General Tips for Choosing Function

Q.

If $f:R\to R$ satisfies $f(x+y)=f\left(x\right)+f\left(y\right)$, for all $x,y\in R$ and $f\left(1\right)=7$ , then ${\sum }_{r=1}^{n}f\left(r\right)$ is

1. 7n+(n+1)

2. $\frac{7n(n+1)}{2}$

3. $\frac{7n}{2}$
   

4. $\frac{7(n+1)}{2}$
   

Q. If $f\left(x_1\right)-f\left(x_2\right)=f\left(\frac{x_1-x_2}{1-x_1{x}_2}\right)$ for $x_1,x_2ϵ$ (-1, 1), then f(x) is

1. $log\frac{2+x}{1-x}$
2. $log\frac{1-x}{1+x}$
3. $ta{n}^{-1}\frac{1-x}{1+x}$
4. $ta{n}^{-1}\frac{1+x}{1-x}$

Q.

If f(xy) = f(x)+f(y), and f(e) = 1, then find the value of $f\left(e^2\right)$

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Q.

If f(x+y) = f(x) . f(y) , then

1. f(x) = a^kx

2. f(x) = 0

3. f(x) = kx

4. f(x) = xⁿ

Q.

If f(x) satisfies f(x+y) = f(x) + f(y) and f(5) = 15 then find f(3)?

1. 15

2. 9

3. 6

4. 21

Q. If a function F is such that F(0)= 2, F (1) = 3, F (x + 2) = 2 F(x) – F (x -1) for x $\le$ 0, then F(5) is equal to

1. -7
2. -3
3. 17
4. 13

Q.

If f(xy) = f(x)+f(y), and f(e) = 1, then find the value of $f\left(e^2\right)$

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Q.

If $f:R\to R$ satisfies $f(x+y)=f\left(x\right)+f\left(y\right)$, for all $x,y\in R$ and $f\left(1\right)=7$ , then ${\sum }_{r=1}^{n}f\left(r\right)$ is

1. $\frac{7n(n+1)}{2}$

2. $\frac{7(n+1)}{2}$
   

3. 7n+(n+1)

4. $\frac{7n}{2}$
   

Q. $3(y-8)+3(6x+2)=24+3y$
Which approximate value of x satisfies the equation above

1. 0.8
2. 1.33
3. 2.33
4. The value cannot be determined from the given equation.

Q. A surveyor in his field book has drawn the plot as shown in the given figure. The area of the plot is

1. $\frac{1}{2}(az+by+ct+dx)$
2. $\frac{1}{2}(bt+cx+ay+az)$
3. $\frac{1}{2}(cx+bt+by+az)$
4. $\frac{1}{2}(d+t)(c+x)+\frac{1}{2}(a+b)(y+z)$

Q. If $3x+\frac{2}{x}=7$, then $9x^2-\frac{4}{x^2}=$

Q. Applying zero product rule for the equation $x^2-ax-30=0$ is $x=10$, then $a=$ _____.

1. $6$
2. $7$
3. $8$
4. $9$