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Important 1 Mark Book Back Questions (New Syllabus) 2020

12th Standard EM

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Maths

Time : 00:20:00 Hrs
Total Marks : 20
    Part A
    20 x 1 = 20
  1. If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

    (a)

    -40

    (b)

    -80

    (c)

    -60

    (d)

    -20

  2. If ρ(A) = ρ([A | B]), then the system AX = B of linear equations is

    (a)

    consistent and has a unique solution

    (b)

    consistent

    (c)

    consistent and has infinitely many solution

    (d)

    inconsistent

  3. If \(\left| z-\cfrac { 3 }{ z } \right| =2\) then the least value |z| is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    5

  4. If \(\omega \neq 1\) is a cubic root of unity and \(\left( 1+\omega \right) ^{ 7 }=A+B\omega \) ,then (A,B) equals

    (a)

    (1,0)

    (b)

    (−1,1)

    (c)

    (0,1)

    (d)

    (1,1)

  5. A polynomial equation in x of degree n always has

    (a)

    n distinct roots

    (b)

    n real roots

    (c)

    n imaginary roots

    (d)

    at most one root

  6. sin−1(cos x)\(=\frac{\pi}{2}-x \) is valid for

    (a)

    \(-\pi \le x\le 0\)

    (b)

    \(0\pi \le x\le 0\)

    (c)

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

    (d)

    \(-\frac { \pi }{ 4 } \le x\le \frac { 3\pi }{ 4 } \)

  7. If sin-1 \(\frac{x}{5}+ cosec^{-1}\frac{5}{4}=\frac{\pi}{2}\), then the value of x is

    (a)

    4

    (b)

    5

    (c)

    2

    (d)

    3

  8. If the normals of the parabola y2 = 4x drawn at the end points of its latus rectum are tangents to the circle (x−3)2+(y+2)2=r2 , then the value of r2 is

    (a)

    2

    (b)

    3

    (c)

    1

    (d)

    4

  9. If \(\vec { a } ,\vec { b } ,\vec { c } \) are three unit vectors such that \(\vec { a } \) is perpendicular to \(\vec { b } \) and is parallel to \(\vec { c } \) then \(\vec { a } \times (\vec { b } \times \vec { c } )\) is equal to

    (a)

    \(\vec { a } \)

    (b)

    \(\vec { b} \)

    (c)

    \(\vec { c } \)

    (d)

    \(\vec { 0 } \)

  10. Distance from the origin to the plane 3x - 6y + 2z 7 = 0 is

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    3

  11. The slope of the line normal to the curve f(x) = 2cos 4x at \(x=\cfrac { \pi }{ 12 } \)

    (a)

    \(-4\sqrt { 3 } \)

    (b)

    -4

    (c)

    \(\cfrac { \sqrt { 3 } }{ 12 } \)

    (d)

    \(4\sqrt { 3 } \)

  12. The point of inflection of the curve y = (x - 1)3 is

    (a)

    (0,0)

    (b)

    (0,1)

    (c)

    (1,0)

    (d)

    (1,1)

  13. The change in the surface area S = 6x2 of a cube when the edge length varies from xo to xo+ dx is

    (a)

    12 xo+dx

    (b)

    12xo dx

    (c)

    6xo dx

    (d)

    6xo+ dx

  14. The value of \(\int _{ 0 }^{ \frac { \pi }{ 6 } }{ { cos }^{ 3 }3xdx } \)

    (a)

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

    (b)

    \(\frac{2}{9}\)

    (c)

    \(\frac{1}{9}\)

    (d)

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

  15. The order and degree of the differential equation \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +{ \left( \frac { dy }{ dx } \right) }^{ 1/3 }+{ x }^{ 1/4 }=0\)are respectively

    (a)

    2, 3

    (b)

    3, 3

    (c)

    2, 6

    (d)

    2, 4

  16. The solution of \(\frac { dy }{ dx } ={ 2 }^{ y-x }\)is

    (a)

    2x+2y=C

    (b)

    2x-2y=C

    (c)

    \(\frac { 1 }{ { 2 }^{ x } } -\frac { 1 }{ { 2 }^{ y } } =C\)

    (d)

    x+y=C

  17. A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is roUed and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  18. Suppose that X takes on one of the values 0, 1, and 2. If for some constant k, P(X = I) = k P(X = i-I) i = 1, 2 and P(X = 0) =\(\cfrac { 1 }{ 7 } \) then the value of k is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  19. If a compound statement involves 3 simple statements, then the number of rows in the truth table is

    (a)

    9

    (b)

    8

    (c)

    6

    (d)

    3

  20. Which one of the following is not true?

    (a)

    Negation of a negation of a statement is the statement itself

    (b)

    If the last column of the truth table contains only T then it is a tautology.

    (c)

    If the last column of its truth table contains only F then it is a contradiction

    (d)

    If p and q are any two statements then p↔️q is a tautology.

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