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12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020

12th Standard EM

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Maths

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

Answer all the questions

25 x 1 = 25
1. If |adj(adj A)| = |A|9, then the order of the square matrix A is

(a)

3

(b)

4

(c)

2

(d)

5

2. 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

3. in+in+1+in+2+in+3 is

(a)

0

(b)

1

(c)

-1

(d)

i

4. A zero of x3 + 64 is

(a)

0

(b)

4

(c)

4i

(d)

-4

5. For real x, the equation $\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| }$ has

(a)

one solution

(b)

two solution

(c)

at least two solution

(d)

no solution

6. The value of sin-1 (cos x),0$\le x\le\pi$ is

(a)

$\pi-x$

(b)

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

(c)

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

(d)

$\pi-x$

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

(a)

7

(b)

6

(c)

5

(d)

none

8. The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

(a)

$0,-\frac { 40 }{ 9 }$

(b)

0

(c)

$\frac { 40 }{ 9 }$

(d)

$\frac { -40 }{ 9 }$

9. 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

10. If $\vec{a}$ and $\vec{b}$ are parallel vectors, then $[\vec { a } ,\vec { c } ,\vec { b } ]$ is equal to

(a)

2

(b)

-1

(c)

1

(d)

0

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

(a)

4

(b)

2$\sqrt { 3 }$

(c)

4$\sqrt { 3 }$

(d)

5$\sqrt { 3 }$

12. The angle between the planes 2x + y - z = 9 and x + 2y + z = 7 is_____________

(a)

cos-1 (5/6)

(b)

cos-1 (5/36)

(c)

cos-1 (1/2)

(d)

cos-1 (1/12)

13. The volume of a sphere is increasing in volume at the rate of 3 πcm3 sec. The rate of change of its radius when radius is $\cfrac { 1 }{ 2 }$ cm

(a)

3 cm/s

(b)

2 cm/s

(c)

1 cm/s

(d)

$\cfrac { 1 }{ 2 } cm/s$

14. The statement " If f has a local extremum at c and if f'(c) exists then f'(c) = 0" is ________

(a)

the extreme value theorem

(b)

Fermats' theorem

(c)

Law of mean

(d)

Rolle's theorem

15. A circular template has a radius of 10 cm. The measurement of radius has an approximate error of 0.02 cm. Then the percentage error in calculating area of this template is

(a)

0.2%

(b)

0.4%

(c)

0.04%

(d)

0.08%

16. 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)

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

17. The value of $\int _{ -4 }^{ 4 }{ \left[ { tan }^{ -1 }\left( \frac { { x }^{ 2 } }{ { x }^{ 4 }+1 } \right) +{ tan }^{ -1 }\left( \frac { { x }^{ 4 }+1 }{ { x }^{ 2 } } \right) \right] dx }$ is

(a)

$\pi$

(b)

$2\pi$

(c)

$3\pi$

(d)

$4\pi$

18. The solution of $\frac{dy}{dx}+$p(x)y=0 is

(a)

$y={ ce }^{ \int { pdx } }$

(b)

$y={ ce }^{ -\int { pdx } }$

(c)

$x={ ce }^{ -\int { pdx } }$

(d)

$x{ce }^{ \int { pdx } }$

19. The solution of $\frac{dy}{dx}+y$ cot x=sin 2x is

(a)

y sin x=$\frac{2}{3}$sin3x+c

(b)

y sec x=$\frac{x^2}{2}+c$

(c)

y sin x =c+x

(d)

2y sin x=sin x-$\frac{sin\ 3x}{3}+c$

20. The population p of a certain bacteria decreases at a rate proportional to the population p. The differential equation corresponding to the above statement is __________.

(a)

$\frac{dp}{dt}=\frac{k}{p}$

(b)

$\frac{dp}{dt}=kt$

(c)

$\frac{dp}{dt}=kp$

(d)

$\frac{dp}{dt}=-kp$

21. A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is
$f(x)=\begin{cases} \begin{matrix} \frac { 2 }{ { x }^{ 3 } } & 0<x>l \end{matrix} \\ \begin{matrix} 0 & 1\le x<2l \end{matrix} \end{cases}$

(a)

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

(b)

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

(c)

$1,\cfrac { { l }^{ 2 } }{ 12 }$

(d)

$\cfrac { 1 }{ 2 } ,\cfrac { { l }^{ 2 } }{ 12 }$

22. If $f(x)={ Cx }^{ 2 }={ cx }^{ 2 },0<x<2$ is the p.d.f, of x then c is

(a)

$\cfrac { 1 }{ 3 }$

(b)

$\cfrac { 4 }{ 3 }$

(c)

$\cfrac { 8 }{ 3 }$

(d)

$\cfrac { 3 }{ 8 }$

23. A binary operation on a set S is a function from

(a)

S ⟶ S

(b)

(SxS) ⟶ S

(c)

S⟶ (SxS)

(d)

(SxS) ⟶ (SxS)

24. Which of the following is a contradiction?

(a)

p v q

(b)

p ∧ q

(c)

q v ~ q

(d)

q ∧ ~ q

25. Which of the following is a statement?

(a)

7+2<10

(b)

Wish you all success

(c)

All the best

(d)

How old are you?