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

12th Standard

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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)

    \(x={ ce }^{ -\int { pdy } }\)

    (d)

    \(x={ce }^{ \int { pdy } }\)

  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
    \(f(x)=\left\{\begin{array}{ll} \frac{1}{l} & 0<x<l \\\ 0 & l \leq x<2 l \end{array}\right.\)
    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)

    \(\cfrac { l }{ 2 } ,\cfrac { { l }^{ 2 } }{ 12 } \)

  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?

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