One Mark Questions

PREPARED BY:R.RAJENDRAN. M.A., M. Sc., M. Ed.,K.C.SANKARALINGA NADAR HR. SEC. SCHOOL,CHENNAI-21

Choose the Correct Answer1. If p is true and q is false then which of the

following is not true?

(a) ~ p is true (b) pq is true

(c) p q is false (d) pq is true

2. Given E (X + c) = 8 and E (X – c) = 12 then the

value of c is

(a) – 2 (b) 4

(c) – 4 (d) 2

Choose the Correct Answer3. In 5 throws of a die, getting 1 or 2 is a success.

The mean number of successes is

(a) 5/3 (b) 3/5

(c) 5/9 (d) 9/5

4. If f (x) is a p.d.f of a normal distribution with

mean then is

(a) 1 (b) 0.5

(c) 0 (d) 0.25

dxxf )(

Choose the Correct Answer5. If X is a discrete random variable then P(X a)

(a) P(X < a) (b) 1 – P(X a)

(c) 1 – P(X < a) (d) 0

6. A particular integral of (D2 – 4D + 4) y = e 2x is

(a) (b) x e 2x

(c) x e–2x (d)

xex 2

2

2xe

x 2

2

Choose the Correct Answer7. The order and degree of the differential

equation y’ + (y’’)2 = (x + y’’) 2 are

(a) 1, 1 (b) 1, 2

(c) 2, 1 (d) 2, 2

8. Which of the following is a contradiction?

(a) p q (b) p q

(c) p –q (d) p –q

Choose the Correct Answer9. The order of [7] in (Z9, + 9) is

(a) 9 (b) 6

(c) 3 (d) 1

Choose the Correct Answer10. Which of the following is correct?

(a) An element of a group can have more than

one inverse.

(b) If every element of a group is its own

inverse, then the group is Abelian.

(c) The set of all 2 2 real matrices forms a

group under matrix multiplication.

(d) (a * b)–1 = a–1 * b–1 for all a, b G

Choose the Correct Answer11. The volume generated by rotating the triangle

with vertices at (0, 0), (3, 0) and (3, 3) about

x-axis is

(a) 18 (b) 2

(c) 36 (d) 9

Choose the Correct Answer12. The arc length of the curve y = f(x) from x = a

and x = b is

(a) (b)

(c) (d)

b

a

dxdx

dyy

2

12

b

a

dxdx

dy2

1

b

a

dxdy

dxy

2

12

d

c

dxdy

dx2

1

Choose the Correct Answer13. The surface area of the solid of revolution of

the region bounded by y = 2x, x = 0 and x = 2

about x – axis is

(a) 85 (b) 25

(c) 5 (d) 45

Choose the Correct Answer14. The differential equation obtained by

eliminating a and b from y = a e3x + b e–3x is

(a) (b)

(c) (d)

02

2

aydx

yd09

2

2

ydx

yd

092

2

dx

dy

dx

yd09

2

2

dx

dy

dx

yd

Choose the Correct Answer15. The integrating factor of

is

(a) ex (b) log x

(c) (d) e–x

2

2

log

1

xyxxdx

dy

x

1

Choose the Correct Answer16. Which of the following function is increasing

in (0,)

(a) ex (b) 1/x

(c) – x2 (d) x–2

17. One of the critical numbers of x3/5 (4 – x) is

(a) 0 (b) 4

(c) 4/3 (d) 3/5

Choose the Correct Answer18. The percentage error in the 11th root of the

number 28 is approximately ----------- times the

percentage error in 28.

(a) 1/28 (b) 1/11

(c) 11 (d) 28

19. The curve 9y2 = x2 (4 – x2) is symmetrical

about

(a) y – axis (b) x – axis

(c) y = x (d) both the axes

Choose the Correct Answer20. The value of is

(a) (b)

(c) 0 (d)

21. The line 5x – 2y + 4k = 0 is a tangent to

4x2 – y2 = 36 then k is

(a) (b)

(c) (d)

0

4 sin dxx

16

316

3

8

3

9

4

3

2

9

4

16

81

Choose the Correct Answer22. The eccentricity of the hyperbola with

asymptotes x + 2y – 5 = 0, 2x – y + 5 = 0 is

(a) 3 (b) 2

(c) 3 (d) 2

23. The point of contact of the tangent y = mx + c

and the parabola y2 = 4ax is

(a) (b)

(c) (d)

m

a

m

a,

22

m

a

m

a 2,

2

2

2,m

a

m

a

m

a

m

a 2,

2

Choose the Correct Answer24. The slope of the normal to the curve y = 3x2 at

the point whose x co-ordinate is 2 is

(a) (b)

(c) (d)

25. If s = t3 – 4t2 + 7, the velocity when the

acceleration is zero is

(a) m/ sec (b) – m / sec

(c) m / sec (d) – m / sec

13

1

14

1

12

1

12

1

3

32

3

163

16

3

32

Choose the Correct Answer26. The polar form of the complex number (i25) 3 is

(a) cos + i sin (b) cos + i sin

(c) cos – i sin (d) cos – i sin

27. z1 = 4 + 5i, z2 = - 3 + 2i then is

(a) (b)

(c) (d)

2

2

2

2

i13

22

13

2 i

13

22

13

2

i13

22

13

2 i

13

22

13

2

2

1

z

z

Choose the Correct Answer28. The value of is

(a) | z | (b) | z |2

(c) 2| z | (d) 2| z |2

29. If a = 3 + i and z = 2 – 3i then the points on the

Argand diagram representing az, 3az and – az

are

(a) vertices of a right triangle

(b) vertices of an equilateral triangle

(c) vertices of an isosceles triangle

(d) collinear

zz

Choose the Correct Answer30. The radius of the director circle of the conic

9x2 + 16y2 = 144 is

(a) 7 (b) 4

(c) 3 (d) 5

31. If , then the area of the quadrilateral PQRS is

(a) 53 (b) 103

(c) 53/2 (d) 3/2

kjiPR 2

kjiQS 23

Choose the Correct Answer32. If and then a

unit vector perpendicular to and is

(a) (b)

(c) (d)

kjia 32

kjib 23

b

a

3

kji

3

kji

3

kji

3

kji

Choose the Correct Answer33. The point of intersection of the lines

and

is

(a) (2, 1, 1) (b) (1, 2, 1)

(c) (1, 1, 2) (d) (1, 1, 1)

34. The distance from the origin to the plane is

(a) (b)

(c) (d)

)2()32(

kjitkjir

)32()532(

kjiskjir

7)52.(

kjir

30

7

7

30

7

3030

7

Choose the Correct Answer35. If , , are three mutually perpendicular

unit vectors, then | + + | =

(a) 3 (b) 9

(c) 33 (d) 3

36. If A = [2 0 1], then the rank of AAT is

(a) 1 (b) 2

(c) 3 (d) 0

a

b

c

a

b

c

Choose the Correct Answer37. If the matrix has an inverse

then the value of k is

(a) k is any real number (b) k = – 4

(c) k – 4 (d) k 4

38. If A is a matrix of order 3, then det (KA) is

(a) k3 det (A) (b) k2 det (A)

(c) k det (A) (d) det (A)

541

31

231

k

Choose the Correct Answer

39. Every homogeneous system

(a) is always consistent

(b) has only trivial solution

(c) has infinitely many solution

(d) need not be consistent

Choose the Correct Answer

40. If and are two unit vectors and is the angle

between them, then( + ) is a unit vector if

(a) (b)

(c) (d)

a

b

a

b

3

4

2

3

2