List of top Mathematics Questions

On the interval \([0,1]\), the function \(f(x) = x^{25}(1-x)^{75}\) attains its maximum value at the point \(x =\)....

If \(f(x) = \int \frac{x}{(x^2+4)(x^2+9)}\,dx\) and \(f(0) = \frac{1}{5}log(\frac{2}{3})\), then \(f(1) =\)

If the line \(ax+by+5 = 0\) is a normal to the curve \(xy = 1\) then .....

If \(y = (x^2+1)^{sinx}\) for \(x > 0\) such that \(\frac{dy}{dx} = y[\frac{2xsinx}{g(x)}+cosx\cdot log[g(x)]]\), then the function \(\frac{1}{g(x)}\) is...

Let \([x]\) denotes the greatest integer less than or equal to x and \(f(x) = [tan^2x]\), then which of the following is true ?

If \(\sqrt{y+x}+\sqrt{y-x} = c\) and \(\frac{dy}{dx} = K-\sqrt{\frac{y^2}{x^2}-1}\) , then the value of \(K\) is

The domain of the function \(f(x) = \sqrt{x-1}+\sqrt{6-x}\) is...

The domain of the function \(f(x) = ^{(10-x)}C_{(x-6)}\) is...

The derivative of \(f(sinx)\) with respect to \(g(secx)\) at \(x = \frac{π}{4}\), given that \(f^'(\frac{1}{\sqrt{2}}) = 3\) and \(g^'(\sqrt{2}) = 1\) is.....

If \(A = \left[ \begin{array}{ccc}3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 2 & 5\end{array} \right]\), \(B = \left[ \begin{array}{c}1 \\ 0 \\ 1\end{array} \right]\) such that \(XA = B^T\) and \(A^{-1}Y = B\), then \(XY =\)

Consider the following statements.
\(p\): If \(3^4 > 4^3\), then \(3^3 > 4^4\)
\(q\): The roots of the equation \(x^2-2x+2 = 0\) are real if and only if Mumbai is in Maharashtra.
\(r\): Statement \(p\) is true or statement \(q\) is false.
Which of the following has truth value T (true)?

\(\underset{x\rightarrow 0}{lim}[\frac{x\cdot log(1+4x)}{(e^{4x}-1)^2}] = \cdots\)

The negation of the inverse of the statement \(\sim p∨\sim q\) is...

Let \(A = [\begin{array}{cc}a & 1 \\ 1 & b\end{array}]\), where \(a\) and \(b\) are the roots of the equation \(x^2-4x+2 = 0\). If \(A+A^{-1} = kI_2\), then the value of \(k\) is ____

Which of the following is/are not true ?
I) If 1 is not a prime number, then 2 is not a prime number.
II) e is a vowel and \(12\times 3 = 36\)
III) It is not true that 14 is a composite number and 3 is even number.
IV) \(\sqrt{5}\) is an irrational number, but \(3+\sqrt{5}\) is a complex number.

If \(θ\) is the eccentric angle of a point on the ellipse \(\frac{x^2}{25}+\frac{y^2}{9} = 1\) such that the distance of the point from the center is \(5\), then \(θ =\).......

The area of a triangle formed by a line with the coordinate axes is \(49\) sq. units. If the perpendicular drawn from the origin to this line makes an angle of \(45^{\circ}\) with the positive X-axis, then the equation of line is....

If the equation \(16x^2-24xy+9y^2-8x+6y-35 = 0\) represents a pair of straight lines, then the equation of the locus of points equidistant from these two lines is..........

The general solution of \(cosx+sinx = cos2x+sin2x\) is \(x = npπ\) or \(x = \frac{nqπ}{3}+\frac{π}{6}\) for \(n\in Z\) then \(p:q =\)

The equation of the circle which passes through the points \((2,3)\) and \((4,5)\) and whose centre lies on a straight line \(4x-y-3 = 0\), is

The number of common solutions of the pair of equations \(2sin^2θ-2cos^2θ+1 = 0\) and \(2sin^2θ+3sinθ-2 = 0\) in the interval \([0,2π]\), is

The value of \(cos15^{\circ}-sin15^{\circ}\) is ......

If \(sec^{-1}(\frac{x^2+y^2}{x^2-y^2}) = 2a\) such that \(y\frac{dy}{dx} = x\cdot f(a)\) then the value of \(f(\frac{2π}{3})\) is

In a right-angled \(△ABC\), the measures of the angles are in an Arithmetic Progression (A.P.) If its smallest side is \(4\) units, then the area of \(△ABC\) is.....

If \(a_1,a_2,a_3,\ldots ,a_n\) are in arithmetic progression with common difference d, then \(tan[tan^{-1}(\frac{d}{1+a_1a_2})+tan^{-1}(\frac{d}{1+a_2a_3})+\ldots +tan^{-1}(\frac{d}{1+a_{n-1}a_n})] =\) ____