List of top Mathematics Questions asked in KCET

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)(0, 2), (3, 0), (6, 0), (6, 8) and (0,5)(0, 5). Let z=4x+6yz = 4x + 6y be the objective function. The minimum value of zz occurs at:
If a random variable XX follows the binomial distribution with parameters n=5n = 5, pp, and P(X=2)=9P(X=3)P(X = 2) = 9P(X = 3), then pp is equal to:
A random variable XX has the following probability distribution: X012P(X)2536k136 \begin{array}{|c|c|c|c|} \hline X & 0 & 1 & 2 \\ \hline P(X) & \frac{25}{36} & k & \frac{1}{36} \\ \hline \end{array} If the mean of the random variable XX is 13\frac{1}{3}, then the variance is:
The plane containing the point (3,2,0)(3, 2, 0) and the line x−31=y−65=z−44\frac{x - 3}{1} = \frac{y - 6}{5} = \frac{z - 4}{4} is

The sine of the angle between the straight line x−23=y−34=4−z5\frac{x - 2}{3} = \frac{y - 3}{4} = \frac{4-z}{5} and the plane 2x−2y+z=52x - 2y + z = 5 is:

The equation xy=0xy = 0 in three-dimensional space represents:
The distance between the two planes 2x+3y+4z=42x + 3y + 4z = 4 and 4x+6y+8z=124x + 6y + 8z = 12 is:
If lines x−1−3=y−22k=z−32\frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2} and x−13k=y−51=z−6−5\frac{x - 1}{3k} = \frac{y - 5}{1} = \frac{z - 6}{-5} are mutually perpendicular, then kk is equal to:
If a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} are three non-coplanar vectors and p⃗,q⃗,r⃗\vec{p}, \vec{q}, \vec{r} are vectors defined by:}\\ p⃗=a⃗×c⃗[a⃗ b⃗ c⃗],q⃗=c⃗×b⃗[a⃗ b⃗ c⃗],r⃗=b⃗×a⃗[a⃗ b⃗ c⃗], \vec{p} = \frac{\vec{a} \times \vec{c}}{[\vec{a} \, \vec{b} \, \vec{c}]}, \quad \vec{q} = \frac{\vec{c} \times \vec{b}}{[\vec{a} \, \vec{b} \, \vec{c}]}, \quad \vec{r} = \frac{\vec{b} \times \vec{a}}{[\vec{a} \, \vec{b} \, \vec{c}]}, then (i⃗+b⃗)⋅p⃗+(b⃗+c⃗)⋅q⃗+(c⃗+a⃗)⋅r⃗(\vec{i} + \vec{b}) \cdot \vec{p} + (\vec{b} + \vec{c}) \cdot \vec{q} + (\vec{c} + \vec{a}) \cdot \vec{r} is:
Let a⃗\vec{a} and b⃗\vec{b} be two unit vectors and θ\theta is the angle between them. Then a⃗+b⃗\vec{a} + \vec{b} is a unit vector if:
The vectors AB→=3i^+4k^\overrightarrow{AB} = 3\hat{i} + 4\hat{k} and AC→=5i^−2j^+4k^\overrightarrow{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k} are the sides of a △ABC\triangle ABC. The length of the median through AA is:
The volume of the parallelepiped whose co-terminous edges are i^+j^,i^+k^,i^+j^\hat{i} + \hat{j}, \hat{i} + \hat{k}, \hat{i} + \hat{j} is:
The family of curves whose xx and yy intercepts of a tangent at any point are respectively double the xx and yy coordinates of that point is:
The solution of edydx=x+1, y(0)=3e^{\frac{dy}{dx}} = x + 1, \, y(0) = 3 is:
The area of the region bounded by the line y=xy = x and the curve y=x3y = x^3 is:
The area of the region bounded by the line y=3xy = 3x and the curve y=x3y = x^3 in sq. units is:
lim⁡n→∞(nn2+12+nn2+22+⋯+nn2+32+⋯+15n)=\lim_{n \to \infty} \left(\frac{n}{n^2 + 1^2} + \frac{n}{n^2 + 2^2} + \dots + \frac{n}{n^2 + 3^2 + \dots + \frac{1}{5n}} \right) =
∫15(∣x−3∣+∣1−x∣) dx=\int_{1}^{5} \left(|x - 3| + |1 - x|\right) \, dx =
∫sin⁡5x2sin⁡x2 dx=\int \frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}} \, dx =
∫1x(6(log⁡x)2+7log⁡x+2) dx=\int \frac{1}{x \left(6(\log x)^2 + 7\log x + 2\right)} \, dx =
∫−ππ(1−x2)sin⁡xcos⁡2x dx=\int_{-\pi}^\pi (1 - x^2)\sin x \cos^2 x \, dx =
∫sin⁡x3+4cos⁡2x dx=\int \frac{\sin x}{3 + 4\cos^2 x} \, dx =
If f(x)=xex1−xf(x) = x e^{x^{1-x}}, then f(x)f(x) is:
The maximum volume of the right circular cone with slant height 66 units is: