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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.