A circuit to verify \(Ohm's\) law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit

A particle of mass \(m\) is moving along the side of a square of side '\(a\)', with a uniform speed \(v\) in the \(x-y\) plane as shown in the figure Which of the following statement is false for the angular momentum \(\vec L\) about the origin ?

A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height H above first liquid. If viewed from above, the apparent shift in the position of bottom of container is 40 cm. The value of H is ______ cm.
(Consider liquids are immisible)

In a Young's double slit experiment \(15\) fringes are observed on a small portion of the screen when light of wavelength \(500 \;\mathrm{nm}\) is used. Ten fringes are observed on the same section of the screen when another light source of wavelength \(\lambda\) is used. Then the value of \(\lambda\) is (in \(\mathrm{nm})\)

A coin placed on a rotating table just slips when it is placed at a distance of \(1\,cm\) from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of from the centre \(............\,cm\)

A \(20\,cm\) long metallic rod is rotated with \(210\,rpm\) about an axis normal to the rod passing through its one end. The order end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field \(0.2\,T\) parallel to the axis exists everywhere. The emf developed between the centre and the ring is \(.......\,mV\).Take \(\pi=\frac{22}{7}\)

A sub-atomic particle of mass \(10^{-30} \mathrm{~kg}\) is moving with a velocity \(2.21 \times 10^6 \mathrm{~m} / \mathrm{s}\). Under the matter wave consideration, the particle will behave closely like _______. \(\left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}\right)\)

Let the points of intersections of the lines \(x-y+1=0\), \(x-2 y+3=0\) and \(2 x-5 y+11=0\) are the mid points of the sides of a triangle \(A B C\). Then the area of the triangle \(\mathrm{ABC}\) is .... .

If \(f(x)\) is continuous and \(f\left( {\frac{9}{2}} \right) = \frac{2}{9}\), then \(\mathop {\lim }\limits_{x \to 0} f \left( {\frac{{1 - \cos \,3x}}{{{x^2}}}} \right)\) is equal to:

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 _______.

The number of seven digit positive integers formed using the digits \(1,2,3\) and \(4\) only and sum of the digits equal to \(12\) is \(...........\).

The slope of normal at any point \((x, y), x > 0, y > 0\) on the curve \(y=y(x)\)  is given by \(\frac{x^{2}}{x y-x^{2} y^{2}-1}\) If the curve passes through the point \((1,1)\), then e. \(y(e)\) is equal to

A complex number z is said to be unimodular if \(\left| z \right| = 1\) . Suppose \(z_1\) and \(z_2\)  are complex number such that \(\frac{{{z_1} - 2{z_2}}}{{2 - {z_1}\overline {{z_2}} }}\) is unimodular and  \(z_2\) is not unimodular . Then the point \(z_1\) lies on a: