COMEDK 2020

Gram molecular volume of oxygen at STP is

Dalton’s law of partial pressures is applicable to
which one of the following systems?

One mole of oxygen at 273 K and one mole of
sulphur dioxide at 546 K are taken in two
separate containers, then

When a sulphur sol is evaporated, sulphur is
obtained. On mixing with water, sulphur sol is
not formed. The sol is

The noble gas mixture is cooled in a coconut bulb
at 173 K. The gases that are not adsorbed are

Which of the following is an intensive property?

Thermodynamic standard conditions of
temperature and pressure are

In which of the following process, a maximum
increase in entropy is observed?

Consider the reaction,
C(s) + O\(_2\)(g) \(\rightarrow\) CO\(_2\)(g) + 393.5 kJ
The signs of \(\Delta H,\Delta S\) and \(\Delta G\) respectively are

Entropy of the universe is

The point on the curve \(y^2=x\), the tangent at which makes an angle 45\(^\circ\) with X-axis is

The length of the subtangent to the curve \({x^2}{y^2} = {a^4}\) at \(( - a,a)\) is

The range in which \(y = - {x^2} + 6x - 3\) is increasing, is

OA and OB are two roads enclosing an angle of
120\(^\circ\). X and Y start from O at the same time. X
travels along OA with a speed of 4 km/h and Y
travels along OB with a speed of 3 km/h. The
rate at which the shortest distance between X
a...

The area enclosed by the pair of lines \(xy=0\), the line \(x-4=0\) and \(y+5=0\) is

The area bounded by the curve \(x=4-y^2\) and the Y-axis is

The ninth term of the expansion \({\left( {3x - {1 \over {2x}}} \right)^8}\) is

The number of common tangents to the circles \(x^2+y^2=4\) and \(x^2+y^2-6x-8y-24=0\) is,

If \(3x+y+k=0\) is a tangent to the circle \(x^2+y^2=10\), the values of k are

The equation to two circles which touch the
Y-axis at (0, 3) and make an intercept of 8 units
on X-axis are

\({x^2} + {y^2} - 6x - 6y + 4 = 0\), \({x^2} + {y^2} - 2x - 4y + 3 = 0\), \({x^2} + {y^2} + 2kx + 2y + 1 = 0\). If the radical centre of the above three circles exists, then which of the following cannot be the value of k?

If the circles \({x^2} + {y^2} - 2x - 2y - 7 = 0\) and \({x^2} + {y^2} + 4x + 2y + k = 0\) cut orthogonally, then the length of the common chord of the circles is

The conjugate of the complex number \({{{{(1 + i)}^2}} \over {1 - i}}\) is

The imaginary part of \(i^i\) is

The amplitude of \({(1 + i)^5}\) is

If \(1,\omega ,{\omega ^2}\) are the cube roots of unity, then \((1 + \omega )(1 + {\omega ^2})(1 + {\omega ^4})(1 + {\omega ^8})\) is equal to

The value of the integral \(\int\limits_0^{\pi /2} {({{\sin }^{100}}x - {{\cos }^{100}}x)dx}\) is

If \(k\int\limits_0^1 {x\,.\,f(3x)dx = \int\limits_0^3 {t\,.\,f(t)dt} }\), then the value of \(k\) is

The differential equation of the family of
straight lines whose slope is equal to y-intercept
is

The order and degree of the differential equation \({\left[ {1 + {{\left( {{{dy} \over {dx}}} \right)}^5}} \right]^{{1 \over 3}}} = {{{d^2}y} \over {d{x^2}}}\) are respectively

If \(y = {2^{\log x}}\), then \({{dy} \over {dx}}\) is

If \(y = {\cos ^2}{{3x} \over 2} - {\sin ^2}{{3x} \over 2}\), then \({{{d^2}y} \over {d{x^2}}}\) is

If \({x^x} = {y^y}\), then \({{dy} \over {dx}}\) is

If the area of the auxillary circle of the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1(a > b)\) is twice the area of the ellipse, then the eccentricity of the ellipse is

If p is any point on the ellipse \({{{x^2}} \over {36}} + {{{y^2}} \over {16}} = 1\), and S and S' are the foci, then \(PS + PS' =\)

If \(f:R \to R\) is defined by \(f(x) = |x|\), then

If \({{{x^2}} \over {36}} - {{{y^2}} \over {{k^2}}} = 1\) is a hyperbola, then which of the following statements can be true?

\({{3{x^2} + 1} \over {{x^2} - 6x + 8}}\) is equal to

The value of \(\int {{1 \over {1 + \cos 8x}}dx}\) is

The value of \(\int {{e^x}({x^5} + 5{x^4} + 1)\,.\,dx}\) is

The value of \(\int {{{{x^2} + 1} \over {{x^2} - 1}}dx}\) is

The value of \(\sin \left[ {2{{\cos }^{ - 1}}{{\sqrt 5 } \over 3}} \right]\) is

The solution of \({\tan ^{ - 1}}x + 2{\cot ^{ - 1}}x = {{2\pi } \over 3}\) is

If \({\sec ^{ - 1}}\left( {{{1 + x} \over {1 - y}}} \right) = a\), then \({{dy} \over {dx}}\) is

\(\mathop {\lim }\limits_{x \to 1} {{\tan ({x^2} - 1)} \over {x - 1}}\) is equal to

If the function \(f(x) = \left\{ {\matrix{ {{{1 - \cos x} \over {{x^2}}},} & {\mathrm{for}\,x \ne 0} \cr {k,} & {\mathrm{for}\,x = 0} \cr } } \right.\) is continuous at x = 0, then the value of k is

\({7^{2{{\log }_7}5}}\) is equal to

The negation of the proposition “If 2 is prime,
then 3 is odd” is

If \(A = \left[ {\matrix{ 1 & { - 1} & 1 \cr 2 & 1 & { - 3} \cr 1 & 1 & 1 \cr } } \right],10B = \left[ {\matrix{ 4 & 2 & 2 \cr { - 5} & 0 & \alpha \cr 1 & { - 2} & 3 \cr } } \right]\) and B is the inverse ...

If \(A = \left[ {\matrix{ 0 & x & {16} \cr x & 5 & 7 \cr 0 & 9 & x \cr } } \right]\) is singular, then the possible values of x are