List of top Mathematics Questions asked in MET

\( \int \frac{dx}{(x+1)\sqrt{4x+3}} \) is equal to
\( \int \left(\frac{2 - \sin 2x}{1 - \cos 2x}\right) e^{x} \, dx \) is equal to
If \( I_{n} = \int \sin^{n} x \, dx \), then \( n I_{n} - (n-1) I_{n-2} \) equals
The line \( x = \frac{\pi}{4} \) divides the area of the region bounded by \( y = \sin x \), \( y = \cos x \) and the x-axis \( (0 \le x \le \frac{\pi}{2}) \) into areas \( A_{1} \) and \( A_{2} \). Then \( A_{1} : A_{2} \) equals
The solution of the differential equation \( \frac{dy}{dx} = \sin(x+y)\tan(x+y) - 1 \) is
The differential equation of the family \( y = a e^{x} + b x e^{x} + c x^{2} e^{x} \) is
The velocity of a particle starting from rest is given in the table. The total distance travelled in 10 s, using Trapezoidal rule, is t (s) & 0 & 2 & 4 & 6 & 8 & 10
v (m/s) & 0 & 12 & 16 & 20 & 35 & 60
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\( \int_{0}^{\pi} \frac{1}{1+\sin x} \, dx \) is equal to
The function $f(x) = x^3 + ax^2 + bx + c, a^2 \le 3b$ has
There is an error of $\pm 0.04$ cm in the measurement of the diameter of a sphere. When the radius is 10 cm, the percentage error in the volume of the sphere is
The radius of the sphere $x^2 + y^2 + z^2 = 12x + 4y + 3z$ is
The image of the point (3, 2, 1) in the plane $2x - y + 3z = 7$ is
If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity is
The perimeter of the triangle with vertices at (1, 0, 0), (0, 1, 0) and (0, 0, 1) is
The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the x and y-axes respectively are
The locus of centre of a circle which passes through the origin and cuts off a length of 4 unit from the line $x=3$ is
The diameters of a circle are along $2x+y-7=0$ and $x+3y-11=0$. Then, the equation of this circle, which also passes through (5, 7), is
The pairs of straight lines $x^2-3xy+2y^2=0$ and $x^2-3xy+2y^2+x-2=0$ form a
The transformed equation of $x^2+y^2=r^2$ when the axes are rotated through an angle 36° is
The area (in square unit) of the circle which touches the lines $4x+3y=15$ and $4x+3y=5$ is
The point on the line $3x+4y=5$ which is equidistant from $(1, 2)$ and $(3, 4)$ is
The equation of the straight line perpendicular to the straight line $3x+2y=0$ and passing through the point of intersection of the lines $x+3y-1=0$ and $x-2y+4=0$ is
The value of \( \lambda \) with \( |\lambda| < 16 \) such that \( 2x^2 - 10xy + 12y^2 + 5x + \lambda y - 3 = 0 \) represents a pair of straight lines, is
The area (in square unit) of the triangle formed by $x+y+1=0$ and the pair of straight lines $x^2-3xy+2y^2=0$ is
If $y = \log(\log x)$, then $dy/dx$ is: