List of top Questions asked in KCET

The natural reservoir of phosphorus is
Which one of the following observations is correct for the features of logarithm function to any base \(b>1\)?
A random variable X has the following probability distribution:
\(X\)012
\(P(X)\)\(\frac{25}{36}\)k\(\frac{1}{36}\)
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?
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
The plane containing the point (3, 2, 0) and the line \(\frac{x-3}{1}= \frac{y-6}{5}=\frac{z-4}{4}\) 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
A die is thrown 10 times. The probability that an odd number will come up at least once is
The distance between the two planes 2x + 3y + 4z = 4 and 4x + 6y +8z = 12 is
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
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 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 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
\(∫\frac{sin\frac{5x}{2'}}{sin\frac{x}{2}}dx=\)
The area of the region bounded by the line y = 3x and the curve y=x2 in sq. units is
The area of the region bounded by the line y = x and the curve y=x3 is
The solution of \(e^{\frac{dy}{dx}} = x+1,y(0) =3\) is
\(∫\frac{1}{x[6(logx)^2+7logx+2]}dx=\)
\(\int\limits_1^5(|x-3|+|1-x|)dx\)=
\(\lim\limits_{n \to \infty} (\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\frac{n}{n^2+3^2}+…+\frac{1}{5n})=\)