A pipe with 30 cm Length is open at both ends, which harmonic mode of the pipe resonates a 1.65 kHz source? (Velocity of sound in air \(=330 \mathrm{~ms}^{-1}\) )

Two point charges \(-q\) and \(+q\) are located at points \((0,0,-a)\) and \((0,0, a)\) respectively. The electric potential at a point \((0,0, z)\), where \(z>a\) is

A particle of mass \(m\) is under an influence of a force \(\mathbf{F}=\left(-k \mathbf{x}+\mathbf{F}_0\right) \mathrm{N}\). The particle when disturbed will oscillate

When an inductor of inductance \(\frac{6}{\pi} \mathrm{H}\), a capacitor of capacitance \(\frac{50}{\pi} \mu \mathrm{F}\) and resistor of resistance \(R\) are connected in series with an AC supply of rms voltage \(220 \mathrm{~V}\) and frequency \(50 \mathrm{~Hz}\), the rms current through the circuit is \(440 \mathrm{~mA}\). Match the inductive reactance, \(X_L\) the capacitive reactance, \(X_C\) the resistance \(R\) and the impedance \(Z\) of the circuit given in List-I with the corresponding values given in List-II.
\(\begin{array}{llll} \hline & \text { List- I } & & \text { List- II } \\ \hline \text {(A) } & X_L & \text { (i) } & 200 \Omega \\ \hline \text {(B) } & X_C & \text { (ii) } & 300 \Omega \\ \hline \text {(C) } & R & \text { (iii) } & 500 \Omega \\ \hline \text {(D) } & Z & \text { (iv) } & 600 \Omega \\ \hline \end{array}\)

A mass \(M\) attached to a horizontal spring executes simple harmonic motion with amplitude \(A_1\). When mass \(M\) passes mean position then a smaller mass \(m\) is attached to it and both of them together executing simple harmonic motion with amplitude \(A_2\). Then the value of \(\frac{A_1}{A_2}\) is

Wrongly matched pair among the following

In the nuclear fusion reaction \({ }_1 \mathrm{H}^2+{ }_1 \mathrm{H}^3 \rightarrow{ }_2 \mathrm{He}^4+\mathrm{n}\), if the repulsive potential energy between the two nuclei is \(2.07 \times 10^{-14} \mathrm{~J}\), then the temperature at which the gases must be heated to initiate the reaction is \(\left(\right.\) Boltzmann constant \(\left.=1.38 \times 10^{-23} \mathrm{JK}^{-1}\right)\)

The equation of a curve passing through the point \((0,1)\), given that the slope of the tangent to the curve at any point \((x, y)\) is equal to the sum of the \(x\)-coordinate and the product of \(x\) and \(y\) coordinates at that point, is

A Carnot engine having efficiency \(60 \%\) receives heat from a source at a temperature 600 K. For the same sink temperature, to increase its efficiency to \(80 \%\), the temperature of the source is

If \(2 \cdot 4^{2 k+1}+3^{3 k+1}=11 t\) and \(2 \cdot 4^{2 k+3}+3^{3 k+4}=11\) \(\left(p t+3^q\right)\), where \(k, t \in Z^{+}\), then \((p, q)=\)

In a potentiometer, a wire of length \(10 \mathrm{~m}\) having resistance \(50 \Omega\) is used. A battery of \(5 \mathrm{~V}\) and a resistor of \(450 \Omega\) are connected in series to the wire. If an unknown battery of emf \(E\) balances the potentiometer at \(450 \mathrm{~cm}\), then the value of \(E\) is

If \(y=\log _2\left(\log _2 x\right)\), then \(\frac{d y}{d x}=\)

On an \(n \times n\) chessboard, the total number of rectangles which are not squares is 350 . Then, the number of white squares on the chessboard is .......