List of top Mathematics Questions asked in KCET

If the middle term of the $A.P$ is $300$ then the sum of its first $51$ terms is

The angle between the lines whose direction cosines are $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)$ and $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)$ is

If the area of the Ellipse is $\frac{x^{2}}{25}+\frac{y^{2}}{\lambda^{2}}=1$ is $20 \pi$ square units, then $\lambda$ is

A vector $\vec{a}$ makes equal acute angles on the coordinate axis. Then the projection of vector $\vec{ b }=5 \hat{ i }+7 \hat{ j }-\hat{ k }$ on $\vec{ a }$ is

The number of solutions of $\frac{d y}{d x}=\frac{y+1}{x-1}$ when $y(1)=2$ is

Solution of Differential Equation $xdy - ydx = 0$ represents

If $\vec{a} \cdot \vec{b}=0$ and $\vec{a}+\vec{b}$ makes an angle $60^{\circ}$ with $\vec{a} $ then

If the area of the parallelogram with $\vec{a}$ and $\vec{b}$ as two adjacent sides is $15$ s units then the area of the parallelogram having $3 \vec{a}+2 \vec{b}$ and $\vec{a}+3 \vec{b}$ as two adjacent sides in s units is

If a plane meets the coordinate axes at $A, B$ and $C$ in such a way that the centroid of triangle $ABC$ is at the point $(1,2,3)$ then the equation of the plane is

If the side of a cube is increased by 5%, then the surface area of a cube is increased by

If $|tan \,A + \cot \,A = 2$, then the value of $\tan^4 A + \cot^ 4 A = $

The number of terms in the expansion of (x + y + z)¹⁰ is

The value of
¹⁶C₉ + ¹⁶C₁₀- ¹⁶C₆ - ¹⁶C₇ is

If z = x +iy then the equation |z + 1| = |z - 1| represents

If P(n) : 2ⁿ < n!
Then the smallest positive integer for which P(n) is true if

If tan A + cot A = 2, then the value of tan⁴ A + cot⁴ A =

The value of sin² 51° + sin² 39° is

If n(A) = 2 and total number of possible relations from Set A to set B is 1024, then n(B) is

If A = {1, 2, 3, 4, 5, 6}, then the number of subsets of A which contain atleast two elements is

Events E₁ and E₂ form a partition of the sample space S. A is any event that P(E₁) = P(E₂) = \(\frac{1}{2}\), P(E₂/A) = \(\frac{1}{2}\) and P(A/E₂) = \(\frac{2}{3}\), then P(E₁/A) is

The probability of solving a problem by three persons A, B and C independently is \(\frac{1}{2}\), \(\frac{1}{4}\) and \(\frac{1}{3}\) respectively. Then the probability of the problem is solved by any two of them is

A die is thrown 10 times, the probability that an odd number will come up atleast one time is

Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let z = px + qy, where p, q > 0. Condition on p and q so that the minimum of z occurs at (3, 0) and (1, 1) is

The feasible region of an LPP is shown in the figure. If Z = 11x + 7y then the maximum value of Z occurs at

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