List of top Mathematics Questions asked in KCET

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

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

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

The value of sin² 51° + sin² 39° is

The value of $\sin^2 51^\circ + \sin^2 39^\circ$ is

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

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

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

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

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

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

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

If A and B are two events such that P(A) = \(\frac{1}{3}\), P(B) = \(\frac{1}{2}\) and P(A ∩ B) = \(\frac{1}{6}\), then P(A'/B) 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 distance of the point (1, 2, -4) from the line \(\frac{x-3}{2}=\frac{y-3}{3}=\frac{z+5}{6}\) 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 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 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 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 general solution of the differential equation x²dy - 2xydx = x⁴cosx dx 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