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$1.1$ The eigenvector(s) of the matrix $\left(\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right), a \neq 0$, is (are) $(0,0, \alpha)$ $(\alpha, 0,0)$...
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1.2 The differential equation, $\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}+\sin$ $y=0$, is linear non-linear homogeneous of degree two
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1.3 Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree 1 2 3 4
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1.4 Which of the following is (are) valid FORTRAN 77 statement(s)? $\mathrm{DO} 131=1$ $\mathrm{A}=\mathrm{DIM}^{* * 7} 7$ READ $=15.0$ GOTO $3=10$
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$1.5$ Fourier series of the periodic function (period $2 \pi$ ) defined by $f(x)=\left\{\begin{array}{ll}0 & -\pi \leq x
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1.6 Which of the following improper integrals is (are) convergent? $\int_{0}^{1} \frac{\sin x}{1-\cos x} d x$ $\int_{0}^{\infty} \frac{\operatorname{cox} x}{1+x} d x$ $\i...
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1.7 The function $f(x, y)=x^{2} y-3 x y+2 y+x$, has no local extremum one local minimum but no local maximum one local maximum but no local minimum one local minimum and ...
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$2.1 \lim _{x \rightarrow 0} \frac{x\left(e^{x}-1\right)+2(\cos x-1)}{x(1-\cos x)}$ is
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2.2 The radius of convergence of the power series $\sum_{0}^{n} \frac{(3 m) !}{(m !)^{3}} x^{i m}$ is
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2.3 If the linear velocity $\overrightarrow{\mathrm{V}}$ is given by $\overrightarrow{\mathrm{V}}=x^{2} y \hat{i}+$ $x y z \hat{j}-y z^{2} k$ the anguarl velocity $\vec{w...
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2.4 Given the differential equation, $\bar{y}=x-y$ with the initial condition $y(0)=0$. The value of $(0.1)$ calculated numerically upto the third place of decimal by the...
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$2.5$ For $\mathrm{X}=4.0$, the value of 1 in the FORTRAN 77 statement \[ I=-2^{* *} 2+5.0 * X / X * 3+\frac{3}{4} \text { is } \]
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2.6 The value of the double integral $\int_{0}^{1} \int_{x}^{1 / x} \frac{x}{1+y^{2}}$ $d x d y$ is
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$2.7$ If $\mathrm{A}=\left(\begin{array}{cccc}1 & 0 & 0 & 1 \\ 0 & -1 & 0 & -1 \\ 0 & 0 & i & i \\ 0 & 0 & 0 & -i\end{array}\right)$ the matrix $\mathrm{A}^{4}$, calculat...
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2.9 The differential equation $y+y=0$ is subjected to the boundary conditions \[ y(0)+0 y(\lambda)=0 \] In order that the equation has non-trivial solution (s), the gener...
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2.10 The Laplace transform of the periodic function $f(t)$ described by the curve below, i.e. $f(t)=\left\{\begin{array}{c}\sin t \text { if }(2 n-1) \pi \leq t \leq 2 n ...
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3.3. Although a laser heam is highly directional, its beam width increases with propagation. This increase is due to coherence diffraction polarization interference
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3.5. While you are listening to a programme from a radio, if a near-by electric light bulb is switched on or switched off, you hear a momentary noise in your radio. This ...
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3.6. Nuclear fusion reactions require very high temperatures so as to overcome. nuclear forces van der waals forces coulomb forces gravitational forces
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3.8. In an hydrogen atom $10.2 . \mathrm{eV}$ is given out as radiation when an electron is de-excited to the ground state. The principal quantum number of the excited st...
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3.9. Typical current voltage characteristic of a solar cell is given in the following figure by curve $A$ curve $B$ curve $C$ curve $D$
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3.10. Consider a solid sphere and a hollow sphere, both of mass $M$, radius $R$ and initially at rest, which start rolling down the same inclined plane without slipping. ...
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3.11. An optical fibre consists of a cylindrical dielectric rod of refractive index $\mathrm{n}^{1}$, surrounded by another dielectric of refractive index $n^{2}$, where ...
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3.12. For a uniformly charged sphere of radius $R$ and charge density $\rho$, the ratio of magnitude of electric fields at distances $R / 2$ and $2 R$ from the centre, i....
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If $(^{n}C_{0} + ^{n}C_{1}) (^{n}C_{1} + ^{n}C_{2}) \dots (^{n}C_{n-1} + ^{n}C_{n}) = k \; ^{n}C_{0} \; ^{n}C_{1} \dots ^{n}C_{n-1},$ then $k$ is equal to $\frac{(n+1)^{n...
Aditya_ answered in Others Aug 1
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Suppose $f : \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function such that $f(x) = \frac{2 – \sqrt{x+4}}{\sin 2x}$ for all $x \neq 0.$ Then the value of $f(0)$ ...
chenna keshava answered in Others Jul 31
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The number of distinct even divisiors of $$\prod_{k=1}^{5} k!$$ is $24$ $32$ $64$ $72$
Aditya_ answered in Others Jul 31
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The roots of the polynomial $p(x)=x^{4}-2x^{3}-2x^{2}+8x-8$ are: $1, -1, 2, 2+3 i$ $1+i, 1-i, 2, -2$ $1, -1+i, 2, 2+3 i$ $1+i, -1+i, 2, -2$
[ Jiren ] answered in Others Jul 28
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