Linear Functions

Q. 21.find the domain of square root of sin x

Q. 29. Find Arg( sin8Π/5 + i [ 1+ cos 8Π/5] )

Q. If $P=\{x:x<3,x\in N\},Q=\{x:x\le 2,x\in W\},$ then $(P\cup Q)\times (P\cap Q)$ is

1. $\left\{\right(0,1),(0,2),(1,1),(1,2),(2,1),(2,2\left)\right\}$
2. $\left\{\right(0,1),(0,2),(0,3),(1,1),(1,2),(1,3),(2,1),(2,2),(2,3)\}$
3. $\varphi$
4. $\left\{\right(0,1),(0,2),(0,3\left)\right\}$

Q. sec^4A-†an^4A=1+2†an^2A. Prov

Q. If $\cos x+\sqrt{3}\sin x=2,\mathrm{then}x=$
(a) $\pi /3$
(b) $2\pi /3$
(c) $4\pi /6$
(d) $5\pi /12$

Q. If a set $A$ has ${}^{\prime }{n}^{\prime }$ distinct elements, then the number of all relations on $A$ is

1. $2^{n^2}$
2. $n^2$
3. $2^n$
4. $2^{n^n}$

Q. The function ‘ t ’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by . Find (i) t (0) (ii) t (28) (iii) t (–10) (iv) The value of C, when t (C) = 212

Q. Let f , g : R → R be defined, respectively by f ( x ) = x + 1, g ( x ) = 2 x – 3. Find f + g , f – g and .

Q. lim x->0 [(sinx)^1/x + (1/x)^sinx] equals

Q. If $(p^2-4p+5,2)=(2p-3,|p-2|)$, then the number of values of $p$ is

1. $0$
2. $1$
3. $2$
4. $3$

Q. If $a\cos 2x+b\sin 2x=c$ has α and β as its roots, then prove that

(i) $\tan \alpha +\tan \beta =\frac{2b}{a+c}$ [NCERT EXEMPLAR]

(ii) $\tan \alpha \tan \beta =\frac{c-a}{c+a}$

(iii) $\tan \left(\alpha +\beta \right)=\frac{b}{a}$ [NCERT EXEMPLAR]

Q. If $3f\left(x\right)+5f\left(\frac{1}{x}\right)=\frac{1}{x}-3$ for all non-zero x, then f(x) =

(a) $\frac{1}{14}\left(\frac{3}{x}+5x-6\right)$
(b) $\frac{1}{14}\left(-\frac{3}{x}+5x-6\right)$
(c) $\frac{1}{14}\left(-\frac{3}{x}+5x+6\right)$
(d) None of these

Q. A function f is defined by f ( x ) = 2 x – 5. Write down the values of (i) f (0), (ii) f (7), (iii) f (–3)

Q. m and M are such that m<=(tan^(-1)x)^(2)+(cos^-1(x))^2<=M then ((M)/(m)) equals

Q. Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from Z to Z defined by f ( x ) = ax + b , for some integers a , b . Determine a , b .

Q. The function $f\left(x\right)=\frac{9x}{5}+32$ is the formula to convert $x^{\circ }C$ to Fahrenheit units. Then at what ${}^{\circ }C$ both Celsius and Fahrenheit is same?

1. ${32}^{\circ }C$
2. $-{32}^{\circ }C$
3. ${40}^{\circ }C$
4. $-{40}^{\circ }C$

Q. Let $A=\left\{\right(a,b,c):a,b,c\in N,a^{\left(bc\right)}=64\},$ then the total number of ordered triplets is

Q. If $f(2x+3y,2x-7y)=20x$, then $f(x,y)$ equals

1. 7x-3y
2. 7x+3y
3. 3x-7y
4. x-4y

Q. 23. If 9sin square thrita + 5cos square thrita = 6 find the value of tan thrita

Q. Let $N$ be the set of natural numbers. Suppose $f:N\to N$ is a function satisfying the following conditions
$\left(a\right)f(m+n)=f\left(m\right)+f\left(n\right)\left(b\right)f\left(2\right)=2$
The value of $\frac{1}{7}\sum _{k=1}^{20}f\left(k\right)$ is

Q. Solve }\vert x^4-x^2-12\vert=\vert x^4-9\vert-\vert x^2+3\vert

Q. Let N = sin x + cos(/3 -x). Cos(/3+x) then the value of log to the base 2

Q. If $A=\{x\in R:|x|<2\}$ and $B=\{x\in R:|x-2|\ge 3\}$ then :

1. $A-B=[-1,2]$
2. $B-A=R-(-2,5)$
3. $A\cup B=R-(2,5)$
4. $A\cap B=(-2,-1)$