List of practice Questions

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
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 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
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 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
\(∫\frac{1}{x[6(logx)^2+7logx+2]}dx=\)
\(∫\frac{sin\frac{5x}{2'}}{sin\frac{x}{2}}dx=\)
\(\int\limits_1^5(|x-3|+|1-x|)dx\)=
\(\lim\limits_{n \to \infty} (\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\frac{n}{n^2+3^2}+…+\frac{1}{5n})=\)
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
\(\frac{d}{dx}[cos^2(cot^{-1}\sqrt{\frac{2+x}{2-x}})]\) is
The function \(x^x; x > 0\) is strictly increasing at
If \(f(x) = x e^{x(1-x)}\) then f(x) is
\(∫\frac{sinx}{3+4cos^2x}dx=\)
\(\int\limits_{-π}^π(1-x^2)sinx.cos^2xdx=\)
Let \(f(x)=\begin{vmatrix}cosx &x& 1\\ 2sinx &x& 2x \\ sinx& x& x\end{vmatrix}\).Then \(\lim\limits_{x \to 0}\frac{f(x)}{x^2}\)=
The function f(x) = |cos x| is
Let the function satisfy the equation f (x + y) = f(x)f(y) for all x, y ∈ R, where f (0)≠0. If f (5) = 3 and f'(0)=2, then f'(5) is