List of top Questions asked in KCET, WBJEE

If \(\alpha, \beta\) are the roots of the equation \(x^{2}-px+q=0\) and \(\alpha>0\), \(\beta>0\), then \[ \alpha^{\frac{1}{4}}+\beta^{\frac{1}{4}}=(p+6\sqrt{q}+4q^{\frac{1}{4}}\sqrt{p+2\sqrt{q}})^{\kappa}, \] where \(\kappa\) is:

The velocity of a particle moving along x-axis is given as \( V = x^2 - 5x + 4 \) (in m/s) where x denotes the x-coordinate of the particle in metres. The magnitude of the acceleration of the particle when the velocity of the particle zero is

The number of chain isomers possible for the hydrocarbon with molecular formula \( \text{C}_5\text{H}_{12} \) is

An electron falls through a distance 1.5 cm in a uniform electric field of magnitude 2.0 \(\times\) 10\(^4\) N/C from rest. The time taken to cover this distance in second is \textunderscore\textunderscore\textunderscore\textunderscore\textunderscore.
(e = 1.6 \(\times\) 10\(^{-19}\) C, m\(_e\) = 9.11 \(\times\) 10\(^{-31}\) kg)

From the given information, select the suitable law of chemical combination:

The compound with molecular formula C\(_{20}\)H\(_{42}\) is

A woman, unable to conceive after many years of regular unprotected coitus, went to a specialized clinic. On complete examination, the woman was found to be normal, while the male partner was diagnosed with Infertility and was unable to inseminate the female due to low sperm count. Suggest the appropriate Assisted Reproductive Technology (ART).

The ends $A, B$ of a straight line segment of constant length $c$ slide upon the fixed rectangular axes $OX, OY$ respectively. If the rectangle $OAPB$ is completed, then the locus of the foot of the perpendicular drawn from $P$ to $AB$ is:

The true set of values of \(K\) for which \(\sin^{-1}\left(\frac{1}{1+\sin^{2}x}\right)=\frac{K\pi}{6}\) may have a solution is:

Bohr's second postulate implies quantisation of

A chromosome with an extremely short and a very long arm is called ________.

Which of the following is the most stable complex?

Cellulose is an important structural component in plants which is made up of

A parallel plate capacitor has a uniform electric field 'E' in the space between the plates. If the distance between the plates is 'd' and area of each plate is 'A', the energy stored in the capacitor is

On the set \(\mathbb{R}\) of real numbers the relation \(\rho\), defined by \(x\rho y\) \((x,y\in\mathbb{R})\) iff:

A car covers the first half of the distance between two places at 40 km/h and another half at 50 km/h. The average speed of the car is

For a 1st order change R \(\rightarrow\) P, the concentration of Reactant R changes from 0.1 M to 0.025 M in 40 minutes. The rate of reaction when the concentration of R is 0.01 M is________.

Pollen grains are well preserved as fossils because of the presence of ________.

Consider the following statements:
Statement I : If $A$ is a non-singular matrix, then $A^{-1}$ exists.
Statement II : If $A$ and $B$ are symmetric matrices of same order, then $(AB - BA)$ is a skew symmetric matrix.
Choose the correct option.

The correct IUPAC name of CH\(_3\) - C(CH\(_3\))\(_{2}\) - O - C\(_2\)H\(_5\) is

In Linear Programming Problem (LPP), the objective function $Z = ax + by$ has the same maximum value at two corner points. The number of points at which $Z_{max}$ occurs is

Which of the following plot(s) is/are correct representation(s) of Boyle's Law?