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

12th Standard EM

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Maths

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

    Answer all the questions

    10 x 1 = 10
  1. If sin-1 x+cot-1\((\frac{1}{2})=\frac{\pi}{2}\), then x is equal to

    (a)

    \(\frac{1}{2}\)

    (b)

    \(\frac{1}{\sqrt{5}}\)

    (c)

    \(\frac{2}{\sqrt{5}}\)

    (d)

    \(\frac{\sqrt3}{2}\)

  2. The eccentricity of the ellipse (x−3)2 +(y−4)2 =\(\frac { { y }^{ 2 } }{ 9 } \) is

    (a)

    \(\frac { \sqrt { 3 } }{ 2 } \)

    (b)

    \(\frac { 1 }{ 3 } \)

    (c)

    \(\frac { 1 }{ 3\sqrt { 2 } } \)

    (d)

    \(\frac { 1 }{ \sqrt { 3 } } \)

  3. The distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z + 7 = 0

    (a)

    \(\frac { \sqrt { 7 } }{ 2\sqrt { 2 } } \)

    (b)

    \(\frac{7}{2}\)

    (c)

    \(\frac { \sqrt { 7 } }{ 2 } \)

    (d)

    \(\frac { 7 }{ 2\sqrt { 2 } } \)

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

    (a)

    \(\cfrac { 1 }{ e } \)

    (b)

    \(\cfrac { 1 }{ 2e } \)

    (c)

    \(\cfrac { 1 }{ { e }^{ 2 } } \)

    (d)

    \(\cfrac { 4 }{ { e }^{ 4 } } \)

  5. 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

  6. If \(\int _{ 0 }^{ x }{ f(t)dt=x+\int _{ x }^{ 1 }{ tf } (t)dt } \) then the value of f (1) is

    (a)

    \(\frac{1}{2}\)

    (b)

    2

    (c)

    1

    (d)

    \(\frac{3}{4}\)

  7. If sin x is the integrating factor of the linear differential equation \(\frac { dy }{ dx } +Pt=Q,\)Then P is

    (a)

    log sin x

    (b)

    cos x

    (c)

    tan x

    (d)

    cot x

  8. If in 6 trials, X is a binomial variate which foUows 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

  9. Subtraction is not a binary operation in

    (a)

    R

    (b)

    Z

    (c)

    N

    (d)

    Q

  10. The dual of ᄀ(p V q) V [p V (p ∧ ᄀr)] is

    (a)

    ᄀ(p ∧ q) ∧ [p V (p ∧ ᄀr)]

    (b)

    (p ∧ q) ∧ [p ∧ (p V ᄀr)]

    (c)

    ᄀ(p ∧ q) ∧ [p ∧ (p ∧ r)]

    (d)

    ᄀ(p ∧ q) ∧ [p ∧ (pV ᄀr)]

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