List of top Mathematics Questions asked in KCET

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

The distance of the point (1, 2, -4) from the line \(\frac{x-3}{2}=\frac{y-3}{3}=\frac{z+5}{6}\) is

If a line makes an angle of \(\frac{\pi}{3}\) with each of x and y-axis, then the acute angle made by z-axis is

The point (1, -3, 4) lies in the octant

If \(|\vec{a}\times\vec{b}|+|\vec{a}.\vec{b}|^2\)=144 and \(|\vec{a}|\) = 6, then \(|\vec{b}|\) is equal to

If the vectors \(2\hat{i}-3\hat{j}+4\hat{k},2\hat{i}+\hat{j}-\hat{k}\) and \(\lambda\hat{i}-\hat{j}+2\hat{k}\) are coplanar, then the value of λ is

If \(\vec{a}\) and \(\vec{b}\) are unit vectors and θ is the angle between \(\vec{a}\) and \(\vec{b}\), then sin\(\frac{θ}{2}\) is

The two vectors \(\hat{i}+\hat{j}+\hat{k}\) and \(\hat{i}+3\hat{j}+5\hat{k}\) represent the two sides \(\vec{AB}\) and \(\vec{AC}\) respectively of a ΔABC. The length of the median through A is

The curve passing through the point (1, 2) given that the slope of the tangent at any point (x, y) is \(\frac{2x}{y}\) represents

The general solution of the differential equation x²dy - 2xydx = x⁴cosx dx is

The order of the differential equation obtained by eliminating arbitrary constants in the family of curves c₁y = (c₂ + c₃)e^x+c₄ is

The area of the region bounded by the line y = 2x + 1, x-axis and the ordinates x = -1 and x = 1 is