List of top Biotechnology Questions on Biochemistry asked in AP PGECET

Let \[ f(x)= \begin{cases} A+2x, & \text{if } x<3,\\[4pt] 1+x^{2}, & \text{if } x\ge3. \end{cases} \] If the function \(f(x)\) is continuous at \(x=3\), then the value of \(A\) is: 

The Newton-Raphson method is used to find the root of \[ f(x)=x^2-x-1=0 \] If the initial guess is \(x_0=1\), then the estimate after two iterations is
Consider the differential equation \[ \frac{d^{2}y}{dx^{2}}+3\frac{dy}{dx}+2y=0 \] with the conditions \(y(0)=20\) and \(y'(0)=10\). Then, the value of \[ y(1)e^{2}-50e+20= \] is
If \(u=\dfrac{xy}{x+y}\), then \(x\dfrac{\partial u}{\partial x}+y\dfrac{\partial u}{\partial y}\) is equal to
If the Laplace transform of a function \(f(t)\) is given by \[ \frac{s+3}{(s+1)(s+2)}, \] then the value of \(f(\ln2)\) is
Using Trapezoidal rule with step size of 0.1, the value of the integral \[ \int_{0}^{0.3} f(x)\,dx \]
For what value of the constant \(k\), the function \[ f(x)= \begin{cases} kxe^{-2x}, & x>0 \\ 0, & \text{otherwise} \end{cases} \] is a probability density function?
The random variable \(X \sim \text{Bin}(11,p)\). If \(P(X=8)=P(X=7)\), then \(p=\)
The system of equations \(2x+y=5,\; x-3y=-1,\; 3x+4y=k\) is consistent when \(k\) is
Let \[ A= \begin{pmatrix} 1 & x & 2x \\ 1 & 3x & 5x \\ 1 & 3 & 4 \end{pmatrix}, \qquad x\neq0. \] If \(\det(A)=0\), then \(x=\)
Assertion (A): Allosteric enzymes show hyperbolic kinetics.
Reason (R): They follow Michaelis-Menten behaviour.
_______ is/ are essential in nucleic acid synthesis.
_______ is a purine.
The Newton-Raphson method is used to find the root of \[ f(x)=x^2-x-1=0 \] If the initial guess is \(x_0=1\), then the estimate after two iterations is
Consider the differential equation \[ \frac{d^{2}y}{dx^{2}}+3\frac{dy}{dx}+2y=0 \] with the conditions \(y(0)=20\) and \(y'(0)=10\). Then, the value of \[ y(1)e^{2}-50e+20= \] is
If the Laplace transform of a function \(f(t)\) is given by \[ \frac{s+3}{(s+1)(s+2)}, \] then the value of \(f(\ln2)\) is
For what value of the constant \(k\), the function \[ f(x)= \begin{cases} kxe^{-2x}, & x>0 \\ 0, & \text{otherwise} \end{cases} \] is a probability density function?
The random variable \(X \sim \text{Bin}(11,p)\). If \(P(X=8)=P(X=7)\), then \(p=\)
Using Trapezoidal rule with step size of 0.1, the value of the integral \[ \int_{0}^{0.3} f(x)\,dx \]
If \(u=\dfrac{xy}{x+y}\), then \(x\dfrac{\partial u}{\partial x}+y\dfrac{\partial u}{\partial y}\) is equal to
The system of equations \(2x+y=5,\; x-3y=-1,\; 3x+4y=k\) is consistent when \(k\) is
Let \[ A= \begin{pmatrix} 1 & x & 2x \\ 1 & 3x & 5x \\ 1 & 3 & 4 \end{pmatrix}, \qquad x\neq0. \] If \(\det(A)=0\), then \(x=\)
Let \(f(x)=\begin{cases A+2x,&\text{if }x \\ 1+x^{2},&\text{if }x\ge3 \end{cases}\). If the function \(f(x)\) is continuous at \(x=3\), then the value of \(A\) is}
Assertion (A): Allosteric enzymes show hyperbolic kinetics.
Reason (R): They follow Michaelis-Menten behaviour.
_______ is a purine.