#### 12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Two

12th Standard

Reg.No. :
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Maths

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

25 x 1 = 25
1. If A = $\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right]$, B = adj A and C = 3A, then $\frac { \left| adjB \right| }{ \left| C \right| }$

(a)

$\frac { 1 }{ 3 }$

(b)

$\frac { 1 }{ 9 }$

(c)

$\frac { 1 }{ 4 }$

(d)

1

2. The rank of the matrix $\left[ \begin{matrix} 1 \\ \begin{matrix} 2 \\ -1 \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} 4 \\ -2 \end{matrix} \end{matrix}\begin{matrix} 3 \\ \begin{matrix} 6 \\ -3 \end{matrix} \end{matrix}\begin{matrix} 4 \\ \begin{matrix} 8 \\ -4 \end{matrix} \end{matrix} \right]$ is

(a)

1

(b)

2

(c)

4

(d)

3

3. The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is

(a)

0

(b)

1

(c)

2

(d)

infinitely many

4. In a homogeneous system if $\rho$ (A) =$\rho$([A|0]) < the number of unknouns then the system has ________

(a)

trivial solution

(b)

only non - trivial solution

(c)

no solution

(d)

trivial solution and infinitely many non - trivial solutions

5. If |z-2+i|≤2, then the greatest value of |z| is

(a)

$\sqrt { 3 } -2$

(b)

$\sqrt { 3 } +2$

(c)

$\sqrt { 5 } -2$

(d)

$\sqrt { 5 } +2$

6. The complex number z which satisfies the condition $\left| \frac { 1+z }{ 1-z } \right|$ =1 lies on

(a)

circle x2+y2 =1

(b)

x-axis

(c)

y-axis

(d)

the lines x+y=1

7. $\frac { (cos\theta +isin\theta )^{ 6 } }{ (cos\theta -isin\theta )^{ 5 } }$ = ________

(a)

cos 11θ - isin 11θ

(b)

cos 11θ + isin 11θ

(c)

cosθ + i sinθ

(d)

$cos\frac { 6\theta }{ 5 } +isin\frac { 6\theta }{ 5 }$

8. The number of positive zeros of the polynomial $\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }$(-1)rxr is

(a)

0

(b)

n

(c)

< n

(d)

r

9. 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

10. ${ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 3 } \right)$is equal to

(a)

$\frac { 1 }{ 2 } { cos }^{ -1 }\left( \frac { 3 }{ 5 } \right)$

(b)

$\frac { 1 }{ 2 } { sin }^{ -1 }\left( \frac { 3 }{ 5 } \right)$

(c)

$\frac { 1 }{ 2 } {tan }^{ -1 }\left( \frac { 3 }{ 5 } \right)$

(d)

${ tan}^{ -1 }\left( \frac { 1}{ 2 } \right)$

11. The number of real solutions of the equation $\sqrt { 1+cos2x } ={ 2sin }^{ -1 }\left( sinx \right) ,-\pi <x<\pi$ is

(a)

0

(b)

1

(c)

2

(d)

infinte

12. If $4{ cos }^{ -1 }x+{ sin }^{ -1 }x=\pi$ then x is

(a)

$\cfrac { 3 }{ 2 }$

(b)

$\cfrac { 1 }{ \sqrt { 2 } }$

(c)

$\cfrac { \sqrt { 3 } }{ 2 }$

(d)

$\cfrac { 2 }{ \sqrt { 3 } }$

13. The radius of the circle passing through the point(6,2) two of whose diameter arex+y=6
and x+2y=4 is

(a)

10

(b)

${2} \sqrt {5}$

(c)

6

(d)

4

14. Equation of tangent at (-4, -4) on x2 = -4y is

(a)

2x - y + 4 = 0

(b)

2x + y - 4 = 0

(c)

2x - y - 12 = 0

(d)

2x + y + 4 = 0

15. $\vec { a } .\vec { b } =\vec { b } .\vec { c } =\vec { c } .\vec { a } =0$ , then the value of $[\vec { a } ,\vec { b } ,\vec { c } ]$ is

(a)

$\left| \vec { a } \right| \left| \vec { b } \right| \left| \vec { c } \right|$

(b)

$\frac{1}{3}$$\left| \vec { a } \right| \left| \vec { b } \right| \left| \vec { c } \right|$

(c)

1

(d)

-1

16. If  $\left| \overset { \rightarrow }{ a } \right| =\left| \overset { \rightarrow }{ b } \right| =1$such that $\overset { \rightarrow }{ a } +2\overset { \rightarrow }{ b }$ and $5\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b }$ are perpendicular to each other, then the angle between $\overset { \rightarrow }{ a }$ and $\overset { \rightarrow }{ b }$ is

(a)

45o

(b)

60o

(c)

cos-1 $\left( \frac { 1 }{ 3 } \right)$

(d)

cos-1 $\left( \frac { 2 }{ 7 } \right)$

17. The area of the parallelogram having diagonals $\overset { \rightarrow }{ a } =\overset { \wedge }{ 3i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k }$ and $\overset { \rightarrow }{ b } =\overset { \wedge }{ i } -3\overset { \wedge }{ j } +4\overset { \wedge }{ k }$ is _______________

(a)

4

(b)

$2\sqrt { 3 }$

(c)

$4\sqrt { 3 }$

(d)

$5\sqrt { 3 }$

18. $\underset { x\rightarrow 0 }{ lim } \frac { x }{ tanx }$ is _________

(a)

1

(b)

-1

(c)

0

(d)

19. 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

20. The cube root of 127 is ............

(a)

5.026

(b)

5.26

(c)

5.028

(d)

5.075

21. The value of $\frac { (n+2) }{ (n) } =90$ then n is

(a)

10

(b)

5

(c)

8

(d)

9

22. The differential equation of the family of curves y = Aex + Be−x, where A and B are arbitrary constants is

(a)

$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +y=0$

(b)

$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -y=0$

(c)

$\frac { { d }y }{ { dx } } +y=0$

(d)

$\frac { { d }y }{ { dx } } -y=0$

23. Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins Rs. 36, otherwise he loses Rs. k2 , where k is the face that comes up k = {1, 2, 3, 4, 5}.
The expected amount to win at this game in Rs. is

(a)

$\cfrac { 19 }{ 6 }$

(b)

$-\cfrac { 19 }{ 6 }$

(c)

$\cfrac { 3 }{ 2 }$

(d)

$-\cfrac { 3 }{ 2 }$

24. If in 6 trials, X is a binomial variable which follows the relation 9P(X = 4) = P(X = 2), then the probability of success is

(a)

0.125

(b)

0.25

(c)

0.375

(d)

0.75

25. The operation * defined by a*b =$\frac{ab}{7}$ is not a binary operation on

(a)

Q+

(b)

Z

(c)

R

(d)

C