- #1

Pagan

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Please help me i am in 11th grade. These were the questions asked to me in a test and after the test was over the teacher asked to sumbmit the complete set of solutions for the test in four days time. There were total thirty questions I was able to do seventeen. I need help please or i will be mincemeat...

I need the step-by-step solutions of the following problems and theorums, axioms used if any.

although i have the correct answers...I want the Working.

well... here goes...:

1] If the expression mx - 1 + 1/x is non negative for all positive real x, then the minimum value of m must be:

(a) -1/2 (b) 0 (c) 1/4 (d) 1/2

2] If a,b,c are the

ab(p-q) + bc(q-r) +ca(r-p) equals

(a) 1 (b) -1 (c) 0 (d) None

3] Given p Arithmatic Progressions, each of which consists of n terms. If their 1st terms are 1,2,3,...,p and common differences are 1,3,5,...,(2p-1)

respectively, then the sum of the terms of all the progressions is:

(a) np(np+1)/2 (b) n(p+1)/2 (c) np(n+1) (d)None

4] the straight line y = x + 2 rotates about a point where it cuts the x-axis and becomes perpendicular to ax + by + c = 0 then its eqn is

(a) ax + by + 2a =0 (b) ax - by - 2a = 0

(c) bx + ay - 2b =0 (d) ay - bx + 2b = 0

5] Points on the line x + y = 4 that lie at a unit distanance from 4x+3y-10=0 are

(a) (3,1)&(7,11) (b) (-3,7)&(2,2) (c) (-3,7)&(-7,11) (d)none of these

6] two lines are given by (x-2y)2 + c(x-2y) = 0 the value of c such that the distance between them is 3 is

(a) c=0 (b) c=±v3

7] drawn from the origin are two mutually perpendicular lines forming an isoceles triangle together with the st. line 2x+y=a then the area of the triangle is

a) (a^2)/2 b) (a^2)/3 c) (a^2)/5

8] The minimum value of (sin a)^2 + (cos a)^4 is

a) 3/8 b) 1 c) 3/4

9]Value of sin 10° + sin 50° + sin 70° =

a) 1/16 b) 1/8

10] If

cos² A + cos² B + cos² C = 1 then triangle ABC is

a) equilateral triangle b)right triangle c)isoseles triangle

11]in a triangle ABC, tan(A/2), tan(B/2), tan(C/2) are in harmonic progression. then cot(A/2)*cot(C/2) is

a)1 b) 2 c) 3

12] If a lies in the third quadrant, then v4(sin a)^4 + (sin a)^2 + 4 [cos{45°+(a/2)}]^2 equals

a)1 b)2 c)-2

13] If a and ß are two distinct roots of a(tan x)+b(sec x)=c, then tan(a+ß) equals

(a) (a^2 - c^2)/(a^2 + c^2) (b) (a^2 + c^2)/(a^2 - c^2)

(c) 2ac/(a^2 + c^2) (d) 2ac//(a^2 - c^2)

correct answers

1] c

2] c

3] a

4] d

5] a

6] b

7] c

8] c

9] a or b(not sure)

10] b or c(not sure)

11] c

12] b

13] d

List of Symbols used by me

+ alt+3544

a alt+3552

ß alt+3553

p alt+3555

S alt+3556

s alt+3557

F alt+3560

O alt+3562

8 alt+3564

f alt+3565

e alt+3566

n alt+3567

± alt+3569

= alt+3570

= alt+3571

˜ alt+3575

° alt+3576

v alt+3579

n alt+3580

² alt+3581

♂ alt+3595

♀ alt+3596

↕ alt+3602

¶ alt+3604

§ alt+3605

T alt+1257

I need the step-by-step solutions of the following problems and theorums, axioms used if any.

although i have the correct answers...I want the Working.

well... here goes...:

1] If the expression mx - 1 + 1/x is non negative for all positive real x, then the minimum value of m must be:

(a) -1/2 (b) 0 (c) 1/4 (d) 1/2

2] If a,b,c are the

**p**th,**q**th,**r**th terms of an Harmonic Progression, thenab(p-q) + bc(q-r) +ca(r-p) equals

(a) 1 (b) -1 (c) 0 (d) None

3] Given p Arithmatic Progressions, each of which consists of n terms. If their 1st terms are 1,2,3,...,p and common differences are 1,3,5,...,(2p-1)

respectively, then the sum of the terms of all the progressions is:

(a) np(np+1)/2 (b) n(p+1)/2 (c) np(n+1) (d)None

4] the straight line y = x + 2 rotates about a point where it cuts the x-axis and becomes perpendicular to ax + by + c = 0 then its eqn is

(a) ax + by + 2a =0 (b) ax - by - 2a = 0

(c) bx + ay - 2b =0 (d) ay - bx + 2b = 0

5] Points on the line x + y = 4 that lie at a unit distanance from 4x+3y-10=0 are

(a) (3,1)&(7,11) (b) (-3,7)&(2,2) (c) (-3,7)&(-7,11) (d)none of these

6] two lines are given by (x-2y)2 + c(x-2y) = 0 the value of c such that the distance between them is 3 is

(a) c=0 (b) c=±v3

7] drawn from the origin are two mutually perpendicular lines forming an isoceles triangle together with the st. line 2x+y=a then the area of the triangle is

a) (a^2)/2 b) (a^2)/3 c) (a^2)/5

8] The minimum value of (sin a)^2 + (cos a)^4 is

a) 3/8 b) 1 c) 3/4

9]Value of sin 10° + sin 50° + sin 70° =

a) 1/16 b) 1/8

10] If

cos² A + cos² B + cos² C = 1 then triangle ABC is

a) equilateral triangle b)right triangle c)isoseles triangle

11]in a triangle ABC, tan(A/2), tan(B/2), tan(C/2) are in harmonic progression. then cot(A/2)*cot(C/2) is

a)1 b) 2 c) 3

12] If a lies in the third quadrant, then v4(sin a)^4 + (sin a)^2 + 4 [cos{45°+(a/2)}]^2 equals

a)1 b)2 c)-2

13] If a and ß are two distinct roots of a(tan x)+b(sec x)=c, then tan(a+ß) equals

(a) (a^2 - c^2)/(a^2 + c^2) (b) (a^2 + c^2)/(a^2 - c^2)

(c) 2ac/(a^2 + c^2) (d) 2ac//(a^2 - c^2)

correct answers

1] c

2] c

3] a

4] d

5] a

6] b

7] c

8] c

9] a or b(not sure)

10] b or c(not sure)

11] c

12] b

13] d

List of Symbols used by me

+ alt+3544

a alt+3552

ß alt+3553

p alt+3555

S alt+3556

s alt+3557

F alt+3560

O alt+3562

8 alt+3564

f alt+3565

e alt+3566

n alt+3567

± alt+3569

= alt+3570

= alt+3571

˜ alt+3575

° alt+3576

v alt+3579

n alt+3580

² alt+3581

♂ alt+3595

♀ alt+3596

↕ alt+3602

¶ alt+3604

§ alt+3605

T alt+1257

Last edited: