COMEDK 2023 Evening Shift

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length \(x\). The maximum area enclosed by the park is

If three numbers \(a, b, c\) constitute both an A.P and G.P, then

Le \(x\) be the arithmetic mean and \(y, z\) be the two geometric means between any two positive numbers, then \(\frac{y^3+z^3}{x y z}=\) -----------

In the set \(\mathrm{W}\) of whole numbers an equivalence relation \(\mathrm{R}\) is defined as follows \(\mathrm{aRb}\) iff both \(\mathrm{a}\) & \(\mathrm{~b}\) leave the same reminder when divided by 5. The equivalence class of 1 is give...

Which of the following is a singleton set?

Let \(X\) and \(Y\) be the set of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then \(n(X \cap Y)\) is equal to

Consider the first 10 natural numbers. If we multiply each number by \(-\)1 and add 1 to each number, the variance of the numbers so obtained is

What can be said regarding a line if its slope is negative?

The ratio in which the line \(3 x+4 y+2=0\) divides the distance between the lines \(3 x+4 y+5=0\) and \(3 x+4 y-5=0\) is

In a \(\triangle A B C\), if coordinates of point \(A\) is \((1,2)\) and equation of the medians through \(B\) and \(C\) are \(x+y=5\) and \(x=4\) respectively, then the coordinates of \(B\) is

The coordinates of the vertices of the triangle are \(A(-2,3,6), B(-4,4,9)\) and \(C(0,5,8)\). The direction cosines of the median \(\mathrm{BE}\) are

\(\mathrm{P} \text { is a point on the line segment joining the points }(3,2,-1) \text { and }(6,2,-2) \text {. If the } x \text { co ordinate of } \mathrm{P} \text { is } 5 \text {, then its } \mathrm{y} \text { coordinate is }\)

The distance of the point \((2,3,4)\) from the line \(1-x=\frac{y}{2}=\frac{1}{3}(1+z)\) is

If the position vector of a point \(A\) is \(\vec{a}+2 \vec{b}\) and \(\vec{a}\) divides \(A B\) in the ratio \(2: 3\), then the position vector of \(B\) is

If the direction ratios of two lines are given by \(3 l m-4 l n+m n=0\) and \(l+2 m+3 n=0\), then the angle between the lines is

\(\text { If } \operatorname{cosec}(90+A)+x \cos A \cot (90+A)=\sin (90+A) \text { then the value of } x \text { is }\)

\(\cos ^6 A-\sin ^6 A \text { is equal to }\)

If \(\cos \alpha=k \cos \beta\) then \(\cot \left(\frac{\alpha+\beta}{2}\right)\) is equal to

The scalar components of a unit vector which is perpendicular to each of the vectors \(\hat{\imath}+2 \hat{\jmath}-\hat{k}\) and \(3 \hat{\imath}-\hat{\jmath}+2 \hat{k}\) are

\(\text { If } \vec{a} \text { and } \vec{b} \text { are unit vectors, then the angle between } \vec{a} \text { and } \vec{b} \text { for which } a-\sqrt{2} \vec{b} \text { is a unit vector is }\)

\(220 \mathrm{~V}\) ac is more dangerous than \(220 \mathrm{~V}\) dc Why?

What should be the inductance of an inductor connected to \(200 \mathrm{~V}, 50 \mathrm{~Hz}\) source so that the maximum current of \(\sqrt{2}\) A flows through it?

The mass number of two nuclei \(\mathrm{P}\) and \(\mathrm{Q}\) are 27 and 125 respectively. The ratio of their radii \(R_P: R_Q\) is given by:

In a nuclear reaction 2 deuteron nuclei combine to form a helium nucleus. The energy released in \(\mathrm{MeV}\) will be: (Given mass of deuteron \(=2.01355 \mathrm{~amu}\). and mass of helium nucleus \(=4.0028 \mathrm{~amu}\).

A particle at rest decays in to two particles of mass \(m_1\) and \(m_2\) and move with velocities \(v_1\) and \(v_2\). The ratio of their de Broglie wave length \(\frac{\lambda_1}{\lambda_2}\) is:

The ground state energy of hydrogen atom is \(-13.6 \mathrm{~eV}\). If the electron jumps from the \(3^{\text {rd }}\) excited state to the ground state then the energy of the radiation emitted will be:

In the head-on collision of two alpha particles \(\alpha_1\) and \(\alpha_2\) with the gold nucleus, the closest approaches are 31.4 fermi and 94.2 fermi respectively. Then the ratio of the energy possessed by the alpha particles $$\alpha_2...

Which of the following statement is true when a gamma decay occurs from the nucleus of an atom?

In the figure, first the capacitors are fully charged by closing the key \(\mathrm{K}\). Then after opening the Key a dielectric material with dielectric constant 2 is filled in the space between the plates of both the capacitor. At this s...

A neutron makes a head on elastic collision with a lead nucleus. The ratio of nuclear mass to neutron mass is 206 . The fractional change in kinetic energy of a neutron is

The current sensitivity of a galvanometer having 20 divisions is \(10 \mu \mathrm{A} /\) div. If the resistance of the galvanometer is \(100 \Omega\) then the value of the resistance to be used to convert this galvanometer in to an voltmete...

The electric flux from cube of side \(1 \mathrm{~m}\) is '\(\Phi\)' When the side of the cube is made \(3 \mathrm{~m}\) and the charge enclosed by the cube is made one third of the original value, then the flux from the bigger cube will be ...

A resistor of wire \(24 \mathrm{~cm}\) length and resistance \(8 \Omega\) is stretched in to a uniform wire of \(48 \mathrm{~cm}\) length, then the new resistance will be :

The SI unit of electrical conductivity is :

A battery is made of 12 cells having emf \(5 \mathrm{~V}\) each. If three cells are unknowingly connected wrong, the resultant emf of the battery will be:

The current drawn by the primary coil of an ideal transformer, which steps up \(22 \mathrm{~V}\) into \(220 \mathrm{~V}\), to operate a device having a load resistance \(110 \Omega\) is:

The current passing through the 100\(\Omega\) resistor in the given electrical circuit is :

In the photoelectric experiment, the frequency of the incident radiation is doubled. What will be its effect on the photoelectric current?

A man grows into a giant such that his height increases to 8 times his original height. Assuming that his density remains same, the stress in the leg will change by a factor of

A spring of force constant \(k\) is cut into lengths of ratio \(1:3:4\). They are connected in series and the new force constant is \(\mathrm{k}\)'. Then they are connected in parallel and force constant is \(\mathrm{k}\)''. Then $$\mathrm{...

One volt induced emf is produced in the secondary coil when the current through the primary coil is changed from \(3 \mathrm{~A}\) to \(1 \mathrm{~A}\) in 100 milliseconds. the mutual inductance of the two coil is:

What feature of the infrared waves make it useful for the haze photography?

Two point charges \(20 \mu \mathrm{C}\) and \(-10 \mu \mathrm{C}\) are separated by a distance of \(1 \mathrm{~m}\) in air. At what point on the line joining the two charges, the electric potential is zero.

A spherical metal ball of density '\(\rho\)' and radius '\(r\)' is immersed in a liquid of density '\(\sigma\)'. When an electric field is applied in the upward direction the metal ball remains just suspended in the liquid. Then the express...

PQRS is square of side \(1 \mathrm{~m}\). A charge of \(100 \mu \mathrm{C}\) is placed at the centre of the square. Then the work done to take \(3 \mu \mathrm{C}\) charge from the corner \(\mathrm{P}\) to the corner \(\mathrm{R}\).

An electron and a proton having mass \(m_e\) and \(m_p\) respectively, initially at rest, move through the same distance '\(s\)' in a uniform electric field '\(E\)'. If the time taken by them to cover that distance is \(t_e\) and \(t_p\) re...

The force between two electric point charges at rest in air is \(F_1\) When the same arrangement is kept inside water, the force between them is \(F_2\). Which of the following statement is correct?

Water from a tap of cross-sectional area \(1 \mathrm{~cm}^2\), falls vertically downwards at \(2 \mathrm{~m} / \mathrm{s}\). The cross sectional area of the stream, \(20 \mathrm{~cm}\) below the tap is (assume that pressure is constant thro...

The acceleration due to gravity at a height of \(7 \mathrm{~km}\) above the earth is the same as at a depth d below the surface of the earth. Then d is

An uniform sphere of mass \(M\) and radius \(R\) exerts a force of \(F\) on a small mass \(m\) placed at a distance of 3R from the centre of the sphere. A spherical portion of diameter \(R\) is cut from the sphere as shown in the fig. The f...