac { \pi }{ 4 } \le x\le \frac { 3\pi }{ 4 }$

10. ·If $\alpha ={ tan }^{ -1 }\left( \cfrac { \sqrt { 3 } }{ 2y-x } \right) ,\beta ={ tan }^{ -1 }\left( \cfrac { 2x-y }{ \sqrt { 3y } } \right)$ then $\alpha -\beta$

(a)

$\cfrac { \pi }{ 6 }$

(b)

$\cfrac { \pi }{ 3 }$

(c)

$\cfrac { \pi }{ 2 }$

(d)

$\cfrac { -\pi }{ 3 }$

11. $cot\left( \cfrac { \pi }{ 4 } -{ cot }^{ -1 }3 \right)$

(a)

7

(b)

6

(c)

5

(d)

none

12. The circle x2+y2=4x+8y+5intersects the line3x−4y=m at two distinct points if

(a)

15< m < 65

(b)

35< m <85

(c)

−85<m < −35

(d)

−35<m <15

13. 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)

$\frac { 98 }{ 12 }$

14. The angle between the tangents drawn from (1, 4) to the parabola y2 = 4x is __________

(a)

$\frac { \pi }{ 2 }$

(b)

$\frac { \pi }{ 3 }$

(c)

$\frac { \pi }{ 5 }$

(d)

$\frac { \pi }{ 5 }$

15. If a vector $\vec { \alpha }$ lies in the plane of $\vec { \beta }$ and $\vec { \gamma }$ , then

(a)

$[\vec { \alpha } ,\vec { \beta } ,\vec { \gamma } ]$ = 1

(b)

$[\vec { \alpha } ,\vec { \beta } ,\vec { \gamma } ]$= -1

(c)

$[\vec { \alpha } ,\vec { \beta } ,\vec { \gamma } ]$= 0

(d)

$[\vec { \alpha } ,\vec { \beta } ,\vec { \gamma } ]$= 2

16. Let $\overset { \rightarrow }{ a }$,$\overset { \rightarrow }{ b }$ and $\overset { \rightarrow }{ c }$ be three non- coplanar vectors and let $\overset { \rightarrow }{ p } ,\overset { \rightarrow }{ q } ,\overset { \rightarrow }{ r }$ be the vectors defined by the relations $\overset { \rightarrow }{ P } =\frac { \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } ,\overset { \rightarrow }{ q } =\frac { \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } ,\overset { \rightarrow }{ r } =\frac { \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] }$ Then the value of  $\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) .\overset { \rightarrow }{ p } +\left( \overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right) .\overset { \rightarrow }{ q } +\left( \overset { \rightarrow }{ c } +\overset { \rightarrow }{ a } \right) .\overset { \rightarrow }{ r }$=

(a)

0

(b)

1

(c)

2

(d)

3

17. 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

18. The straight lines $\frac { x-3 }{ 2 } =\frac { y+5 }{ 4 } =\frac { z-1 }{ -13 }$ and $\frac { x+1 }{ 3 } =\frac { y-4 }{ 5 } =\frac { z+2 }{ 2 }$ are

(a)

parallel

(b)

perpendicular

(c)

inclined at 45o

(d)

none

19. Let $\overset { \rightarrow }{ u } ,\overset { \rightarrow }{ v } ,\overset { \rightarrow }{ w }$ be vectors such that $\overset { \rightarrow }{ u } +\overset { \rightarrow }{ v } +\overset { \rightarrow }{ w } =\overset { \rightarrow }{ 0 }$. If $\left| \overset { \rightarrow }{ u } \right|$= 3$\left| \overset { \rightarrow }{ v } \right|$= 4$\left| \overset { \rightarrow }{ w } \right|$=5  then $\overset { \rightarrow }{ u } .\overset { \rightarrow }{ v } +\overset { \rightarrow }{ v } .\overset { \rightarrow }{ w } +\overset { \rightarrow }{ w } .\overset { \rightarrow }{ u }$ is ______________

(a)

25

(b)

-25

(c)

5

(d)

$\sqrt { 5 }$

20. If the slope of the curve 2y2=ax2+b at (1,-1) is - 1, then the values of a, b is

(a)

2, 0

(b)

0, 2

(c)

0, 0

(d)

2, 2

21. The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?

(a)

$\frac{1}{31}$

(b)

$\frac15$

(c)

5

(d)

31

22. The value of $\int _{ 0 }^{ 1 }{ { ({ sin }^{ -1 }x) }^{ 2 } } dx$

(a)

$\frac { { \pi }^{ 2 } }{ 4 } -1$

(b)

$\frac { { \pi }^{ 2 } }{ 4 } +2$

(c)

$\frac { { \pi }^{ 2 } }{ 4 } +1$

(d)

$\frac { { \pi }^{ 2 } }{ 4 } -2$

23. The solution of the differential equation $\frac { dy }{ dx } =2xy$is

(a)

y = Cex2

(b)

y= 2x2 +C

(c)

y = Ce−x2 +C

(d)

y = x2 +C

24. A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is
$f(x)=\left\{\begin{array}{ll} \frac{1}{l} & 0<x<l \\\ 0 & l \leq x<2 l \end{array}\right.$
The mean and variance of the shorter of the two pieces are respectively

(a)

$\cfrac { l }{ 2 } ,\cfrac { { l }^{ 2 } }{ 3 }$

(b)

$\\ \cfrac { l }{ 2 } ,\cfrac { { l }^{ 2 } }{ 6 }$

(c)

$l,\cfrac { { l }^{ 2 } }{ 12 }$

(d)

$\cfrac { l }{ 2 } ,\cfrac { { l }^{ 2 } }{ 12 }$

25. Subtraction is not a binary operation in

(a)

R

(b)

Z

(c)

N

(d)

Q