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

12th Standard

    Reg.No. :
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Maths

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

    Answer all the questions

    10 x 1 = 10
  1. The augmented matrix of a system of linear equations is \(\left[\begin{array}{cccc} 1 & 2 & 7 & 3 \\ 0 & 1 & 4 & 6 \\ 0 & 0 & \lambda-7 & \mu+5 \end{array}\right]\). The system has infinitely many solutions if

    (a)

    \(\lambda=7, \mu \neq-5\)

    (b)

    \(\lambda=-7, \mu=5\)

    (c)

    \(\lambda \neq 7, \mu \neq-5\)

    (d)

    \(\lambda=7, \mu=-5\)

  2. If |z1| = 1, |z2| = 2, |z3| = 3 and |9z1z+ 4z1z+ z2z3| = 12, then the value of |z1+z2+z3| is 

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  3. When the eccentricity of a ellipse becomes zero, then it becomes a __________

    (a)

    straight line

    (b)

    circle

    (c)

    point

    (d)

    parabola

  4. The angle between the lines \(\frac{x-2}{3}=\frac{y+1}{-2}, z=2 \text { and } \frac{x-1}{1}=\frac{2 y+3}{3}=\frac{z+5}{2}\) is

    (a)

    \(\frac{\pi}{6}\)

    (b)

    \(\frac{\pi}{4}\)

    (c)

    \(\frac{\pi}{3}\)

    (d)

    \(\frac{\pi}{2}\)

  5. The number given by the Mean value theorem for the function \(\frac { 1 }{ x } \), x ∈ [1, 9] is

    (a)

    2

    (b)

    2.5

    (c)

    3

    (d)

    3.5

  6. Linear approximation for g(x) = cos x at \(x=\frac{\pi}{2}\) is

    (a)

    \(x+\frac{\pi}{2}\)

    (b)

    \(-x +\frac{\pi}{2}\)

    (c)

    \(x - \frac{\pi}{2}\)

    (d)

    \(-x - \frac{\pi}{2}\)

  7. The degree of the differential equation \(y(x)=1+\frac { dy }{ dx } +\frac { 1 }{ 1.2 } { \left( \frac { dy }{ dx } \right) }^{ 2 }+\frac { 1 }{ 1.2.3 } { \left( \frac { dy }{ dx } \right) }^{ 3 }+....\) is

    (a)

    2

    (b)

    3

    (c)

    1

    (d)

    4

  8. 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 - \(\frac{sin\ 3x}{3}+c\)

  9. In the set Q define a⊙b = a+b+ab. For what value of y, 3⊙(y⊙5) = 7?

    (a)

    y = \(\frac{2}{3}\)

    (b)

    y = \(\frac{-2}{3}\)

    (c)

    y = \(\frac{-3}{2}\)

    (d)

    y = 4

  10. Which of the following is a contradiction?

    (a)

    p v q

    (b)

    p ∧ q

    (c)

    q v ~ q

    (d)

    q ∧ ~ q

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