Which of the following statements has the truth value T ?
A: cube roots of unity are in Geometric progression and their sum is 1
B: \(4+7>10\) iff \(2+8 < 10\)
C: \(\exists x \in \mathbb{N}\) such that \(x^2-3 x+2=0\) and \(\exists \mathrm{n} \in \mathbb{N}\) such that n is an odd number
D : \(3+\mathrm{i}\) is a complex number or \(\sqrt{2}+\sqrt{3}=\sqrt{5}\)

If \(y=3 \cos (\log x)+4 \sin (\log x)\), then \(x^2 y_2+x y_1=\)

If \(\lim _{x \rightarrow \infty}\left(\frac{x^2+x+1}{x+1}-a x-b\right)=4\) then

The general solution of the differential equation of all circles having centre at $A\left(-1,2\right)$ is ________

The value of \(\cos ^{-1}\left(\cos \frac{8 \pi}{3}\right)\) is

Let K be the set of all real values of \(x\), where the function \(\mathrm{f}(x)=\sin |x|-|x|+2(x-\pi) \cos |x|\) is not differentiable. Then the set K is

If \(\bar{a}=(2 \hat{i}+2 \hat{j}+3 \hat{k}), \bar{b}=(-\hat{i}+2 \hat{j}+\hat{k}) \quad\) and \(\overline{\mathrm{c}}=(3 \hat{\mathrm{i}}+\hat{\mathrm{j}})\) such that \((\overline{\mathrm{a}}+\lambda \overline{\mathrm{b}})\) is perpendicular to \(\bar{c}\), then the value of \(\lambda\) is

The ionic charges on chromate ion and dichromate ion respectively is

Which of the following pair of compounds does not demonstrate the law of multiple proportion?

Which from following equations is used to express the angular momentum of an electron in a stationary state?

Select the correct statement/s regarding blood groups in human.
i. Some genetically determined blood group systems are ABO, Rh, Duffy, Lewis, Bombay blood group etc.
ii. Three types of agglutinogens are present on surface of human RBCs such as A, B and D.
iii. Individuals with blood group "AB Rh +ve" have A, B and D antigens on the surface of their RBCs and both antibodies 'a' and 'b' in their plasma.
iv. Haemolytic disease of Newborn occurs when mother with Rh-ve blood group conceives Rh -ve foetus.
v. Individuals with 'AB' blood group are called universal donors while those with 'O' blood group are called universal acceptors, with reference to blood transfusion.

Which of the following molecules has zero dipole moment?

In a series $LCR$ circuit $R=300\mathrm{\Omega },L=0.9\mathrm{H},C=2\mathrm{\mu }\mathrm{F},\omega =1000\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}.$ The impedance of the circuitis