Q 1: Which one of the following methods requires specifying an initial interval containing the root (i.e. bracketing) to obtain the solution of f(x) = 0, where f(x) is a continuous non-linear algebraic function?
Q 2: The correct combination is
| P | tanh x | I | \frac{e^x+e^{-x}}{e^x-e^{-x}} |
| Q | coth x | II | \frac2{e^x+e^{-x}} |
| R | sech x | III | \frac2{e^x-e^{-x}} |
| S | cosech x | IV | \frac{e^x-e^{-x}}{e^x+e^{-x}} |
Q 3: Consider the following continuously differentiable function
v(x,y,z)=3x^2y\;i+8y^2z\;j+5xyz\;kwhere I, j, and k represent the respective unit vectors along the x, y, and z directions in the Cartesian coordinate system. The curl of this function is
Q 4: Sum of the eigenvalues of the matrix \begin{bmatrix}2&4&6\\3&5&9\\12&1&7\end{bmatrix} is ____________ (round off to nearest integer).
Q 5: In a box, there are 5 green balls and 10 blue balls. A person picks 6 balls randomly. The probability that the person has picked 4 green balls and 2 blue balls is
Q 6: The maximum value of the function f(x)=-\frac53x^3+10x^2-15x+16 in the interval (0.5,3.5) is
Q 7: Given \frac{dy}{dx}=y-20 , and {\left.y\right|}_{x=0}=40 the value of y at x = 2 is _________ (round off to nearest integer).
Q 8: Consider the following dataset
| x | 1 | 3 | 5 | 15 | 25 |
| f(x) | 6 | 8 | 10 | 12 | 5 |
The value of the integral \int_1^{25}f(x)\operatorname dx using Simpson’s 1/3rd rule is ___________ (round off to 1 decimal place).