- #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 pth,qth,rth terms of an Harmonic Progression, then
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 pth,qth,rth terms of an Harmonic Progression, then
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
Last edited:
