Q 1: The value of \lim\limits_{x \to 0}\frac{\tan\left(x\right)}x is ______________.
Q 2: The real part of 6e^{i\pi/3} is ________.
Q 3: The number of positive roots of the function f(x) shown in the range 0 < x < 6 is _____.
Q 4: Let i and j be the unit vectors in the x and y directions, respectively. For the function
F(x,y)=x^3+y^2the gradient of the function i.e. ∇F is given by
Q 5: The marks obtained by a set of students are 38, 84, 45,70, 75, 60, 48. The mean and median marks, respectively, are
Q 6: For the initial value problem
\frac{dy}{dt}=\sin\left(t\right),\;\;x(0)=0The value of x at t = π/3, is ________________.
Q 7: Match the problem type in Group 1 with the numerical method in Group 2.
| Group 1 | Group 2 |
| (P) System of linear algebraic equations | (I) Newton-Raphson |
| (Q) Non-linear algebraic equations | (II) Gauss-seidel |
| (R) Ordinary differential equations | (III) Simphson’s Rule |
| (S) Numerical integrations | (IV) Runge-Kutta |
Choose the correct set of combinations.
Q 8: A box has 6 red balls and 4 white balls. A ball is picked at random and replaced in the box, after which a second ball is picked. The probability of both the balls being red, rounded to 2 decimal places, is ________.