A wedge \(Y\) with mass of \(10\) kg and all frictionless surfaces and the inclined surface making \(37°\) with horizontal. A block \(X\) with mass \(2\) kg is placed at the highest point of the wedge as shown in figure is at rest. At \(t = 0\) wedge \((Y)\) is pulled toward right with constant force \((f)\) of \(24\) N. Taking the block \(X\) at rest at \(t = 0\), the time taken by it to slide down \(8.8\) m on the slope, while \(Y\) is on the move, is _____ s.
(take \(\tan(37°) = 3/4\) and \(g = 10\) m/s\(^2\))

Young's modulus is determined by the equation given by \(\mathrm{Y}=49000 \frac{\mathrm{m}}{\ell} \frac{\text { dyne }}{\mathrm{cm}^2}\) where \(\mathrm{M}\) is the mass and \(\ell\) is the extension of wre used in the experiment. Now error in Young modules \((\mathrm{Y})\) is estimated by taking data from \(M-\ell\) plot in graph paper. The smallest scale divisions are \(5 \mathrm{~g}\) and \(0.02\) \(\mathrm{cm}\) along load axis and extension axis respectively. If the value of \(M\) and \(\ell\) are \(500 \mathrm{~g}\) and \(2 \mathrm{~cm}\) respectively then percentage error of \(\mathrm{Y}\) is _______.

A letter \('A'\) is constructed of a uniform wire with resistance \(1.0\,\Omega \) per \(cm\) , The sides of the letter are \(20\, cm\) and the cross piece in the middle is \(10\, cm\) long. The apex angle is \(60\) . The resistance between the ends of the legs is close to ................ \(\Omega\)

\(1\) mole of rigid diatomic gas performs a work of \(Q / 5\) when heat \(Q\) is supplied to it. The molar heat capacity of the gas during this transformation is \(\frac{ x R }{8},\) The value of \(x\) is \(\ldots \ldots \ldots .\) \([ K =\) universal gas constant \(]\)

A magnetic dipole in a constant magnetic field has 

If speed \((V)\), acceleration \((A)\) and force \((F)\) are considered as fundamental units, the dimension of Young’s modulus will be

A physical quantity \(P\) is given as \(P=\frac{a^2 b^3}{c \sqrt{d}}\) The percentage error in the measurement of \(a, b, c\) and \(d\) are \(1 \%, 2 \%, 3 \%\) and \(4 \%\) respectively. The percentage error in the measurement of quantity \(P\) will be \(.......\%\)

As per given figure \(A , B\) and \(C\) are the first, second and third excited energy level of hydrogen atom respectively. If the ratio of the two wavelengths \(\left(\right.\) i.e. \(\left.\frac{\lambda_1}{\lambda_2}\right)\) is \(\frac{7}{4 n}\), then the value of \(n\) will be

The total number of matrices \(A = \left[ {\begin{array}{*{20}{c}}
0&{2x}&{2x}\\
{2y}&y&{ - y}\\
1&{ - 1}&1
\end{array}} \right];\,\left( {x,y \in R,\,x \ne y} \right)\) for which \({A^T}A = 3{I_3}\)

An elastic spring under tension of \(3 \mathrm{~N}\) has a lengtha. Its length is \(b\) under tension \(2 \mathrm{~N}\). For its length\((3 a-2 b)\), the value of tension will be_______. \(\mathrm{N}\).

Let \(f ( x )\) be a polynomial of degree \(6\) in \(x ,\) in which the coefficient of \(x^{6}\) is unity and it has extrema at \(x=-1\) and \(x=1\). If \(\lim _{x \rightarrow 0} \frac{f(x)}{x^{3}}=1,\) then \(5 \cdot f (2)\) is equal to .............

Sodium light of wavelengths \(650\, nm\) and \(655\, nm\) is used to study diffraction at a single slit of aperture \(0.5\, mm\). The distance between the slit and the screen is \(2.0 \,m\). The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is \(\times 10^{-5} \,m\)

Identify the logic operation performed by the given circuit.