List of top Mathematics Questions asked in MHT CET

If \(\int g(x)dx=f(x)\) then \(\int \frac{g(x)}{9-[f(x)]^{2}}dx\) is equal to

If \(\int \frac{x+1}{x(1+xe^{x})^{2}}dx=\log |\frac{xe^{x}}{1+xe^{x}}|+f(x)+c\), then \(f(x)=\)

If \(h(x)=2g\{3g[4g(5g(x))]\}\) such that \(g(0)=0\) and \(g'(0)=2\) then \(h'(0)=\)

If \(y=f\left(\frac{2x-1}{x^{2}+1}\right)\) and \(f'(x)=\sin x^{2}\), then \(\frac{dy}{dx}\) is equal to

If \(y^{1/n}+y^{-1/n}=2x\), then \((x^{2}-1)\frac{d^{2}y}{dx^{2}}+x\frac{dy}{dx}=\ldots\)

If \(A=\begin{bmatrix} 1 & -1 & 1 \\ 2 & -1 & 0 \\ 1 & 0 & 0 \end{bmatrix}\), then which of the following is not true?

Let \(y^{2}=a\cos ^{2}x+b\sin ^{2}x\) be such that \(a+b=2024\) and \(a>0,b>0\) follows \(y^{4}+y^{3}y^{''}=k\). If \(\lambda\) is the maximum possible value of \(k\), then \(\lambda =\)

If \(p,q,r\) are statements with truth values F, T, F respectively then the truth values of \((p\wedge q)\leftrightarrow \sim p\) and \(q\rightarrow (p\vee \sim r)\) are respectively _____

If \(\sum _{x=1}^{2025}\tan ^{2}(\sec ^{-1}x)=\frac{2024\times 2025\times k}{6}\), then \(k=\ldots\)

If \(f(9)=36\), \(u(9)=9\), \(f'(9)=12\), \(u'(9)=4\), then \(\lim _{x\rightarrow 9}\frac{\sqrt{f(x)}-2\sqrt{u(x)}}{\sqrt{x}-3}=\ldots\)

The logical statement \(\sim [(p\rightarrow q)\leftrightarrow (p\wedge \sim q)]\) is

Let \(X=\begin{bmatrix} 4 & 2 \\ -1 & 3 \end{bmatrix}\), \(Y=\begin{bmatrix} -1 & 2 \\ 1 & -3 \end{bmatrix}\), then \((XY)^{-1}\) is equal to

If the line \(4x-3y+k=0\) touches the ellipse \(5x^{2}+9y^{2}=45\), then the value of \(k\) is

If the length of the tangent segment from the point \((8,-3)\) to the circle \(x^{2}+y^{2}-2x+ky-23=0\) is \(\sqrt{10}\), then the value of \(k\) is

The area of the triangle (in sq. units) formed by the pair of lines \(x^{2}-4y^{2}-8x+16=0\) and the line \(x=2\) is

If \(f(x)=\frac{10^{x}+7^{x}-14^{x}-5^{x}}{1-\cos x}\), for \(x\neq 0\) and \(f(0)=k\) is continuous at \(x=0\), then the value of \(k\) is _____

In \(\triangle ABC\), with usual notations, if \(A=60^{\circ }\) and \(a=4\), then the maximum possible area (in sq. units) of \(\triangle ABC\) is...

If \(\alpha\) and \(\beta\) are complex cube roots of unity, then the difference between the values of \(\alpha ^{2}+\beta ^{2}+\alpha \beta\) and \(\alpha ^{4}+\beta ^{4}+\alpha ^{-1}\beta ^{-1}\) is

If two sides of a triangle are the roots of the equation \(x^{2}-\sqrt{10}x+2=0\) and angle between them is \(60^{\circ }\), then the third side is

If the equation \(ax^{2}-y^{2}+2y+c=1\) represents a pair of perpendicular lines, then the values of \(a\) and \(c\) respectively are...

If \(p_{1}\) and \(p_{2}\) are the lengths of perpendiculars from the origin to the lines \(x\sec \theta +y\csc \theta =a\) and \(x\cos \theta -y\sin \theta =a\cos (2\theta )\) respectively, then \(4p_{1}^{2}+p_{2}^{2}=\)

The digit present at the unit place of the sum \((1!+2!+3!+4!+\ldots +2026!)\) is

If \(\sec 2\theta =p+\tan 2\theta\) then, the value of \(\cos ^{2}\theta\) is

In \(\triangle ABC\), with usual notations, if \(\sin 2A+\sin 2B=\sin 2C\), then the type of the triangle is

If \(f(x)=\log _{e}\left(\frac{1-x}{1+x}\right)\), \(|x|\lt 1\), then \(f\left(\frac{4x}{4+x^{2}}\right)\) is equal to