A tuning fork with frequency \(800 \;\mathrm{Hz}\) produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Surface. Successive resonance are observed at length \(9.75 \;\mathrm{cm}, 31.25\; \mathrm{cm}\) and \(52.75\; \mathrm{cm} .\) The speed of sound in air is ......\(m/s\)

A proton and an \(\alpha\) -particle are accelerated from rest to the same energy. The de Broglie wavelengths \(\lambda_{\mathrm{p}}\) and \(\lambda_{\alpha}\) are in the ratio,

Two rods \(A\) and \(B\) of different materials are welded together as shown in  figure.Their thermal conductivities are \(K_1\) and \(K_2\)  The thermal conductivity of the composite rod will be

Photons with energy \(5\,\, eV\) are incident on a cathode \(C\) in a photoelectric cell. The maximum energy of emitted photoelectrons is \(2\,\, e V.\) When photons of energy \(6\,\, eV\) are incident on \(C,\) no photoelectrons will reach the anode \(A,\) if the stopping potential of \(A\) relative to \(C\) is  ............ \(V\)

The rotational kinetic energy of a solid sphere of mass \(3 \;kg\) and radius \(0.2\; m\) rolling down an inclined plane of height \(7\; m\) is 

Angular width of the central maxima the Fraunhofer diffraction for \(\lambda=6000 \;\mathring A\) is \(\theta_{0} .\) When the same slit Is lluminated by another monochromatic light, the angular wildth decreases by \(30 \% .\) The wavelength of this light is.......\(\mathring A\)

A particle moving in a circle of radius \(R\) with a uniform speed takes a time \(T\) to complete one revolution. If this particle were projected with the same speed at an angle ' \(\theta\) ' to the horizontal, the maximum height attained by it equals \(4 \mathrm{R}\). The angle of projection, \(\theta\), is then given by

Select the incorrect statements with reference to Rh grouping :
A. Erythroblastosis foetalis is a condition observed having foetus with \(Rh ^{-v e}\) blood and mother with Rh \(+v e\) blood.
B. Rh antigen is observed on RBCs in the majority of human beings.
C. Before blood transfusion, Rh group should also be matched.
D. Rh incompatibility is observed when a pregnant mother is \(Rh ^{-v e}\) and the foetus is \(Rh ^{+v e}\).
E. Erythroblastosis foetalis can be avoided by administering anti-Rh antibodies to the mother immediately after the delivery of the second child.
Choose the answer from the options given below :

The correct order of strengths of the carboxylic acids is

The magnetic field on the axis of a circular loop of radius \(100\,cm\) carrying current \(I=\sqrt{2}\,A\), at point \(1\,m\) away from the centre of the loop is given by

In Young's double slit experiment the separation \(d\) between the slits is \(2\,\, mm,\) the wavelength \(\lambda\) of the light used is \(5896 Å \)  and distance \(D\) between the screen and slits is \(100\,\, cm.\) It is found that the angular width of the fringes is \(0.20^o \) . To increase the fringe angular width to \(0.21 ^o \) (with same \(\lambda\) and \(D\)) the separation between the slits needs to be changed to ......\(mm\)

Which one of the following groups of animals reproduces only by sexual means?

Match the following

(a) Inhibitor of catalytic activity	(i) Ricin
(b) Possess peptide bonds	(ii) Malonate
(c) Cell wall material in fungi	(iii) Chitin
(d) Secondary metabolite	(iv) Collagen

Choose the correct option from the following :\((a)-(b)-(c)-(d)\)