The function \(f(x)=-\frac{3}{4} x^4-8 x^3-\frac{45}{2} x^2+163\) has a local maxima at

If a person rides his motorbike \(x km\) at 30 km per hour, he has to spend ₹ 3 per kilometer on petrol; if he rides \(y km\) at a faster speed of 40 km per hour, the petrol cost increases to ₹ 4 per kilometer. If he has ₹ 100 to spend on petrol and wishes to find the maximum distance he can travel within one hour, then linear programming problem (LPP) formulation is:

A function \(f: R \rightarrow R\) defined by \(f(x)=\frac{x}{x^2+1}\) is (where \(R\) is the set of real numbers) :

The region represented by the system of inequalities \(x \geq 0 ; y \geq 0\),
\(2 x+y \geq 8\) and \(x+2 y \geq 10\) is :

The values of \(x\) which satisfy the inequality \(|x-3|<2\) lie in :

If the matrix \(\left[\begin{array}{ccc}x-y & 1 & -2 \\ 2 x-y & 0 & 3 \\ 2 & -3 & 0\end{array}\right]\) is skew-symmetric, then the values of \(x\) and \(y\) are respectively:

The solution of the differential equation \((x+1) \frac{d y}{d x}+1-2 e^{-y}=0 ; y(0)=0\) is

Read the passage carefully and answer the Questions
In the formation of coordination complexes, if the inner \(d\) orbital \((n-1) d\) is used in hybridisation, the complex, is called an inner orbital or low spin or spin paired complex. And if it uses outer \(d\) orbital ( \(n d\) ) in hybridisation (like \(s p^3 d^2\) ), it is called outer orbital or high spin or spin free complex. The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the complex. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting. For coordination complexes, the magnetic moment is determined by the number of unpaired electrons and is calculated by using the 'spin-only' formula, \(\mu=\sqrt{n(n+2)}\) where \(n\) is the number of unpaired electrons and \(\mu\) is the magnetic moment in units of Bohr magneton (BM). The coordination compounds are of great importance. These compounds are widely present in the mineral, plant and animal worlds and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine.
Fe(II) octahedral complexes can show different 'spin only' magnetic moments for arrangements in the presence of weak and strong ligands. The 'spin only' magnetic moments of these complexes with weak and strong ligands, respectively, are

Which of the following pair of contrasting traits was not studied by Mendel ?

Read the passage carefully and answer the questions based on the passage:
Pollen pistil interaction involves all events from the landing of pollen grains on the stigma until the pollen tube enters the embryo sac (when the pollen is compatible). When a pollen tube grows through the style and enters into the ovules, it finally discharges two male gametes in one of the synergids. Syngamy and triple fusion are two fusion events occur in angiosperms. Thus, angiosperms exhibit double fertilization. The products of these fusions are the diploid zygote and triploid primary endosperm nucleus. Zygote develops into embryo and primary endosperm cell forms the endosperm tissue. The developing embryo passes through different stages before maturation.
With reference to reproduction in flowering plants, which one of the following is incorrect?

Match List-I with List-II

List-I (Terms)	List-II (Features)
(A) Natality	(I) Exit of individuals
(B) Mortality	(II) Entry of individuals
(C) Immigration	(III) Death rate
(D) Emigration	(IV) Birth rate

Choose the correct answer from the options given below:

Meiotic division taking place during oogenesis is an unequal division resulting in the formation of a:

A \( 14.0 \, \mu\text{F} \) capacitor is connected to a 220 V, 50 Hz source. The value of peak current in the circuit is (Given: \( \pi = \frac{22}{7} \) and \( \sqrt{2} = 1.414 \)):