MCQ(Mean Theorem)

1) If f(x)= Ax² + Bx + C is such that f(a)= f(b), then find the value of c in Rolle's theorem

A) a B) b C) a+ b D) (a+ b)/2.

2) n is a positive integer. If the value of c prescribed in Rolle's theorem for the function f(x)= 2x( x- 3)ⁿ on the interval [0, 2√3] is 3/4, find the value of n

A) 1 B) 2 C) 0 D) 3.

3) Find the value of c prescribed by Lagrange's mean value theorem for the function f(x)= √(x² - 4) defined in (2,3).

A) √2 B) √3 C) √4 D) √5

4) For the function f(x)= x + 1/x, x belongs to (1,3), the value of c for the Lagrange's mean value theorem is

A) 1 B) √3. C) 2 D) none

5) If from Lagrange's mean value theorem, we have

f'(x)= (f(b) - f(a))/(b - a), then

A) a< x ≤ b B) a≤ x < b

C) a< x < b. D) a≤ x ≤ b

6) The value of c in Rolle's theorem when f(x)= 2x³ - 5x² - 4x + 3, x belongs to (1/3, 3) is

A) 2. B) -1/3 C) -2 D) 2/3

7) When the tangent to the curve y= x log x is parallel to the chord joining the points (1,0) and (e,e), the value of x is

A) ₑ 1/(1- e). B) ₑ(e - 1)

C) ₑ (2e - 1/(e - 1) D) (e -1)/e

8) The value of c in Rolle's theorem for the function f(x)={x(x +1)/eˣ} defined on (-1,0) is

A) 0.5 B) (1+ √5)/2 C) (1- √5)/2. D) - 0.5

9) The value of c in Lagrange's mean value theorem for the function f(x)= x(x - 2) when x belongs to (1,2) is

A) 1 B) 1/2 C) 2/3 D) 3/2.

10) The value of c in Rolle's theorem for the function f(x)=x³ - 3x in the interval (0, √3) is

A) 1. B) -1 C) 3/2 D) 1/3

11) If f(x)= eˣ sinx in (0,π), then c in Rolle's theorem is

A) π/6 B) π/4 C) π/2 D) 3π/4.

MCQ(Inverse Trigonometry)

1) Value of sin⁻¹(-√3/2)+ sin⁻¹(- 1/2)

A) π B) π/3 C) π/2 D) π/4

2) If sin⁻¹x + sin⁻¹y +sin⁻¹z= 3π/2, then the value of x+y+z

A) 0 B) 1 C) 2 D) 3 

3) If x> 1, then the value of sin⁻¹{2x/(1+ x²)} in terms of tan⁻¹x

A) π/2 - 2tan⁻¹x

B) π/3 - 2tan⁻¹x

C) π/4 - 2tan⁻¹x

D) π - 2tan⁻¹x

4) If x< 0, then the value of cos⁻¹{(1- x²)/(1+ x²)} in terms of tan⁻¹x

A) π/2 - 2tan⁻¹x

B) π/3 - 2tan⁻¹x

C) π/4 - 2tan⁻¹x

D) - 2tan⁻¹x

5) write the value of tan⁻¹ x + tan⁻¹ (1/x) for x> 0.

A) π/2 B) π/3 C) π/4 D) π

6) write the value of tan⁻¹ x + tan⁻¹ (1/x) for x < 0.

A) - π/2 B) π/3 C) π/4 D) π

7) write the value of cos⁻¹ cos(2π/3) + sin⁻¹sin (2π/3).

A) π/2 B) π/3 C) π/4 D) π

8) If -1< x< 0, then write the value of sin⁻¹{2x/(1+ x²)} + cos⁻¹ {(1- x²)/(1+ x²)}.

A) π/2 B) π/3 C) π/4 D) 0

9) write the value of sin(cot⁻¹ x)

A) 1/√(1- x²) B) - 1/√(1- x²) C) 1/√(1+ x²)  D) -1/√(1+ x²)

10) write the value of cos⁻¹(1/2) + 2 sin⁻¹ (1/2).

A) π/2 B) 2π/3  C) π/4 D) π

11) write the value of cos⁻¹(cos 1540°)

A) 120 B) 110 C) 100 D) 60

12) write the value of sin⁻¹sin(-600°).

A) 120 B) 110 C) 100 D) 60

13) write the value of cos sin⁻¹(1/3).

A) 1/2.B) 1/3 C) 7/4 D) 7/9

14) write the value of sin⁻¹ sin(1550°)

A) 120 B) 100 C) 80 D) 70

15) write the value of 1/2 cos⁻¹(4/5).

A) π/2 B) 1/3 C) 1/10 D) 1/√10

16) write the value of sin tan⁻¹(3/4).

A) 1/2 B) 4/3 C) 3/4 D) 3/5

17) Value of cos⁻¹tan⁻¹ (3π/4).

A) π/2 B) π/3 C) π/4 D) π

18) write the value of cos(2 sin⁻¹ (1/2))

A) 1/2  B) 1 C) 1/√2 D) √3/2

19) Value of cos⁻¹ cos(350°) - sin⁻¹ sin(350°).

A) 100 B) 30 C) 40 D) 20

20) value of cos²(1/2 cos⁻¹ (3/5))

A) 3/2 B) 4/3 C) 5/4 D) 4/5

21) If tan⁻¹ x + tan⁻¹y +  tan⁻¹z=π/4, then the value of x+ y +z.

A) 0 B) 3 C) 1 D) -1

22) value of cos⁻¹ (cos 6)

A) 0 B) 6 C) -6 D) 2π- 6

23) value of sin⁻¹ cos(π/9).

A) π/2 B) 7π/3 C) 7π/8 D) 7π

24) write the value of sin{π/3 - sin⁻¹(-1/2)

A) 0 B) 1 C) -1 D) 1/2

25) value of tan⁻¹ tan(15π/4)

A) π/2 B) -π/3 C) π/4 D) - π/4

26) value of tan⁻¹(a/b) - tan⁻¹ {((a - b)/(a+ b)} 

A) π/2 B) π/3 C) π/4 D) π

27) value of sin⁻¹{2x √(1- x²)} in + sin⁻¹ x.

A) 2sin⁻¹ x B) sin⁻¹ x C) 3 sin⁻¹ x D) - sin⁻¹ x

28) value of cos⁻¹ cos(5π/4).

A) π/4 B) 3π/4. C) 2π D) π

29) If tan⁻¹[{√(1+ x²) - √(1- x²)}/{√(1+ x²) + √(1- x²)} = K, then x² is

A) sin 2k B) sin k C) cos 2k D) cos K

30) value of tan{cos⁻¹(1/5√2) - sin(4/√17) is

A) √29/3 B) 29/3 C) √3/29 D) 3/29

31) value of 2 tan⁻¹{cosec (tan⁻¹x) tan(cot⁻¹x)

A) cot⁻¹x B) cot⁻¹(1/x) C) tan⁻¹x D) none

32) If cos⁻¹(x/a) + cos⁻¹(y/b) = K, then x²/a² - (2xy cos K)/ab + y²/b² is

A) sin²K B) cos²K C) tan²K D) cot² K

33) If sin⁻¹x - cos⁻¹x =π/6, then x

A) 1/2 B) √3/2 C) -1/2 D) none

34) sin[cot⁻¹{tan(cos⁻¹x)}] =

A) x B) √(1- x²) C) 1/x D) none

35) The number of solutions of tan⁻¹2x + tan⁻¹3x =π/4.

A) 2  B) 3 C) 1 D) none

36) K= tan⁻¹tan(5π/4) and M= tan⁻¹(- tan(2π/3)), then

A) 4K= 3M  B) 3K= 4M C) K - M= 7π/12 D) none

37) The number of real solutions of the equation √(1+ cos 2x)= √2 sin⁻¹(sin x), -π≤ x ≤ π.

A) 0 B) 1C) 2 D) infinite 

38) If x<0, y< 0 such that xy = 1, then tan⁻¹x + tan⁻¹y equals to

A) π/2 B) - π/2  C) - π D) none

39) If u= cot⁻¹√tan x - tan⁻¹√tan x then, tan(π/4 - u/2)=

A) √tanx B) √cotx C) tan x D) cotx

40) If cos⁻¹(x/3) + cos⁻¹(y/2)= k/2, then 4x² - 12xy cos(k/2)+ 9y² = 0.

A) 36 B) 36- cos k C) 18 - 18 cos k D) 18+ 18 cos k

41) If k= tan⁻¹{√3 x/(2y - x)}, m= tan⁻¹{(2x - y)/√3 y}, then k - m= 

A) π/6 B) π/3 C) π/2 D) - π/3

42) tan⁻¹(1/11) + tan⁻¹(2/11) =

A) 0 B) 1/2 C) - 1 D) 1

43) cos⁻¹(x/2) + cos⁻¹(y/3)= k, then 9x² - 12xy cos k + 4y² = 

A) 36 B) -36 sin²k C) 36 sin²k  D) 36 cos² k

44) If tan⁻¹3 + tan⁻¹x = tan⁻¹8, then x=

A) 5 B) 1/5 C) 5/14 D) 14/5

45) value of sin⁻¹cos(33π/5) is

A) 3π/5 B) - π/10 C) π/10 D) 7π/5

46) value of cos⁻¹cos(5π/3)+ sin⁻¹sin(5π/3) is

A) π/2 B) 5π/3 C) 10π/3 D) 0

47) value of sin{cos⁻¹(-3/5)} 

A) 6/25 B) 24) 25 C) 4/5 D) -24/25

48) If k= sin⁻¹{sin(-600°)}, then possible value of k is

A) π/3 B) π/2 C) 2π/3 D) - 2π/3

49) If 3 sin⁻¹{2x/(1+ x²)} - 4 cos⁻¹{(1- x²)/(1 + x²) + 2 tan⁻¹{2x/(1- x²)}= π/3 is equal to

A) 1/√3 B) - 1/√3 C) √3 D) - √3/4

50) 4 cos⁻¹x + sin⁻¹x = π, then the value of x is

A) 3/2 B) 1) √2 C) √3/2 D) 2/√3

51) If tan⁻¹{(x +1)/(x - 1)} + tan⁻¹{(x - 1)/x} = tan⁻¹(-7), then the value of x is

A) 0 B) -2 C) 1 D) 2

52) If sin⁻¹x - cos⁻¹x =π/6, then x is

A) 1/2 B) √3/2 C) - 1/2 D) - √3/2

53) The value of sin(1/4 sin⁻¹(√63/8)) is

A) 1/√2 B) 1/√3 C) 1/2√2 D) 1/3√3

54) cot(π/4 - 2 cot⁻¹3)= 

A) 7. B) 6 C) 5 D) none

55) If tan⁻¹(cotx)= 2x, then x =

A) ±π/3 B) ±π/4 C) ±π/6 D) none 

Revision/Test (Remainder and Factor Theorem)

1) Given f(x)= x³+ 5x² + 2x -8. Find

A) f(1)

B) f(-2)

C) f(-4)

Hence find all the factors of f(x)

2) Find the values of p and q if (x+3) and (x - 4) are factors of f(x)= x³ - px² - qx +24.

3) Factorise completely:

A) x³ - 7x² - 14x -8.

B) 6x³ - 11x² - 3x + 2.

4) Using factor Theorem, find out whether g(x)= x - 3 is the factor or not of (x)= x³+ x² - 2x - 30.

5) Find the values of p and q if g(x)= x + 2 is a factor of f(x)= x³ - p x² + x + q and f(2)= 4.

6) Find the values of a and b if p(x)= x + 2 is a factor of q(x)= ax³ - b x² + 2(x - 2) and q(2)= 20.

7) Find the remainder when, if g(x)= 2x + 1 is divided f(x)= 2x³ - 3x² - 4x - 5.

8) Find the values of p if the polynomial f(x)= x³ - p x² - x + 3 is divided by g(x)= x² - 1.

9) Find the values of p and q if the polynomial f(x)= px³ + 6x² + qx + 6 is divided by g(x)= x² + 4x + 3.

10) Find the values of q for which the polynomial f(x)= 2x³ + q x² - x - 15 has g(x)= 2x +3 as one of the factors. Hence find the remaining two factors.

11) Find the values of q if the polynomial f(x)= 2x³ + qx² - 7x - 12 is divided by g(x)= x + 4. Hence find all the factors of f(x).

12) Find the values of q if the polynomial f(x)= x³ - 2x² - 13x + q is divided by g(x)= x - 2. Hence find all the factors of f(x).

13) Find the values of p and q, if the polynomial f(x)= px³ + qx² - 8x - 12 is divided by g(x)= x² - 4. Hence find all the factors of f(x).

14) Find the values of p if the polynomial f(x)= x³ + p x² - 16x + 8 is divided by g(x)= x - 2 as one of the factors. Hence find the remaining two factors.

Revision/test (Inverse Trigonometry)

TEST

1) Prove: sin⁻¹(8/17) + sin⁻¹(3/5) = sin⁻¹(77/85).                              (2)

2) Evaluate: sin(3 sin⁻¹0.4).        (2)

3) If x, y, z belongs to [-1, 1] such that sin⁻¹x + sin⁻¹y + sin⁻¹z = 3π/2, find the value of x²⁰²⁰ + y²⁰²¹+ z²⁰²² - 9/(x²⁰²⁰+ y²⁰²¹ + z²⁰²²).              (3)

4) Prove: sin[cot⁻¹{cos(tan⁻¹x)}] = √{(x²+1)/(x²+2)}.                       (5) 

OR

Tan⁻¹(1/2 tan 2A) + tan⁻¹(cotA) + tan⁻¹(cot³A). Evaluate 

5) Compulsory

A) The value of sin(1/4 sin⁻¹(√63/8) is

a) 1/√2 b) 1/√3 c) 1/2√2 d) 1/3√3

B) If tan⁻¹(cot A)= 2A, then A=

a) ±π/3 b) ±π/4 c) ±π/6 d) none

C) 4 cos⁻¹x + sin⁻¹x =π, then the value of x is

b) 3/2 b)1/√2 c) √3/2 d) 2/√3

REVISION 

Prove

1) 2tan⁻¹1/5 + tan⁻¹1/8=tan⁻¹4/7

2) 1/2 tan⁻¹x = 

  cos⁻¹√[{1√(1+x²)}/2√(1+x²)]

3) sin⁻¹4/5 +sin⁻¹16/65= π/2

4) sin (π/3 - sin⁻¹(-1/2)) = 1

5) cot (π/4 - 2 cot⁻¹3) =7

6) If cos⁻¹x+ cos⁻¹y+ cos⁻¹z=π then prove x²+y²+z²+2xyz=1

7) If tan⁻¹x+tan⁻¹y+tan⁻¹z=π/2 then prove xy +yz+zx =1

8) If tan⁻¹x+ tan⁻¹y+ tan⁻¹z = 0 then prove x+y+z=xyz

9) prove tan⁻¹(1/2 tan  2A)  + tan⁻¹(cot A)+ tan⁻¹(cot³A) =0

10)a) solve: tan⁻¹3x+ tan⁻¹2x =π/4

b) tan⁻¹(cos x) =tan⁻¹(2 cosec x)

c) tan⁻¹(x+1) +tan⁻¹(x-1) =tan⁻¹8/31

d) sin⁻¹x/√(1+x²) - sin⁻¹1/√(1+x²) = sin⁻¹{(1+x)/(1+x²)}

e) Sin⁻¹(x/2)+cos⁻¹(x+√3/2) =π/6

f) If Sin⁻¹x +Sin⁻¹y+Sin⁻¹z=3π/2, then prove x²+y²+z²+2xyz=1

Simplify:

11) a) Cos⁻¹(x+ 1/2) +Cos⁻¹x+ Cos⁻¹(x - 1/2) = 3π/2.

b) Tan⁻¹{(2sin2θ)/1+2cos2θ)} - 1/2  sin⁻¹{(3sin2θ)/(5+4cos2θ)}

c) tan⁻¹1 + tan⁻¹1/2 + tan⁻¹1/3

d) sin(sin⁻¹1/3 + sec⁻¹3) + cos(tan⁻¹1/2 + tan⁻¹2)

e) sin{sin⁻¹√5/4 + tan⁻¹√(5/11)}

f) tan⁻¹sin cos⁻¹√(2/3)

Prove:

12)a) cos⁻¹3/5+ cos⁻¹12/13 + cos⁻¹63/65  = π/2

b) 1/2 tan⁻¹x = cos⁻¹√{(1+√(1+x²))}/2√(1+x²)

c) prove tan⁻¹x + cot⁻¹(x+1) = tan⁻¹(x²+x+1)

d) tan(2 tan⁻¹m) = 2tan(tan⁻¹m+ tan⁻¹m³)

e) tan⁻¹(1/2  tan 2A) + tan⁻¹(cotA)+ tan⁻¹(cot³A) = 0

Solve:

13)a) 3(Cos⁻¹x + 2sin⁻¹x) = 7π

b) tan⁻¹(cot2x) + tan⁻¹(-cot 3x) = x

c) sin⁻¹{2a/(1+a²)} - cos⁻¹{(1-b²)/(1+b²) = 2 tan⁻¹x

d) tan⁻¹x tan⁻¹2x tan⁻¹3x = π

e) 3 tan⁻¹{1/(2+√3)} - tan⁻¹( = 1/x) = tan⁻¹1/3

f) sin⁻¹x + sin⁻¹(1-x) = cos⁻¹x

g) tan⁻¹(x+1)+tan⁻¹(x-1)= tan⁻¹8/31

h) tan⁻¹{(x-1)/(x-2)} + tan⁻¹{(x+1)/(x+2)} = π/4

i) tan⁻¹{(1/(2x+1)}+ tan⁻¹{1/(4x+1)= tan⁻¹(2/x²)

14)  if α+β= tan⁻¹m, α-β=tan⁻¹n Express tan 2α and tan2β in terms of m,n.

15) If  sin⁻¹x = tan⁻¹y then find the value of 1/x² - 1/y²

16) If r²= x²+y²+z², prove tan⁻¹yz/xr + tan⁻¹zx/yr + tan⁻¹xy/zr = π/2

Solve:

17)a) cos(2tan⁻¹1/7) =  sin(4tan⁻¹x)

b) cos(tan⁻¹x) = sin(cot⁻¹3/4).

prove :

18)a) cos⁻¹(63/65)+2tan⁻¹(1/5) = sin⁻¹(3/5).

  

b) 4 tan⁻¹1/5 - tan⁻¹1/70 + tan⁻¹1/99  =π/4

c) sin⁻¹{x/√(1+x²)} +   cos⁻¹{(x+1) √(x²+2x+2)} =  tan⁻¹(x²+x+1)

d) cot(π/4 - 2 cot⁻¹3) = 7

e) sin cot⁻¹ cos(tan⁻¹x) = √{(1+x²)/(2+x²)

f) sin⁻¹√3/2 + 2 tan⁻¹1/√3 = 2π/3

g) tan⁻¹1/3 +tan⁻¹1/5 + tan⁻¹1/7 + tan⁻¹1/8 = π/4

h) tan⁻¹(1/2 tan 2A) +tan⁻¹(cot A)+ tan⁻¹(cot³A) = 0

Solve:

19)a) tan⁻¹(2+x)+ tan⁻¹(2-x) =tan⁻¹2/3

b) sin⁻¹5/x + sin⁻¹12/x = π/2

c) sin⁻¹6x + sin⁻¹(6√3 x)= - π/2

d) sin⁻¹{2a/(1+a²)} + sin⁻¹{2b/(1+b²)} = 2 tan⁻¹x

e) sin{2 cos⁻¹ cot(2 tan⁻¹x)}=0

20) If tan⁻¹a + tan⁻¹b + tan⁻¹c = π then Prove that a+ b + c = abc

21) If tan⁻¹a + tan⁻¹b + tan⁻¹c = π/2 prove ab + bc + ca = 2

22) If cos⁻¹a/2 + cos⁻¹b/3  = K prove 9x² - 12 xy cos K + 4y² = 36 sin²K

Prove:

23)a) tan⁻¹(1/2) + tan⁻¹(1/3) = π/4

b) 4tan⁻¹1/5 + tan⁻¹1/70 + tan⁻¹1/89 =π/4

c) tan⁻¹(1/4)+tan⁻¹2/9= 1/2cos⁻¹3/5

d) sin⁻¹4/5 + sin⁻¹5/13 + sin⁻¹16/65 =π/2

e) 1/2 tan⁻¹x = cos⁻¹√[{(1+√(1+x²)}/2√(1+x²)]

f) tan⁻¹x + cot⁻¹(x+1)= tan⁻¹(x²+x+1)

g) tan⁻¹1+tan⁻¹2+tan⁻¹3 = 0

h) 2(tan⁻¹1+tan⁻¹1/2 +tan⁻¹1/3) =π

i) tan(2tan⁻¹a) = 2tan(tan⁻¹a+ tan⁻¹a³)

j)  tan⁻¹(1/2 tan 2A)+ tan⁻¹(cot A)+ tan⁻¹(cot³A) =0

Solve:

24)a) tan⁻¹(x+1)+tan⁻¹(x-1) = tan⁻¹8/31

b) tan⁻¹(x-1)+tan⁻¹x+tan⁻¹(x+1) = tan⁻¹3x

c) tan⁻¹{(x-1)/(x-2)}+ tan⁻¹{(x+1)/(x+2)} = π/4

25) If cos⁻¹x + cos⁻¹y + cos⁻¹z =π prove x²+y²+z²+2xyz =1

26) prove sin⁻¹(12/13) + cos⁻¹(4/5)  + tan⁻¹(63/16) = π .

Solve :

27)a) cos⁻¹(sin cos⁻¹x) = π/6

b) solve) cos (sin⁻¹x)= 1/7

c) value of tan(2 tan⁻¹ 1/5)

d) tan⁻¹{1/(2x+1)} +  tan⁻¹{1/(4x+1)} = tan⁻¹2/x²

e) tan⁻¹{(x+1)/(x-2)} +tan⁻¹{(x-1)/x} = tan⁻¹(-7)

28) If tan⁻¹x +tan⁻¹y+tan⁻¹z= π prove x+y+z=xyz

29) if tan⁻¹x+tan⁻¹y+tan⁻¹z=π/2 show that xy+yz+zx=1

29)  prove tan(π/4 + 1/2cos-¹ 1/3) + Tan(π/4 - 1/2 cos-¹ 1/3) =6

 30) solve cos⁻¹(sin (cos⁻¹x))=π/3. 

                                         

 Prove :

31) a) Sin(2tan⁻¹3/5-sin⁻¹7/25) =304/425

32) If tan⁻¹x + tan⁻¹y + tan⁻¹z=0, prove that x+ y +z = xyz.

33) prove: tan⁻¹1/4 + tan⁻¹2/9 = 1/2 cos⁻¹3/5

Revision/Test(Compound Angle)

1) Prove: tan 11A tan 7A tan 4A = tan 11A - tan 7A - tan 4A.

2) If sin(x+ y)= 4/5, cos(x - y)= 12/13, Find tan 2x.

3) Show: cos 2x cos 2y + sin²(x - y)- sin²(x + y)= cos(2x + 2y).

4) Prove: 4 sin(π/3  - x) sin(π/3 + x)= 3 - 4 sin²x.

5) Show that tan 75= {(√3+ 1)/(√3 - 1)}= 2+ √3. Hence show that tan 75 - cot 75 = 4 sin60.

Revision/Test (SET THEORY)

1) If A={1,2,3,4,5,6,7,9,11,13,15} and B={2,4,6,8,10,12,14,16} find A - B and B - A. 

2) The production manage of a company examined 100 items and furnished the following report:

Defect in measuring 50, defect in coloring 30, defect in quality 23, defect in measurement and coloring 8, defect in quality and measurement 20, defect in quality and coloring 10 and 5 are defective in all respects. The manager was penalised for the report. Use set theory to explain the reason for penal measure.

3) If A={1,2,3,4} and B={3,4,5} and C={1,4,5} then verify find A - (B U C)= (A- B)∩(A - C).

4) A market research group conducted a survey of 1000 customers and reported that 700 consumers like product A and 480 consumers like product B. What is the least number that must have liked both the products?

5) If A={1,2,3,4} and B={2,4,5, 6} and C={1,3,4,6,8} then find A ∩(B U C).

6) In a class of 75 students, 48 read Bengali, 33 read mathematics and 19 read both the subjects. How many of them read none of these subjects!

7) If A={1,2,3,4} and B={2,4,5, 6} and C={3,4,6} then find A - (B U C) and (A- (B∩ C).

8) If A={x, y, z{ then write down the power set of A.

9) If S={1,2,3,4,5,6,7,8,9,10}, A={1,2,3,4} and B={2,4,6,8,10} then find (A UB)' And (A∩B)'

10) Three sets A, B, C be such that A- B={2,4,6}; A- C={2,3,5}; find 

  A - (B U C) and A- (B∩C).

11) Using set theory, find the LCM and HCF of 4, 6 and 8.

12) If A={p,q,r,s} and B={r,s,t} and C={p,s,t} then verify find A - (B U C)= (A- B)∩(A - C).

13) If A={1,4} and B={4,5} and C={5,7} then find (A x B) U(A x C)

14) If A={x:x is an integer and 1 ≤ x ≤ 10} and B={x:x is a multiple of 3 and 5 ≤ x ≤ 30}, find A∩B.

15) Using set theory find the HCF of 15, 40, 105.

16) Find the power set of {2,3,5}.

17) If A={1,2,3} and B={4,6,8} then find A x B.

18) If A={x:x is a natural number and x ≤ 6} and B={x:x is the natural numbers and 3 ≤ x ≤ 8}, find A - B and A∩B.

19) In a class of 100 students, 55 students studied history, 41 students studied English and 25 students studied both the subjects. Find the number of students who study neither of the subjects.

20) If A={1,2} find the power set of A.

21) If A={1,2,3,4} and B={2,4,5,8} and C={3,45,6,7} then find A U (B ∩C) and A ∩(B U C).

22) Each students in a class of 40, plays atleast one of the games hockey, football and cricket; 16 play hockey, 20 football, 26 cricket, 5 play hockey and football, 14 football and cricket and hockey, football and cricket. Find the number of students who play hockey and cricket but not football.

23) If A={x: x²- 5x +6= 0}, B={2,4} and C={4,5} then AX (B ∩ C) is

A) a null set 

Revision/Test(Quadratic equation)

1) 36x²+ 23= 60x. 

2) 3x² -17 x +25= 0. 

3) 15x² -28 x = x.

4) x² + 3x - 3= 0 (upto 2 decimal places). 

5) (x² + 8)/11= 5x - x² - 5. 

6) 2x/(x- 4) + (2x - 5)/(x - 3)= 25/3. 

7) (x+ 6)/(x- 4)- (x + 1)/(x +2)= 1/(3x +1). 

8) (x+1)(x+2)(x+3)(x+4) + 1= 0. 

9) x(x- 1)(x+2)(x- 3)(x+4) + 8= 0.    

10) √(x² - 3x) = 4x² - 12x -3.     

11) √{(x²+2)/x²-2)}+ 6√{(x²-2)/(x²+2)}= 5.

12) Find the nature of following:

a) x² - 5x -2= 0.

b) 4x² - 4x +1= 0.

c) x² + px - q²= 0.

13) Find the value of m so that the roots of the equation (4- m)x² +(2m +4)x + (8m +1)= 0 may be equal. 0,3

14) If (1- p) is a root of the equation x² + px + (1- p) = 0. Then its roots are

a) 0, -1 B) -1,1 C) 0,1 D) -1,2

15) √{x/(1- x)} + {(1- x)/x} = 13/6.

16) (x+1)(x+2)(x+3)(x+4) = 120.  

17) 2x² + 2x -3= 0 (upto two decimal places).