If 525 = (10 + K) (mod 7) where \(K \in N\), then the least value of K is:

Area of the region bounded by \(y=x^2\) and the line \(y=16\) is

In a 500 m race, the ratio of speeds of two participants, A and B, is 4 : 5 respectively.
If A has a start of 180 m, then the distance by which A wins is :

Consider the following data:

Year(x)	2010	2011	2012	2013	2014
Sale(in crore Rs.)(y)	9	18	21	29	38

A straight line trend by the method of least squares is:

The value of \(\lambda\), so that the lines \(\frac{1-x}{3}=\frac{7 y-14}{2 \lambda}=\frac{z-3}{2}\) and \(\frac{7-7 x}{3 \lambda}=\frac{y-5}{1}=\frac{6-z}{5}\) are perpendicular is:

Mr. X purchased a house for ₹ 7,00,000 and made a down payment of ₹ 1,50,000 .
He repays the balance in 25 years by equal monthly installments as \(9 \%\) per annum compounded monthly. The equated monthly installment (EMM) is :
[Given that \((1.0075)^{-300}=0.106\) ]

If \(A\) is a square matrix of order 3 such that \(|A|=2\), then \(\operatorname{adj}(\operatorname{adj} A)\) is :

When a ferromagnetic substance is placed in a magnetic field, it becomes a permanent magnet because:

The sequencing of fragments using automated DNA sequencers in HGP, worked on the principle of the method that was developed by:

A steady current flows in a metallic conductor of non-uniform cross-section. The quantity that is constant along the length is

The properties which depend on the number of solute particles irrespective of their nature relative to the total number of particles in the solution are called colligative properties. These are relative lowering of vapour pressure of the solvent, depression of freesing point of the solvent, elevation of boiling point of the solvent and osmotic pressure of the solution. All of these properties help in calculating the observed molar mass of the solute.
Determination of osmotic pressure is considered best for the determination of molecular mass of the solute.
The binary liquid mixtures which show negative deviation from Raoult's law are :
(A) n-hexane and n-heptone
(B) phenol and acetone
(C) ethanol and acetone
(D) chloroform and acetone
(E) benzene and toluene
Choose the correct answer from the options given below :

Elements of group-15, 16 and 17 form compounds with hydrogen with general formula MH3, \(H2M\) and HX (called hydrogen halides). Stability of these hydrides, along with M-H bond strength and basic nature decreases down the group. Boiling point of these hydrides mainly depends on the strength of their inter molecular forces.
Which of the following is most basic among the following hydrides of group 16?

Zeolite can be used to soften hard water when :