List of top Mathematics Questions

A wire of length 20 units is divided into two parts such that the product of one part and the cube of the other part is maximum. The product of these parts is:
If \( y = 5\cos x - 3\sin x \), then \( \frac{d^2y}{dx^2} + y \) equals:
The value of \( \sin(\cot^{-1}(x)) \) is:
Switching current of \( (p \land q) \lor (p \land (q \lor p \lor r)) \)?
Find the value of \( (a + b) \cdot p + (b + c) \cdot q + (c + a) \cdot r \):
If \( y = \sec(\tan^{-1} x) \), find \( \frac{dy}{dx} \), given that \( x = 1 \):
If \( x^y = e^{x-y} \), at \( x = 1 \), find \( \frac{dy}{dx} \)?
The number of four-letter words that can be formed using the letters of the word "BARRACK" is:
If \( f \) is a real valued function from \( A \) onto \( B \) defined by \( f(x) = \frac{1}{\sqrt{|x| - |x|}} \), then \( A \cap B \) is:}

Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where

\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]

The number of integral values of \(\lambda\) for which \(x^2 + y^2\) +\(\lambda\) x + (1 - \(\lambda\))y + 5 = 0 is the equation of a circle whose radius does not exceed 5 is

If \[ \tan\beta = 2\sin\alpha \sin\gamma \cdot \csc(\alpha+\gamma), \] then \(\cot\alpha,\; \cot\beta,\; \cot\gamma\) are in:
If \[ \cos^{-1}\alpha+\cos^{-1}\beta+\cos^{-1}\gamma = 3\pi, \] then the value of \(\alpha\beta+\beta\gamma+\gamma\alpha\) is:
If n integers taken at random are multiplied together, the probability that the last digit of the product is 1, 3, 7 or 9 is
The ratio of the distances from the points (1,–1,3) and (3,3,3) to plane \(5x+2y-7z+9=0\) is
The number of values of c such that the straight line \(y=4x+c\) touches the curve \(\frac{x^2}{4}+y^2=1\) is
A line cuts the \(x\)-axis at \(A(7,0)\) and the \(y\)-axis at \(B(0,-5)\). A variable line \(PQ\) is drawn perpendicular to \(AB\) cutting the \(x\)-axis and \(y\)-axis at \(P\) and \(Q\) respectively. If \(AQ\) and \(BP\) intersect at \(R\), then the locus of \(R\) is:
The plane x - 2y + 3z = 17 divides the line joining the points (-2, 4, 7) and (3, -5, 8) in the ratio
A straight line through the origin \(O\) meets the parallel lines \(4x+2y=9\) and \(2x+y+6=0\) at points \(P\) and \(Q\) respectively. The point \(O\) divides the segment \(PQ\) in the ratio:
If the mean deviation of the numbers 1, 1+d, 1+2d, … , 1+100d from their mean is 255, then the common difference d is
If \(y=f(x)\) passing through \((1,2)\) satisfies the differential equation \[ y(1+xy)\,dx - x\,dy = 0, \] then \(f(x)=\)
If \[ y=(1-x)(1+x^2)(1+x^4)\cdots(1+x^{2^n}), \] then \(\dfrac{dy}{dx}\) at \(x=0\) is equal to
Consider \(p(x)\) a polynomial of degree 5 having extremum at \(x=-1,1\). Given \[ \lim_{x\to0}\left(\frac{p(x)}{x}-2\right)=4, \] the value of \(p[1]\) (greatest integer function) is}
If \(g(x)=\cos x^2\), \(f(x)=\sqrt{x}\) and \(\alpha,\beta\;(\alpha<\beta)\) are the roots of \(18x^2-9\pi x+\pi^2=0\), then the area bounded by the curve \(y=(g\circ f)(x)\) and the lines \(x=\alpha,\;x=\beta\) and \(y=0\) is:
If \[ \int \sin(101x)\,\sin^{99}x\,dx = \frac{\sin(100x)\sin^{100}x}{k+5}+c, \] then \(\dfrac{k}{19}=\)