List of top Questions asked in JEE Main, KCET

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is: \\ \\

Let line L pass through the point \( (0, 1, 2) \), intersect the line \( {2 = {3 = {4 \), and be parallel to the plane \( 2x + y - 3z = 4 \). Find the distance of the point \( P(1, -9, 2) \) from line L. \\

Let the vectors \( , , \) represent three coterminous edges of a parallelepiped of volume \( V \). Then the volume of the parallelepiped, whose coterminous edges are represented by \( , + \) and \( + 2 + 3 \) is equal to: \\ \\

Find out the major products from the following reactions

Which one of the following observations is correct for the features of logarithm function to any base \(b>1\)?

The number of terms of an $AP$ is even. The sum of the odd terms is $24$ and of the even terms is $30$. The last term exceeds the first by $10\frac{1}{2}$. Then the number of terms in the series is ______.

Two thin convex lenses of focal lengths f1 and f2 are separated by a horizontal distance d (where d < f1, d < f2) and their centers are displaced by a vertical separation Δ as shown in the figure.

Taking the origin of coordinates, O at the center of the first lens, the x and y-coordinates of the focal point of this lens system, for a parallel beam of rays coming from the left, are given by

A random variable X has the following probability distribution:

If the mean of the random variable X is \(\frac{1}{3}\), then the variance is

The incorrect statement about Hall-Heroult process is :

The equation xy = 0 in three-dimensional space represents

The value of C in (0, 2) satisfying the mean value theorem for the function \(f(x)=x(x-1)^2, x∈[0,2]\) is equal to

If two primary spermatocytes and two primary oocytes undergo meiosis simultaneously, what will be the ratio of spermatozoa and ova produced at the end of the gametogenesis?

The plane containing the point (3, 2, 0) and the line \(\frac{x-3}{1}= \frac{y-6}{5}=\frac{z-4}{4}\) is

If a random variable X follows the binomial distribution with parameters n = 5, p and P (X=2) =9P (X=3), then p is equal to

A die is thrown 10 times. The probability that an odd number will come up at least once is

Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let z=4x+6y be the objective function.The minimum value of z occurs at

If lines \(\frac{x-1}{-3}=\frac{y-2}{2k}=\frac{z-3}{2}\) and \(\frac{x-1}{3k}=\frac{y-5}{1}=\frac{z-6}{-5}\) are mutually perpendicular then k is equal to

The vectors \(\overrightarrow {AB}=3\hat i+4\hat k\) and \(\overrightarrow {AC}=5\hat i-2\hat j+4\hat k\) are the sides of a △ABC. The length of the median through A is

The volume of the parallelopiped whose co-terminous edges are \(\hat j+\hat k,\hat i+\hat k\) and \(\hat i+\hat j\) is

Let \(\overrightarrow a\) and \(\overrightarrow b\) be two unit vectors and θ is the angle between them. Then \(\overrightarrow a +\overrightarrow  b\) is a unit vector if

If \(\overrightarrow a,\overrightarrow b,\overrightarrow c\) are three non-coplanar vectors and p,q,r are vectors defined by
\(\overrightarrow p=\frac{\overrightarrow a\times \overrightarrow c}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\) ,\(\overrightarrow q=\frac{\overrightarrow c\times \overrightarrow a}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\),\(\overrightarrow r=\frac{\overrightarrow a\times \overrightarrow b}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\)then
\((\overrightarrow a+\overrightarrow b).\overrightarrow p+(\overrightarrow b+\overrightarrow c).\overrightarrow q+(\overrightarrow c+\overrightarrow a).\overrightarrow r\) is

The distance between the two planes 2x + 3y + 4z = 4 and 4x + 6y +8z = 12 is

The sine of the angle between the straight line \(\frac{x-2}{3}=\frac{y-3}{4}=\frac{4-z}{-5}\) are the plane 2x-2y+z=5 is

The area of the region bounded by the line y = 3x and the curve y=x² in sq. units is