List of top Mathematics Questions asked in MHT CET

If \(f(x) = \left\{ \begin{array}{cc}\frac{(8-2x)^{\frac{1}{3}}-2}{3-(243+5x)^{\frac{1}{5}}}, & \text{if }x\neq 0 \\ k, & \text{if }x = 0\end{array} \right.\) is continuous at \(x = 0\), then \(k =\)

The domain of the function \(f(x) = e^{\sqrt{5x-3-2x^2}}\) is

Let \(f(x) = x-5\).
If \(g(x) = [f(4h(x)+3)]^2\) and \(h(1) = 4,h^'(1) = -2\), then \(g^'(1) =\) .....

If \(y = x+e^x\), then \(\frac{d^2x}{dy^2}\) is equal to

If \(A = \left[ \begin{array}{ccc}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array} \right]_{3\times 3}\), and \(A^{-1} = \left[ \begin{array}{ccc}γ & -1 & 1 \\ α & 6 & -5 \\ β & -2 & 2\end{array} \right]_{3\times 3}\), then \(|α\cdot β\cdot γ| =\) _____ (where \(|\cdot |\) denotes the absolute value)

With usual notations, in \(△ABC\), \((b-c)^2cos^2\frac{A}{2}+(b+c)^2sin^2\frac{A}{2} =\)

With usual notations, in \(△ABC\), if \(2a^2 = b^2+c^2\), then \(\frac{cos3A}{cosA}+2 =\)

In a triangle ABC, with usual notations if \(\frac{s-a}{11} = \frac{s-b}{12} = \frac{s-c}{13}\) and \(λtan^2\frac{A}{2} = 455\), then \(λ =\)

Consider the statement patterns
A. \((q\rightarrow p)∨(p\rightarrow q)\)
B. \((\sim p∨\sim q)\leftrightarrow \sim (p∧q)\)
C. \([(p∨q)∧\sim p]∧\sim q\)
D. \((p∧q)∧(\sim p∨\sim q)\)
then statement patterns

Let \(A = [\begin{array}{cc}-5 & -3 \\ 2 & 1\end{array}]\). The Row transformation \(R_1\rightarrow R_1+3R_2\) will transform matrix A into

The area of the triangle formed by the co-ordinate axes and a line \(px+qy = r\) (where p, q and r are positive real numbers) is \(\frac{1}{54}\) sq.units, then ....

The joint equation of the pair of lines through the origin and making an angle of \(\frac{π}{4}\) with the line \(3x+y-6 = 0\) is

A point on the parabola \(y^2 = \frac{36}{5}x\) at which the ordinate increases at thrice the rate of the abscissa is .....

The area of the triangle formed by the lines joining the vertex of the parabola \(x^2 = 48y\) to the ends of its latus rectum, is .....

\(\underset{x\rightarrow 0}{lim}[\frac{log|2+x|-log|2-x|}{tanx}] =\) .......

If a circle with center \((-1,1)\) touches the line \(x+2y+4 = 0\), then the co-ordinates of the point of contact are

The number of solutions in \([0,\frac{π}{2})\) of the equation \(cos3x\cdot tan5x = sin7x\) is

\(tan105^{\circ} =\) ......

The polar form of the complex number \(z = \frac{1}{1+i}\), (where \(i = \sqrt{-1}\)) is

The number of cubic equations that can be formed with the coefficients 0, 3, 2, 4, 5, 6 when repetition of coefficients is allowed, is....

If events A and B are such that \(P(A) = \frac{1}{4}\), \(P(A\cap B) = \frac{1}{10}\) and \(P(A/B) = 2P(B/A)\) then \(P(B) =\)...........

The probability mass function of a random variable X is given by
\(P(X = x) = \frac{^5C_x}{2^5}\), for \(x = 0,1,2,3,4,5\) and \(= 0\), otherwise.
Then which of the following is correct?

If the centroid of a tetrahedron \(OABC\) is \((1,2,-1)\), where O is the origin, \(A(a,2,3),B(1,b,2),C(2,1,c)\) are the other vertices, then the distance of the point \(P(a,b,c)\) from the origin is...

If \(X\sim B(n,p)\), then the value of \(\frac{P(X = k)}{P(X = k-1)}\) is

If the lines \(\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4}\) and \(\frac{x-3}{1} = \frac{y-c}{2} = \frac{z}{1}\) intersect, then the radius of circle \(x^2+y^2-4x+10y+c = 0\) is