.A rod of glass ( $mu$ = 1.5) and of square cross section is bent into the shape shown in the figure. A parallel beam of light falls on the plane flat surface A as shown in the figure. If d is the width of a side and R is the radius of circular arc then for what maximum value of $fraction numerator d over denominator R end fraction$ light entering the glass slab through surface A emerges from the glass through B

A prism having an apex angle $4 to the power of ring operator end exponent$ and refraction index 1.5 is located in front of a vertical plane mirror as shown in figure. Through what total angle is the ray deviated after reflection from the mirror

In steel the young's modulus and the strain at the breaking point are $2 cross times 10 to the power of 11 straight N over straight m squared$ and 0.15 respectively the stress at the breaking point for steel is therefore

Hail stones fall from certain height If only 2% of the mass of the hail stone melt on reaching the ground,, the height from which they fall is ( g = 10 ms^-2, L = 80 cal/gm and J = 4.2J/cal)

maths-

$Sin invisible function application 4530 to the power of ring operator$ =

maths-General

A fish rising vertically up towards the surface of water with speed 3 $m s to the power of negative 1 end exponent$ observes a bird diving vertically down towards it with speed 9 $m s to the power of negative 1 end exponent$ . The actual velocity of bird is

The image of point P when viewed from top of the slabs will be

A cube of side 2 m is placed in front of a concave mirror focal length 1m with its face P at a distance of 3 m and face Q at a distance of 5 m from the mirror. The distance between the images of face P and Q and height of images of P and Q are

Two transparent slabs have the same thickness as shown. One is made of material A of refractive index 1.5. The other is made of two materials B and C with thickness in the ratio 1 : 2. The refractive index of C is 1.6. If a monochromatic parallel beam passing through the slabs has the same number of waves inside both, the refractive index of B is

Maths-

$L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 minus cos space m x over denominator 1 minus cos space n x end fraction comma n not equal to 0$

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means $fraction numerator 0 over denominator 0 space end fraction o r space fraction numerator plus-or-minus infinity over denominator plus-or-minus infinity end fraction.$

$L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 minus cos space m x over denominator 1 minus cos space n x end fraction comma n not equal to 0$

Maths-General

maths-

If $log subscript 10 space 100 minus 2 comma log subscript 10 space 101 minus 2.004 comma log subscript 10 space 102 equals 2.0086 comma log subscript 10 space 103 equals 2.0128$ , then $integral subscript 100 superscript 103 log subscript 10 space x d x$ by trapezoidal rule is

maths-General

Maths-

$Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 minus cos space 2 m x over denominator sin squared space n x end fraction left parenthesis m comma n element of Z right parenthesis$

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means $fraction numerator 0 over denominator 0 space end fraction space o r space fraction numerator plus-or-minus infinity over denominator plus-or-minus infinity end fraction.$

$Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 minus cos space 2 m x over denominator sin squared space n x end fraction left parenthesis m comma n element of Z right parenthesis$

Maths-General

A wire of length L and radius r is rigidly fixed at one end on stretching the other end of the wire a force F the increase in its lengths is L. If another wire of same material but of length 2 L and radius 2r, is stretched with a force of 2F, the increase in its length will he

Consider the situation shown in figure. Water $open parentheses mu subscript w end subscript equals fraction numerator 4 over denominator 3 end fraction close parentheses$ is filled in a breaker upto a height of 10 cm. A plane mirror fixed at a height of 5 cm from the surface of water. Distance of image from the mirror after reflection from it of an object O at the bottom of the beaker is

One side of a glass slab is silvered as shown. A ray of light is incident on the other side at angle of incidence $i equals 4 5 to the power of o end exponent$ . Refractive index of glass is given as 1.5. The deviation of the ray of light from its initial path when it comes out of the slab is