List of top Mathematics Questions asked in MHT CET

The area of the region lying in the first quadrant and bounded by the curve \(y = 4x^2\), the Y-axis, and the lines \(y = 2\), \(y = 4\) is...
If \(\int _0^1\frac{dx}{\sqrt{x+1}-\sqrt{x}} = \sqrt{2}k\), then the value of \(k\) is...
If \(f(x) = \int \frac{x}{(x^2+4)(x^2+9)}\,dx\) and \(f(0) = \frac{1}{5}log(\frac{2}{3})\), then \(f(1) =\)
A spherical iron ball \(10\) cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of \(50 \text{cm}^3/\text{min}\). When the thickness of ice is \(5\) cm, the rate at which the thickness of ice decreases is...
On the interval \([0,1]\), the function \(f(x) = x^{25}(1-x)^{75}\) attains its maximum value at the point \(x =\)....
\(\int (e^{log(sinx)}+cosx)x\,dx =\)
If the line \(ax+by+5 = 0\) is a normal to the curve \(xy = 1\) then .....
\(\int \frac{x^4(x^{10}-1)}{x^{20}+3x^{10}+1}\,dx = \cdots\)
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...
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
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...
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.....
Let \([x]\) denotes the greatest integer less than or equal to x and \(f(x) = [tan^2x]\), then which of the following is true ?
\(\underset{x\rightarrow 0}{lim}[\frac{x\cdot log(1+4x)}{(e^{4x}-1)^2}] = \cdots\)
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)?
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.
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 ____
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 \(XY =\)
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 \(θ =\).......
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 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 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....
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