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Syllabus

a)3

b)4

c)5

d)6

a)1

b)-1

c)-2

d)2

a)21

b)23

c)30

d)66

The Domain of f(x) =log_{1}_{/2}.log_{4}.log_{3}[(x-lambda)^{2}] (where [ ] denotes the greatest integer function) is (-infinity,2] U [6,infinity) , then thevalue of lambda is:-^{2x}- 7^{x}- 5^{2x }* 35 + 7^{x }* 35 = 0find value of x??

a)1

b)0

c)2

d)3

1. 1/sqrt(4x-|x^2 -10x +9|)

2. sin-1 (1/|x^2 -1|) + 1/sqrt(sin^2 x +sinx +1)

3. squt(sin-1 (3x-4x^3)) +squt(cos-1 (x))

cos-1 is cos inverse of sin-1 is sin inverse of ^represents to the power

please explain the marked step

y=3[x]+7

y=4[x-3]+4 then find [x+y].

f(x)=(4

^{x}-44^{x})^{1/2}+ 3^{x}/log_{4}(1-x)f:R->R, f(x)=(ax^2 +6x -8)/(a+6x-8x^2) is onto then range of a is?

$\mathbf{51}\mathbf{.}\mathbf{}Therangeofthefunctiony=\frac{8}{9-{x}^{2}}is\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(A\right)\left(-\infty ,\infty \right)-\left\{\pm 3\right\}\left(B\right)[\frac{8}{9},\infty )\left(C\right)\left(0,\frac{8}{9}\right)\left(D\right)\left(-\infty ,0\right)\cup [\frac{8}{9},\infty )$

NO LINKS PLEASEQ.$\text{IfF(x)=}\frac{\left(x-b\right)\left(x-c\right)}{\left(a-b\right)\left(a-c\right)}+\frac{\left(x-c\right)\left(x-a\right)}{\left(b-c\right)\left(b-a\right)}+\frac{\left(x-a\right)\left(x-b\right)}{\left(c-a\right)\left(c-b\right)},$

Show that F(0)=1.

_{2}(log_{2}x) + log_{1/2}[log_{2}2(2)^{1/2}x]=1^{2}+ 3x + 4