List of top Questions asked in MET- 2011

If \( x \) is real, then the value of \[ \frac{x^2 + 34x - 71}{x^2 + 2x - 7} \] does not lie between:

The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line \( y - 4x + 3 = 0 \), is:

The number of solutions of \[ \log_4 (x - 1) = \log_2 (x - 3) \] is/are:

The degree and order of the differential equation of the family of all parabolas whose axis is the x-axis, are respectively:

The value of \[ \int \frac{x^2}{(x^2 + 2)(x^2 + 3)} \, dx \] is equal to:

The differential equation satisfied by the family of curve \( y = ax \cos \left( \frac{1}{x} + b \right) \), where \( a, b \) are parameters, is:

Integrating factor of the equation: \[ (x^2 + 1) \frac{dy}{dx} + 2xy = x^2 - 1 \] is:

Which of the following statements is/are correct?
I. Adjoint of a unit matrix is a unit matrix.
II. \( A (\text{adj } A) = (\text{adj } A) A = |A|I \)
III. Adjoint of a symmetric matrix is symmetric.
IV. Adjoint of a diagonal matrix is a diagonal matrix.

The value of \[ \int \frac{dx}{x \sqrt{1 - (\log x)^2}} \] is:

The value of \[ \left| \begin{array}{ccc} (a+1)^2 & (b+1)^2 & (c+1)^2 (a-1)^2 & (b-1)^2 & (c-1)^2 \end{array} \right| \] is:

Smile : Laugh : Cry

Let \( A \) be a square matrix all of whose entries are integers. Then, which one of the following is true?

If \[ q_1x + b_1y + c_1z = 0, \quad a_2x + b_2y + c_2z = 0, \quad a_3x + b_3y + c_3z = 0 \] then the given system has:

Music : Guitar : Performer

Chair : Door : Stick

Stirrup : Anvil : Drum

Kennedy : Indira : Palme

Village : City : Suburb

Hair : Brush : Wig

An ideal gas at constant temperature and pressure expands, then its:

At which temperature nitrogen under 1.00 atm pressure has the same root mean square speed as that of CO\(_2\) at STP?

Kanha : Periyar : Dachigam

Majlis : Diet : Knesset

Knot : Watt : Fathom

(\( \Delta H - \Delta U \)) for the formation of carbon monoxide (CO) from its elements at 298 K is (R = 8.314 J K\(^{-1}\) mol\(^{-1}\)):