List of top Mathematics Questions asked in KEAM

Let ⊙ be a binary operation on Q - {0} defined by a⊙b=\(\frac{a}{b}\). Then 1⊙(2⊙(3⊙4)) is equal to

Let (3+x)¹⁰ = a₀+a₁(1+x)+a₂(1+x)²+..... a₁₀(1+x)¹⁰, where a₁, a₂, ... a₁₀ are constants. Then the value of a₀+a₁+a₂+.... a₁₀ is equal to

The three vertices of a triangle are (0, 0), (3, 1) and (1, 3). If this triangle is inscribed in a circle, then the equation of the circle is

If ⁿC₅ + ⁿC₆ = ⁵¹C₆, then the value of n is equal to

The equation of the circle touching the x-axis at (5, 0) and the line y = 10 is

The set of all x satisfying the inequality |3x+4| ≤ 7 is

If \(y=e^{3\log(2x+1)}\), then \(\frac{dy}{dx}=\)

If \(\bar a\ and\ \bar b\) are position vectors of the points (a, 3, 0) and (1, 0, 0) respectively and if the angle between the vectors \(\bar a\ and\ \bar b\ is\ \frac{\pi}{4}\), then the value of a is equal to

The end points of the major axis of an ellipse are (2, 4) and (2,-8). If the distance between foci of this ellipse is 4, then the equation of the ellipse is

If α and β are two acute angles of a right triangle, then (sinα+sinβ)²+(cosα+cosβ)²=

The domain of the function \(f(x) = (x^2-2x-63)^{\frac{3}{2}}\), x ∈ R is

The centre of the ellipse x²+7y²-14x+28y+49=0 is

If the line y = mx + c is perpendicular to y=1+x and passes through the point (1, 2), then the value of c is equal to

If the lines 2x-3y+5=0, 9x-5y+14=0 and 3x-7y+λ=0 are concurrent, then the value of λ is equal to

Let \(\begin{vmatrix} 2&1&-2\\1&1&-1\\1&0&\ \ 3 \end{vmatrix}\)and let B=|A|adj(A). Then |B|=

The number of subsets containing exactly 4 elements of the set {2, 4, 6, 8, 10, 12, 14, 16, 18) is equal to

If A is non-singular matrix and if \(A^{-1}=\frac{1}{2}\begin{bmatrix} -10&-4\\2&1\end{bmatrix}\), then adj(A)=

Let \(f(x) =   \begin{cases}     3x+6,       & if\ x\geq c \\       x^2-3x-1,       & if\ x\lt c   \end{cases}\), where x∈R and c is a constant. The values of c for which f is continuous on R are

If \(\cos\theta=\frac{5}{11}\) and \(\tan\theta\lt0\), then the value of \(\sin\theta\) is equal to

The range of the function f(x) = 2sin(3x) +1 is equal to

Let A = {1,2,3,4,5} and let B={1,2,3,4}. If the relation R : A → B is given by (a, b) ∈ R if and only if a+b is even, then n(R) is equal to

If \(z^4=7-5i\), then \(\text{Im}((\bar{z})^4)\) is equal to

The eccentricity of the hyperbola \(\frac{(x-3)^2}{9}+\frac{4(y-1)^2}{45}=1\) is equal to

The solutions of the equation \(cos\theta=2-3sin(\frac{\theta}{2})\ in\ the\ interval\ 0\leq\theta\leq\pi\ are\)