List of top Questions asked in MET- 2010

The point in the interval [0, 2π], where $f(x)=eˣsin~x$ has maximum slope, is

If a particle is moving such that the velocity acquired is proportional to the square root of the distance covered, then its acceleration is

If $f(x)=(ax+b)sin~x+(cx+d)cos~x$, then the values of a, b, c and d such that $f^\prime(x)=x~cos~x$ for all x, are

If $y=sin(m~sin^-1x)$, then $(1-x²)y^\prime\prime-xy^\prime}$ is equal to

If $f(x)=logₓ(log~x)$, then $f^\prime(x)$ at $x=e$ is

The locus of the equation $xy+yz=0$ is

The direction cosines of any normal to the xy-plane are

If \( f(x) = \begin{cases} b, & 0 \leq x < 1 \\ x + 3, & 1 < x \leq 2 \\ 4, & x = 1 \end{cases} \) , then the value of \( (a, b) \) for which \( f(x) \) cannot be continuous at \( x = 1 \) is

The reflection of the point (2, 1, 3) in the plane $3x-2y-z=9$ is

The number of real tangents that can be drawn to the ellipse $3x²+5y²=32$ passing through (3, 5) is

The tangent and normal to a rectangular hyperbola $xy=c²$ at a point cut off intercepts $a₁, a₂$ on one axis and $b₁, b₂$ on the other, then $a₁a₂ + b₁b₂$ is equal to

If $e$ is the eccentricity of the hyperbola $x²/a² - y²/b² = 1$ and $θ$ is the angle between the asymptotes, then $\cos(θ/2)$ is equal to

If $(mᵢ, 1/mᵢ)$ are four distinct points on a circle, then

If the normal to the parabola $y²=4ax$ at the point $(at², 2at)$ cuts the parabola again at $(aT², 2aT)$, then

If the equation $lx²+2mxy+ny²=0$ represents a pair of conjugate diameters of the hyperbola $x²/a² - y²/b² = 1$, then

To the lines $ax²+2hxy+by²=0$ the lines $a²x²+2h(a+b)xy+b²y²=0,$ are

The equation $3x²+7xy+2y²+5x+5y+2=0$ represents

The locus of the point of intersection of tangents to the circle $x=a\cosθ, y=a\sinθ$ at the points whose parametric angles differ by $π/2$ is

Consider four circles $(x ± 1)² + (y ± 1)² = 1$, then the equation of smaller circle touching these four circles is

The length of the common chord of the two circles $(x-a)²+(y-b)²=c²$ and $(x-b)²+(y-a)²=c²$ is

The equation of the circle passing through (1, 0) and (0, 1) and having the smallest possible radius is

If the axes be turned through an angle $\tan^-12$, what does the equation $4xy-3x²=a²$ become?

The distance of the point (2, 3) from the line $2x-3y+9=0$ measured along a line $x-y+1=0$ is

If $t₁, t₂$ and $t₃$ are distinct, the points $(t₁, 2at₁+at₁³), (t₂, 2at₂+at₂³), (t₃, 2at₃+at₃³)$ are collinear if

The equation of the straight line which passes through the intersection of the lines $x-y-1=0$ and $2x-3y+1=0$ and is parallel to x-axis, is