List of top Mathematics Questions asked in MHT CET

\(\int _0^{log5}\frac{e^x\sqrt{e^x-1}}{e^x+3}\,dx =\)

\(\int \frac{(x+1)(x+logx)^2}{x}\,dx =\)

\(\int \frac{cos^3x}{sin^2x+sinx}\,dx =\)

The minimum value of \(\frac{logx}{x}\) in the interval \((2,\infty )\) is

A triangle has two fixed vertices A \((a,0)\) and B\((0,b)\) . Let its third vertex C is moving along the line \(x = y\). If \(s\) is the area of triangle ABC, then \(\frac{ds}{dx} =\)

The derivative of \(log_8(log_5x)\) w. r. t. \(x\) is

If \(y^{\frac{1}{m}}+y^{\frac{-1}{m}} = 2x\) , then \((x^2-1)y_1^2 =\)

The function \(f(x) = tan^{-1}(sinx+cosx)\) is an increasing function in the interval.....

\(sin^{-1}(\frac{12}{13})+cos^{-1}(\frac{4}{5})+tan^{-1}(\frac{63}{16}) =\)

If \(y = tan^{-1}[\frac{x-\sqrt{1-x^2}}{x+\sqrt{1-x^2}}]\) , then \(\frac{dy}{dx} =\)

\(cos(cos^{-1}(-\frac{1}{2})+\frac{π}{3}) =\)

Inverse of \([\begin{array}{cc}3 & -2 \\ 1 & 4\end{array}]\) is

If \(A = [\begin{array}{cc}5a & -b \\ 3 & 2\end{array}]\) and \(A\,(\text{adj }A) = AA^T\), Then \(5a+b =\)

If \(f(x) = \frac{4x+3}{6x-4}\), \(x\neq \frac{2}{3}\) and \((\text{fof})(x) = g(x)\) where \(g:R-\{\frac{2}{3}\}\rightarrow R-\{\frac{2}{3}\}\), then \((g\,o\,g\,o\,g\,o\,g\,o\,g)\,(3) =\)

In a triangle ABC, with usual notations \(a = \sqrt{3}+1\), \(b = \sqrt{3}-1\) and \(\angle C = 60^{\circ}\) then the values of \(\angle A\) and \(\angle B\) respectively are

With usual notations in \(△\)ABC, if \(bcos^2\frac{C}{2}+ccos^2\frac{B}{2} = \frac{3a}{2}\) then

Simplest form of the following switching circuit is

The equations of the tangent to the curve \(x^2+y^2 = 10\), where the tangent is parallel to the line \(2x+y-1 = 0\), are

If the line \(y = 2x+λ\) is a tangent to the hyperbola \(36x^2-25y^2 = 3600\), then \(λ =\)

\(\underset{x\rightarrow 0}{lim}\frac{(5^x-1)^4\,\text{cosec}\,(xlog5)}{tan(xlog5)\cdot log(1+x^2log25)} = \ldots \ldots\)

If \(0\leq x\leq \frac{π}{2}\) , then the number of values of \(x\) for which \(sinx-sin2x+sin3x = 0\) is

If \(4ab = 3h^2\), then the ratio of the slopes of the lines represented by \(ax^2+2hxy+by^2 = 0\) is...

The number of arrangements of the numbers strictly between 10 and 1000 formed with the digits 0, 1, 2, 3, 4, 5, 6 without repetition is

The value of \(\frac{sin^23A}{sin^2A}-\frac{cos^23A}{cos^2A}\) is

The number of lines passing through A (3, 4) and the sum of whose non-zero intercepts is zero is (are)