If the radius of the earth were to shrink by $1\%$ and its mass remained the same,the acceleration due to gravity on the earth's surface would

Two lenses in contact made of materials with dispersive powers in the ratio $2 : 1$,behave as an achromatic convex lens of focal length $10\, cm$. The individual focal lengths of the lenses are

In the visible region,the dispersive powers and the mean angular deviations for crown and flint glass prisms are $\omega, \omega'$ and $d, d'$ respectively. The condition for getting deviation without dispersion when the two prisms are combined is

If the angle between the pair of lines $x^2+2 \sqrt{2} x y+k y^2=0, k>0$ is $45^{\circ}$,then the area (in square units) of the triangle formed by the pair of bisectors of the angles between these lines and the line $x+2 y+1=0$ is

For the reaction $CH_{4(g)} + 2O_{2(g)} \rightleftharpoons CO_{2(g)} + 2H_2O_{(l)} \, \Delta H_r = -170.8 \, kJ \, mol^{-1}$,which of the following statements is not true?

Let $2 \sin^2 x + 3 \sin x - 2 > 0$ and $x^2 - x - 2 < 0$. ($x$ is measured in radians). The $x$ lies in the interval