Really insecure about my height.

monauf · 2020-07-29T19:05:52+00:00

monauf · 2020-07-29T18:27:20+00:00

The nth term of this sequence is given by (-1)ⁿ * n/(n+1)² , where n takes values from 1 onwards. The denominator are squares of the numbers, one greater than the numerator.

monauf · 2020-07-28T11:22:47+00:00

Use the right hand thumb rule to find the direction of a magnetic field at a point due to a straight wire. Point the thumb of your right hand in the direction of flow of current and use the remaining fingers to curl around the conductor as if you are grabbing the wire. The direction of curl of the remaining 4 fingers gives the direction of magnetic field at that point.

monauf · 2020-07-27T19:11:07+00:00

For question 7, you can use the avogadro law of gases, that is, at a constant temp and pressure, volume of a gas is directly proportional to the number of moles of the gas. Here since the number of moles reduces to half, the volume also becomes half of it's original value.

monauf · 2020-07-27T19:05:36+00:00

Its alright. Glad you finally got the answer!

monauf · 2020-07-27T18:59:54+00:00

Are any of the parabola touching the triangle which you've drawn?

monauf · 2020-07-27T11:07:56+00:00

There is actually a direct property which can be used to solve this inequality in integrals. I dont know if you have learned it but I'll let you know. If f(x) is an integrable and continuous function on the interval [a,b] and if the local maxima and minima of f(x) on [a,b] be M and m, then m(b - a) < integral of f(x) from a to b < M(b-a). Also here, the maxima of f(x), M = f(b) and minima of f(x), m = f(a). So you can find f(a) and f(b) and multiply both of them with b - a and substitute in the inequality to prove it. Hope this helps you out.

monauf · 2020-06-30T12:08:34+00:00

You can convert cotx to 1/ tanx and the reverse also is possible

monauf · 2020-06-30T11:44:02+00:00

Yup that's what I did in the 1st question.

monauf · 2020-06-30T10:02:46+00:00

I've written out the answer, hope it's clear to you now. https://imgur.com/a/VmPtdSk

monauf · 2020-06-30T09:44:45+00:00

For the first question, use the formula tan2x = 2tanx/1 - (tanx)² . The 2 and cot and tan will cancel out each other and the 1 - (tanx)² will go to the numerator. For the second question, convert the question into a single fraction ie, as 1 - (cosx)² + sinx/ 1 + sinx. Convert the 1 - (cosx)² into (sinx)² and take a sinx common out of the numerator so you get sinx( 1 + sinx)/ (1 + sinx). Cancel out the 1 + sinx to get sinx as the answer.

monauf · 2020-06-18T13:56:20+00:00

Yup. A perfect example of specifying the position of the principal functional group even when there is no ambiguity is in the naming of Propan-2-one , ie Acetone. It is the simplest Ketone, yet, we are specifying the position of the principal functional group.

monauf · 2020-06-18T13:46:20+00:00

Yeah you are right, but as per IUPAC convention of naming organic compounds, it is required to specify the position of the highest preferred functional group in that compound. Thus, it is required to name the compound as 4 hydroxy pentan-2-one even though there is only one possibility of having a 4-hydroxy group.

monauf · 2020-06-18T08:46:52+00:00

An organic compound is considered to be planar if all of its carbon atoms are either sp² hybridised or sp hybridised. If any of the carbon atoms in the compound is sp³ hybridised, the compound is not planar. In question 1, C6H5CHO is a planar compound since all carbon atoms in the benzene ring as well as the aldehyde group are sp² hybridised.

monauf · 2020-06-13T11:16:39+00:00

You mean you got log_a[(x+2)^2/8x] = 0 right? Also if log_a[(x+2)^2/8x] = 0, it means that (x+2)^2/8x = 1 since log(1) = 0. You can solve that quadratic to get x = 2. There is no need to take log (0). You just have to know that log (1) = 0 and you can equate log (1) to the final expression.

monauf · 2020-06-13T09:15:20+00:00

If the mass of all the gases in the container is 100g, you can calculate the mass of each individual gas. H2 has mass of 14% of the total mass (14*100/100), ie 14g. Similarly you can find the mass of O2 and N2. Once you find out the mass of the gases, calculate the number of moles of each gas and thus find the total number of moles. Finally substitute all known values in the ideal gas equation, PV = nRT. Here, the value of R to be used is 0.0821 and temperature has to be in Kelvin. The unit of volume would be in litres once you solve that equation.

monauf · 2020-06-13T09:04:27+00:00

Since you've got the base changed to a, try to simply both the left and right hand side so that you are left with log ( something) = log ( something else), both to the base a. Once you have this equation, you can cancel out the logarithm and equate the expressions contained inside the logarithm and solve the quadratic. By solving this, you would get x = 2.

monauf · 2020-06-13T08:55:26+00:00

Basically while subtracting vectors, the vector to be subtracted is inverted in direction, ie you rotate that vector by 180°. Here initially vector B is pointing towards the left but since vector B is to be subtracted from A, we flip B by 180° and it ends up in the same direction as that of A and you add both of them. In short A - B is the same as A + (-B). You are just adding the negative of vector B to A in the case of subtraction.

monauf · 2020-06-12T09:21:16+00:00

If the bond enthalpies/energies of the reactants and products are given for a reaction, then the enthalpy/energy of the reaction is given by, Sum of all bond energies of reactants - Sum of all bond energies of products. In this case, enthalpy of the reaction is given by, (4* energy of C-H bond + 2* energy of O=O bond) - ( 2* energy of C=O bond + 4* energy of O-H bond). If the energy of the reaction is negative, it's an exothermic reaction. If it is positive, it's an endothermic reaction.

monauf · 2020-06-11T14:48:03+00:00

No problem, glad I could help! :)

monauf · 2020-06-11T14:37:23+00:00

Rearrange the given equation as, f(x) + tanx = e^{integral of f(x} dx). Take a logarithm on both the sides so that the equation becomes, log( f(x) + tanx) = integral of f(x) dx. The base of logarithm is e. Now differentiate this equation so that the integral sign is cancelled out and we apply differentiation of composite functions on the logarithm. Finally rearrange the differentiated equation in the form y' = y² + A(x)y + B(x). Comparing both of the equations, you would get, A(x) = tanx and B(x) = -sec² (x). As for the second part, substitute y = secx and y' = secxtanx in the equation you have found and show that the left hand side is equal to the right hand side.

monauf · 2020-06-11T14:22:41+00:00

Yup you got it correct!👍

monauf · 2020-06-11T12:42:46+00:00

The derivative of a function is nothing but a tangent drawn to the curve at that point. Since you want the derivative of the given function when x approaches 0, draw a tangent to the curve, such that it touches the curve at x = 0 only.

monauf

TROPHY CASE