Rational Function

Q.

$f\left(x\right)=2x^2+bx+c$ and $f\left(0\right)=3$ and $f\left(2\right)=1$, then $f\left(1\right)$ is equal to

1. $0$

2. $-1$

3. $1$

4. $2$

Q.

If a rubber ball is taken at the depth of 200 m in a pool, its volume decreases by 0.1%. If the density of the water is $1\times {10}^{3}kg/m^3$ and $g=10m/s^2$, then the volume elasticity in $n/m^2$ will be

1. ${10}^8$

2. $2\times {10}^8$

3. ${10}^9$

4. $2\times {10}^9$

Q. The range of $\frac{3x^2+9x+17}{3x^2+9x+7}$ is

1. $[1,41]$
2. $(0,10]$
3. $[11,\infty )$
4. $(1,41]$

Q.

$li{m}_{x\to \infty }$$\frac{\left(\sqrt{n}\right)}{(\sqrt{n}+(\sqrt{n+1}\left)\right)}$ =

1. 1

2. 1/2

3. 0

4. 

Q.

If f(x)=|x-2| and g(x) =fof(x), then for x>20, g'(x) is equal to.

1. 1

2. 2

3. 3

4. 0

Q. If $F\left(x\right)=f\left(x\right).g\left(x\right)and{f}^{\prime }\left(x\right)g^{\prime }\left(x\right)=c$ , where ‘c’ is a constant then $\frac{f‘‘}{f}+\frac{g‘‘}{g}+\frac{2C}{fg}$=

1. 
2. 
3. 
4. 

Q.

What is Youngs modulus?

Q.

Find the value of $\sqrt{7\left(\sqrt{7\sqrt{7}}\right)}$

1. 

2. 

3. 7²

4. 

Q.

The only elastic modulus that applies to fluids is

1. Young's modulus

2. Shear modulus

3. Modulus of rigidity

4. Bulk modulus

Q.

Bulk modulus was first defined by

1. Young

2. Bulk

3. Maxwell

4. None of the above

Q.

If $\left\{x\right\}$ represents the fractional part of $x$, then $\left\{\frac{5^{200}}{8}\right\}$ is

1. $\frac{1}{8}$
2. $\frac{1}{4}$
3. $\frac{3}{8}$
4. $\frac{5}{8}$

Q.

If R is a relation then which of the following is correct?

1. 
2. 
3. 
4. 

Q. A spherical ball contracts in volume by $0.02\%$ when subjected to a normal uniform pressure of $100\text{atm}$. The bulk modulus of its material is

1. $2.02\times {10}^{10}{\text{N/m}}^2$
2. $1.01\times {10}^{11}{\text{N/m}}^2$
3. $5.05\times {10}^{10}{\text{N/m}}^2$
4. $1.01\times {10}^{10}{\text{N/m}}^2$

Q.

The adiabatic elasticity of a gas is equal to

1. $\gamma \times$ density
2. $\gamma \times$ volume
3. $\gamma \times$ pressure
4. $\gamma \times$ specific heat

Q.

A solid sphere of radius 20 cm is subjected to a uniform pressure of ${10}^{6}N{m}^{-2}$. If the bulk modulus of the solid is $1.7\times {10}^{11}N{m}^{-2}$, the decrease in the volume of the solid is approximately equal to

1. $0.2c{m}^3$

2. $0.3c{m}^3$

3. $0.4c{m}^3$

4. $0.5c{m}^3$

Q.

If f(x) = $\sqrt{x}$ and $g\left(x\right)=x$ , then $\left(\frac{f}{g}\right)\left(x\right)$ equals to $(x\ne 0)$

1. $\sqrt{x}$

2. $x^{\frac{3}{2}}$

3. $x$

4. $\frac{1}{\sqrt{x}}$

Q. If f(x) +f(x+a)+f(x+2a)+....+f(x+na)= constant; $\forall x$ $ϵRanda>0$ and f(x) is periodic, then period of f(x), is

1. (n+1) a
2. 
3. na
4. e^{na}

Q. Let $f\left(x\right)=x^2$ and $g\left(x\right)=3x+4$ . Then the value of $\frac{(f+g)\left(x\right)}{(f-g)\left(x\right)}$= when x = 1

1. $\frac{4}{3}$
2. $\frac{3}{4}$
3. $\frac{-4}{3}$
4. $\frac{-3}{4}$

Q. If $f\left(x\right)=x^3-\frac{1}{x^3}$, show that $f\left(x\right)+f\left(\frac{1}{x}\right)=0.$

Q.

$\sqrt{-3}\sqrt{-75}$

1. 15i

2. 15

3. 115i

4. -15

Q. Bulk modulus of an incompressible liquid is

1. Zero
2. Infinity
3. Unity
4. Between Zero & Unity

Q. If f is a function such that $f\left(0\right)=2,f\left(1\right)=3andf(x+2)=2f\left(x\right)-f(x+1)$ for every real x then f(5) is

1. 7
2. 13
3. 1
4. 5

Q. The approximate depth of an ocean is $2700\text{m}$. The compressibility of water is $50\times {10}^{-11}{\text{Pa}}^{-1}$ and density of water is ${10}^3{\text{kg/m}}^3$. What fractional compression of water will be obtained at the bottom of the ocean?

1. $1.5\times {10}^{-2}$
2. $1.35\times {10}^{-2}$
3. $1.2\times {10}^{-2}$
4. $1.0\times {10}^{-3}$

Q. If $f\left(x\right)+2f(1-x)=x^2+1\forall xϵR$ then f(x) is

1. 
2. 
3. 
4. 

Q. The value of the limit $\underset{x\to -\infty }{lim}(\sqrt{4x^2-x}+2x)$ is

1. $-\infty$
2. $0$
3. $\frac{1}{4}$
4. $-\frac{1}{4}$

Q. The bulk modulus of rubber is $9.8\times {10}^8{\text{N/m}}^2$. To what depth a rubber ball must be taken in a lake so that its volume is decreased by $0.1\%$?
(Neglect atmospheric pressure)

1. $25\text{m}$
2. $100\text{m}$
3. $200\text{m}$
4. $500\text{m}$

Q. The range of the function $f\left(x\right)=\frac{x^2+x+2}{x^2+x+1},x\in R$ is

1. $(1,\infty )$
2. $(1,\frac{11}{7})$
3. $(1,\frac{7}{3}]$
4. $(1,\frac{7}{5})$

Q. If $f\left(x\right)=\frac{x+1}{x-1}$, show that f[f[(x)]] = x.

Q. If $f^{\prime \prime }\left(x\right)=-f\left(x\right)$ and g(x)=$f^{\prime }\left(x\right)$ and F(x)=${\left(f\left(\frac{x}{2}\right)\right)}^2+{\left(g\left(\frac{x}{2}\right)\right)}^2$ and given that F(5) =5 then F(10) is equal to

1. 0
2. 15
3. 5
4. 10

Q.

Let $f\left(x\right)=x^2$ and $g\left(x\right)=3x+4$. Find the value of $\frac{(f+g)\left(x\right)}{(f-g)\left(x\right)}$ when $x=1$

1. $\frac{4}{3}$

2. $\frac{3}{4}$

3. $\frac{-4}{3}$

4. $\frac{-3}{4}$