List of top Mathematics Questions asked in MHT CET

If the function \(f(x) = ax^3+bx^2+11x-6\), defined on \([1,3]\), satisfies all the conditions of Rolle's theorem for \(c = 2+\frac{1}{\sqrt{3}}\), then

If \(\left[ \begin{array}{ccc}2 & 1 & -1 \\ -1 & 2 & 1 \\ 1 & -1 & 2\end{array} \right]\left[ \begin{array}{c}a \\ b \\ c\end{array} \right] = \left[ \begin{array}{c}4 \\ 0 \\ -2\end{array} \right]\) then the distance of point \(P(a,b,c)\) from the plane \(2x+y+2z = 10\) is

If \(cot(cos^{-1}x) = sec(tan^{-1}\frac{a}{\sqrt{b^2-a^2}})\), then the value of \(x\) is

Let the function f be defined by \(f(x) = \frac{x-|x|}{x}\), for \(x\neq 0\) and \(f(0) = 2\) then f is

If \(g(x) = x^2+x-2\) and \(\frac{1}{2}(g\circ f)(x) = 2x^2-5x+2\) then \(f(x)\) is equal to

Consider the following statements
\(r\): If \(p\rightarrow q\) is false then \(p∨q\) is false.
\(s\): If \(p\leftrightarrow q\) is false then \(p∨q\) is false.
The truth values of \(r\rightarrow s\) and \(s\rightarrow r\) are respectively ____

The ellipse \(4x^2+9y^2 = 1\) intersects positive Y-axis at point A. If S and S' are its foci, then the area (in sq. units) of \(\Delta SAS^'\) is _____

If \(A = \left[ \begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array} \right]\) then which of the following is true ?

In triangle ABC, with usual notations, if the angles are in Arithmetic Progression and \(3c^2 = 2b^2\), then the measure of angle A is

\(\underset{x\rightarrow 1}{lim}[\frac{x-2}{x^2-x}-\frac{1}{x^3-3x^2+2x}] =\)

If \(A = \{1,2,3,4,5,6\}\) then which of the following is not true?

In \(\Delta ABC\), if \(\angle A = 90^{\circ}\), then \(sin(B-C) =\)

The value of \(cos^210^{\circ}-cos10^{\circ}cos50^{\circ}+cos^250^{\circ}\) is equal to....

The general solution of \(cos4θ = cos3θ\) is \(θ =\).....

If the distance between the lines represented by \((x-2y)^2+k(x-2y) = 0\) is \(3\) units and \(k > 0\) then the equations of the lines are

If the equation \(3x^2+(3-p)xy+qy^2-2px = 8pq\) represents a circle, then the area (in sq. units) of this circle is

The line \(2x+y = 4\) intersects X and Y axes at points A and B respectively. Let \(C(p,q)\) be the point such that the lines AC and BC are perpendicular. The distance of point C from the midpoint of segment AB is...

If \(α\) and \(β\) are the roots of the equation \(x^2+x+1 = 0\) then \(α^{2026}+β^{2026} =\)

The number of ways that 8 beads of different colours can be strung to form a necklace is

If the lines \(L_1:\frac{x-1}{-3} = \frac{y-2}{2k} = \frac{z-3}{2},L_2:\frac{x-1}{3k} = \frac{y-5}{1} = \frac{z-6}{-5}\) are perpendicular to each other, then the equation of a plane containing the line \(L_1\) and parallel to the line \(L_2\) for the value of \(k\) that satisfies this condition is ...

A plane meets the coordinate axes at points A, B and C, such that the centroid of a triangle ABC is \((2,-\frac{2}{3},\frac{1}{2})\). The perpendicular distance from the origin to this plane is...

Two cards are drawn at random from a standard pack of \(52\) cards. Then the probability that the draw consists of exactly one face card and exactly one ace card is...

If the following function is probability density function of r.v. X
\(f(x) = kx^2(1-x)\), for \(0 < x < 1 = 0\), otherwise, then the value of \(k\) is

The point at which the maximum value of \(x+y\) subject to constraints \(x+2y\leq 70\) and \(2x+y\leq 95,x\geq 0,y\geq 0\) is.

Let \(X\sim B(n,p)\). If \(E(X) = 2\) and \(\text{Var}(X) = 1\), then the probability of getting at most one success is .....