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Worksheets

Mathematics class 12

Total questions: 50

Worksheet time: 25mins

Name
Class
Date
1.

How many three-digit numbers can be formed by using the integers 4, 5, 6, 8 with repetition?

a)

64

b)

27

c)

24

d)

6

2.

Solution of 3x = 1 in ℤ4 is

a)

0

b)

1

c)

2

d)

3

3.

If one of the roots of the equation x2 + ax + b = 0 and x2 + bx + a = 0 is coincident, then the numerical value of (a + b) is

a)

0

b)

-1

c)

2

d)

5

4.

If the system of equations is 3x - 2y = 1 and - x + 4y = 3 then

a)

D ≠ D1

b)

D1 ≠ D2

c)

D = D1 = D2

d)

D ≠ D3

5.

The eccentricity of the ellipse 4x2 + 9y2 = 36 is

a)

1/(2√3)

b)

1/√3

c)

√5/3

d)

√5/6

6.

If a→ and b→ are two vectors then the value of (a→ - b→) × (a→ + b→) is equal to

(Check)

a)

2(a→ × b→)

b)

a2→ - b2

c)

-2(a→ × b→)

d)

2(a2→ × b2→)

7.

The range of probability of any event A is

a)

0 ≤ P(A) ≤ 1

b)

0 ≤ P(A) < 1

c)

-1 ≤ P(A) ≤ 1

d)

0 < P(A) < 1

8.

∫x cos x2 dx is equal to

a)

-(1/2) sin2 x + c

b)

(1/2) sin2 x + c

c)

-(1/2)sin x2 + c

d)

(1/2) sin x2 + c

9.

The simplex method was developed by

a)

George Dantzig

b)

Pythagoras

c)

Issac Newton

d)

Abel

10.

If two like parallel forces of (P/Q)N and (Q/P)N have a resultant of 2N, then

a)

P = Q

b)

P = -Q

c)

P = 2Q

d)

2P = Q

11.

What is the vertex of the parabola y = x2 - 2x + 1

a)

(-1, 0)

b)

(1, 0)

c)

(0, -1)

d)

(0, 1)

12.

In the expansion of (1+x)50, the sum of the coefficient of odd power of x is

a)

0

b)

249

c)

250

d)

251

13.

If arg z < 0 then arg (-z) - arg (z) is equal to

a)

π

b)

c)

-(π/2)

d)

π/2

14.

If Σn = 55, then Σn2 is equal to

a)

385

b)

506

c)

115

d)

3025

15.

The equation √3 sin x + cos x = 4 has

a)

Only one solution

b)

Two solutions

c)

Infinitely many solutions

d)

No solution

16.

If projections of any line on co-ordinates axes are 3, 4 and 5, then its length is

a)

12

b)

50

c)

5√2

d)

3√2

17.

What would be the range of the square of the correlation coefficient (r2)?

a)

-1 to +1

b)

0 to 1

c)

-∞ to +∞

d)

-1 to 0

18.

If y = 4x - 5 is tangent to the curve y2 = px3 + q at (2, 3), then

a)

p = 2, q = -7

b)

p = -2, q = 7

c)

p = -2, q = -7

d)

p = 2, q = 7

19.

The second order differential equation is

a)

y'2 + x = y2

b)

y' y" + y = sin x

c)

y''' + y" + y = 0

d)

y' = y

20.

In Gauss elimination method, the coefficient of the first variable in first equation must be

a)

zero

b)

non-zero

c)

negative

d)

positive

21.

If a constant force of 'F' N acts on a body of mass 'm' kg for 't' seconds and brings it into motion with an acceleration 'a' m/sec2 and velocity Vm/sec, what will be its impulse?

a)

ma

b)

Fa

c)

Ft

d)

Fv

22.

How many words can be made from the letters of the word INSURANCE, if all videos come together?

a)

18270

b)

17280

c)

12780

d)

None of these

23.

For the set of G = {0, 1, 2, 3, 4} under congruence modulo addition, +, the inverse of 1 is

a)

0

b)

2

c)

3

d)

4

24.

If one root of the equation x2 + px + q = 0 is 2 + √3, then values of p and q are

a)

-4, 1

b)

4, -1

c)

2, √3

d)

-2, -√3

25.

If the equation 2x2 + 5x + k = 0 has the reciprocal roots, what will be the value of k?

a)

-5/2

b)

5/2

c)

-2

d)

2

26.

The system of equations cannot be solved by crammer's rule if

a)

D = 0

b)

D1 = 0

c)

D2 = 0

d)

D3 = 0

27.

The foci of the ellipse 25(x + 1)2 + 9(y + 2)2 = 225 are all

a)

(-1, 2) and (-1, -6)

b)

(-1, 2) and (6, 1)

c)

(-1, 2) and (1, -6)

d)

(-1, -2) and (1, 6)

28.

The unit vector perpendicular to 3i^ + 2j^ -k^ and 12i^ + 5j^ - 5k^ is

(Check)

a)

(5i^ - 3j^ - 9k^)/√115

b)

(5i^ + 3j^ - 9k^)/√115

c)

(-5i^ + 3j^ - 9k^)/√115

d)

(5i^ + 3j^ + 9k^)/√115

29.

A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour is

a)

5/108

b)

18/108

c)

30/108

d)

48/108

30.

∫x cos x2dx is equal to

a)

-(1/2)sin2 x + c

b)

1/2 sin2 x + c

c)

-(1/2) sin x2 + c

d)

(1/2) sin x2 + c

31.

In the simplex method, the slack and surplus variables are restricted to be

a)

multiplied

b)

divided

c)

negative

d)

non-negative

32.

If P and Q are two like parallel forces then the resultant is

a)

P + Q

b)

P - Q

c)

P2 + Q2

d)

P2 - Q2

33.

Find the producer surplus of the supply function is y = 2x2 + 4 and the quantity x is 2

a)

32/3

b)

31/3

c)

34/3

d)

35/3

34.

If coefficient of (2r + 3)th and (r - 1)th terms in the expansion of (1 + x)15 are equal then values of r is

a)

5

b)

6

c)

4

d)

3

35.

The argument of complex number -1 + i√3 is

a)

-60°

b)

60°

c)

120°

d)

240°

36.

If x, y, z are in AP and tan-1 x, tan-1 y, tan-1 z are also in AP, then

a)

2x = 3y = 6z

b)

6x = 3y = 2z

c)

6x = 4y = 3z

d)

x = y = z

37.

If tan-1 x + tan-1 y + tan-1 z = π, then x + y + z is equal to

a)

xzy

b)

0

c)

1

d)

2xyz

38.

The length of the perpendicular from the origin to the plane 3x + 4y + 12z = 52 is

a)

3

b)

4

c)

5

d)

None of the above

39.

Karl Pearson's correlation coefficient measures

a)

the strength of relationship between two quantitative variables

b)

the direction of relationship between two quantitative variables

c)

both the strength and the direction of relationship between two quantitative variables

d)

none of the above

40.

The derivative of esinh 2x is

a)

esinh 2x

b)

θcosh 2x

c)

2 cosh 2x esinh 2x

d)

2 esinh 2x

41.

The differential equation of all straight line passing through the point (1, -1) is

a)

y = (x + 1) dy/dx + 1

b)

y = (x + 1) dy/dx - 1

c)

y = (x - 1) dy/dx + 1

d)

y = (x - 1) dy/dx - 1

42.

The system of equations 2x + y = 7 and x + 3y = 11 is

a)

consistent and independent

b)

inconsistent and independent

c)

consistent and dependent

d)

inconsistent and dependent

43.

If the max. range up an inclined plane be one-third of the max. range down the plane then the inclination of the plane is the horizontal is

a)

15°

b)

30°

c)

45°

d)

60°

44.

The number of ways in which a committee of 6 members can be formed from 8 gentleman and 4 ladies so that the committee contains at least 3 ladies is

a)

252

b)

672

c)

444

d)

420

45.

For the set of natural number ℕ under the binary operation multiplication, which one of the following statement is not true?

a)

Closure property is satisfied

b)

Identity element (e) exists and belongs to ℕ

c)

Associative property is satisfied

d)

Inverse of every element also belongs to ℕ

46.

If α, β be the roots is the equation 2x2 + 35x + 2 = 0 then the value of (2α - 35)³ (2β - 35)³ is equal to

a)

1

b)

64

c)

8

d)

None of these

47.

If the system of equations is x + 3y = 4 and x - y = 0 then the value of D =

a)

-4

b)

2

c)

3

d)

0

48.

In the ellipse, mirror acid is 8 and eccentricity is √5/3. Then major axis is

a)

6

b)

12

c)

10

d)

16

49.

Four boys and three girls stand in a queue for an interview, probability that they will be in alternate position is

a)

1/34

b)

1/35

c)

1/17

d)

1/68

50.

In simplex method, the slack and surplus variables are restricted to be

a)

multiplied

b)

divided

c)

negative

d)

non-negative