List of top Mathematics Questions asked in MET

\((\sim p \wedge q)\) is logically equivalent to

If \((G,*)\) is a group such that \((a*b)^2 = (a*a)*(b*b)\) for all \(a,b \in G\) then \(G\) is

A graph which has no edges or nodes is known as

Find the greatest value of \(xyz\) for positive values of \(x,y,z\) subject to the condition \(xy + yz + zx = 12\)

\(a,b,c\) are prime numbers, \(x\) is an even number, \(y\) is an odd number. Which of the following is/are never true? I. \(a + x = b\) II. \(b + y = c\) III. \(ab = c\) IV. \(a + b = c\)

\((p \wedge \neg q) \wedge (\neg p \wedge q)\) is

If all edges are directed in a graph then it is called as

\(\log_2(9 - 2^x) = 10^{\log(3-x)}\) solve for \(x\)

In an equilateral triangle, the in-radius, circum-radius and one of the ex-radii are in the ratio

\(G\) is a set of all rational numbers except \(-1\) and \(*\) is defined by \(a*b = a + b + ab\) for all \(a,b \in G\). In the group \((G,*)\) the solution of \(2^{-1} * x * 3^{-1} = 5\) is

In a triangle, the length of the two larger sides are 24 and 22, respectively. If the angles are in AP, then the third side is

If \(G\) is an abelian group then for all \(a,b \in G\), \(b^{-1} * a^{-1} * b * a\) is equal to

3 numbers are in GP therefore, their logarithms are in

If \(\frac{1}{x(x+1)(x+2)\ldots(x+n)} = \frac{A_0}{x} + \frac{A_1}{x+1} + \frac{A_2}{x+2} + \ldots + \frac{A_n}{x+n}\) then \(A_r\) is equal to

The slope of the tangent at \((x,y)\) to a curve passing through \(\left(1, \frac{\pi}{4}\right)\) is given by \(\frac{y}{x} - \cos^2\left(\frac{y}{x}\right)\) then the equation of the curve is

The degree of the differential equation \(\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^2 = x\sin\left(\frac{d^2y}{dx^2}\right)\) is

The solution of the equation \(\frac{dy}{dx} = \frac{x(2\log x + 1)}{\sin y + y\cos y}\) is

The curve for which the length of the normal is equal to the length of the radius vector, are

The area of the figure bounded by the parabola \((y-2)^2 = x-1\), the tangent to it at the point with the ordinate 3 and the \(x\)-axis is

If \(\int \frac{dx}{x^2(x^n + 1)^{(n-1)/n}} = -[f(x)]^{1/n} + c\) then \(f(x)\) is

The value of \(\int_a^b \frac{|x|}{x} dx\) is

The value of \(\lim_{n \to \infty} \left\{\frac{1}{na} + \frac{1}{na+1} + \frac{1}{na+2} + \ldots + \frac{1}{nb}\right\}\) is

\(y = \int_{1/8}^{\sin^2 x} \sin^{-1}\sqrt{t} dt + \int_{1/8}^{\cos^2 x} \cos^{-1}\sqrt{t} dt, 0 \leq x \leq \pi/2\)

The area of the region \([(x,y): x^2 + y^2 \leq 1 \leq x + y]\) is

The interval for which \(2\tan^{-1}x + \sin^{-1}\frac{2x}{1+x^2}\) is independent of \(x\) is