math

Question 1

roots of f(x) = f^-1(x) lie on which line?

Answer 1

y = x

Question 2

if two roots of ax² + bx + c = 0 are in the ratio m:n

Answer 2

mnb² = (m+n)²ac

Question 3

if a₁x² + b₁x + c₁ =0 and a₂x² + b₂x + c₂ =0 have a common real root

Answer 3

(a₁c₂ - a₂c₁)² = (b₁c₂ - b₂c₁)(a₁b₂ - a₂b₁)

Question 4

incentre

Answer 4

x = (ax₁ + bx₂ + cx₃)/(a + b + c)

Question 5

excentre

Answer 5

-ve of incentre

Question 6

area of triangle in terms of a, b, c

Answer 6

area = (1/2)ab sinc

Question 7

log_a1 = ?

Answer 7

0

Question 8

log_aa = ?

Answer 8

1

Question 9

log_amn = ?

Answer 9

log_am + log_an

Question 10

log_amⁿ = ?

Answer 10

nlog_am

Question 11

log_a^bm = ?

Answer 11

(1/b)log_am

Question 12

log_ba = ?

Answer 12

(log_ma)/(log_mb)

Question 13

a^log_am = ?

Answer 13

m

Question 14

∫a^xdx

Answer 14

a^x/ln a + c

Question 15

2 points (x₁, y₁) and (x₂, y₂) lie on the same side of straight line ax + by + c = 0 if ?

Answer 15

ax₁ + by₁ + c and ax₂ + by₂ + c have the same sign

Question 16

ⁿC_r/ⁿC_r-1

Answer 16

(n-r+1)/r

Question 17

area of triangle formed by tangents and CoC

Answer 17

(RL³)/(R² + L²)

L= √S₁

Question 18

a^log_cb = b^log_ca

Answer 18

yea