The solution set of the system of equations, is

If x & y are real numbers and  then ' y ' cannot take the value(s) :

In this question, we have to which value y cannot give. Here ‘y’ is always non-negative, so it never given the negative value.

Statement 1:In the process of drying dishes with a towel, the wetting agent is the dish and the drying agent is the towel

Statement 2:The wetting agent gets wet during the process

Which of the following are correct ?

In this question, we have to find which option is correct. Check every option which one is satisfy. Use the properties of the logarithmic which going to help to get the answer.

Statement 1:The reaction between  and  occurs in an acidic medium 
Statement 2: is reduced to  in acidic medium

Number of cyphers after decimal before a significant figure comes in  is

In this question, we have to find the number of cyphers. We need to remember that the cypher number can be found from the logarithmic calculation but to find the actual value or to visualize it we need to remove the logarithm. Here, log₁₀5 = 0.6990 and log₁₀3 = 0.4770.

The value of p for which both the roots of the quadratic equation,  are less than 2 lies in :

In this question, we have to find where the p lies. Here, we use discriminant, which is . if D > 0 and D = 0 then real solution but if D < 0 then imaginary solution. Here we also us Factorization of quadratic equations.

If  where  determine b –

Just like we can change the base b for the exponential function, we can also change the base b for the logarithmic function. The logarithm with base b is defined so that 

Statement 1:The two Fe atoms in  have different oxidation numbers
Statement 2:  ions decolourise   solution

, where  and  is

In this question, we have to find the . Here Solve first B. In B, rationalize it means multiply it denominator by sign change in both numerator and denominator

Statement 1:The equivalence point refers the condition where equivalents of one species react with same number of equivalent of other species.
Statement 2:The end point of titration is exactly equal to equivalence point

If  and  are the roots of the equation  then the value of  equals

Statement 1:Iodimetric titration are redox titrations.
Statement 2:The iodine solution acts as an oxidant to reduce the reductant 

Statement 1:Diisopropyl ketone on reaction with isopropyl magnesium bromide followed by hydrolysis gives alcohol
Statement 2:Grignard reagent acts as a reducing agent

The first noble gas compound obtained was:

Given that  and  then value of  equals –

These four basic properties all follow directly from the fact that logs are exponents. 
log_b(xy) = log_bx + log_by.
log_b(x/y) = log_bx - log_by.
log_b(xⁿ) = n log_bx.
log_bx = log_ax / log_ab.