List of top Questions asked in KEAM

When two different liquids of same mass but at two different temperatures $27^\circ C$ and $47^\circ C$ are mixed together, the resulting temperature of the mixture is $35^\circ C$. The ratio of their specific heat capacities is

The energy stored in a soap bubble of diameter 4 cm is nearly (surface tension of soap solution is 0.07 N/m)

Which of the following has the maximum Young’s modulus value?

The gravitational potential energy of a system of two bodies each of mass $m$ and distance $r$ between them is (G = gravitational constant, g = acceleration due to gravity)

When two spheres of radii $r$ and $\frac{r}{2}$ are brought in contact, the gravitational force of attraction between them is proportional to

The radius of gyration of a regular solid cylinder of radius $R$ about its axis is

If $P$ is the pressure at which the heart is pumping the blood and the volume of blood pumped per second is $V$, then the power of the heart is given by

When a spring of spring constant $k$ is cut into two pieces whose lengths are $l_1$ and $l_2$, then the ratio of their spring constants $k_1$ and $k_2$ is

In a ‘tug of war’ game, two persons pull each other through a massless rope. The person who wins is

A particle is describing a uniform circular motion with a certain constant speed. The INCORRECT statement is

A projectile is given an initial velocity of $(\hat{i} + \hat{j})$ m/s, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical direction. The equation of its trajectory is $(g = 10 \, \text{m/s}^2)$.

A man loses 50% of his velocity after running a distance of 100 m. If his retardation is uniform, the distance he will cover before coming to rest is

Dimensions of the physical quantity $X$ in the equation \[ {Force} = \frac{X}{{Volume}} \] are

In an oil drop experiment, 'n' numbers of electrons are stripped from an oil drop to make it positively charged. A vertical electric field of magnitude 4.9x10¹⁴ N/C is applied to balance the force due to gravity on the oil drop. If the mass of oil drop is 80 μg,the value of 'n' will be:(Take g =9.8 m/s² and charge of an electron = 1.6 x 10^-19 C)

$\text{The value of } cosec20°tan60°-sec20° \text{is }$

If the coefficients of $(5r+4)th$ term and $(r-1)th$ term in the expansion of $(1+x)^{25}$ are equal, then $r$ is

The area of the region in the first quadrant which is above the parabola $y = x^2$ and enclosed by the circle $x^2 +y^2 = 2 $ and the y-axis is

The area of the region in the first quadrant enclosed by the curves$ y=√x,y=-x+6 $and the x-axis is

The kinetic energy of a particle of mass m₁ moving with a speed V is same as the kinetic energy of a solid sphere of mass m₂rolling on the plane surface. If the speed of the Centre of the sphere is also V,then m₁/m₂ is:

For $i=1,2,3,4$, suppose the points$(\cosθi,\secθi)$ lie on the boundary of a circle,where $θi∈[0,\frac{π}{6})$ are distinct. Then $\cosθ_1\ \cosθ_2\ \cosθ_3\ \cosθ_4$ equals

A thin convex lens of refractive index 1.5 has a focal length of 10 cm in air. When the lens is immersed in a fluid,its focal length becomes 70 cm. The refractive index of the fluid is

Car P is heading east with a speed V and car Q is heading north with a speed $\sqrt{3}$. What is the velocity of car Q with respect to car P?

For any $n≥0$ the value of $\sum_{r=0}^n \dfrac{(4r+3).(nC_r)^2}{(2n+3)}$ is

A ring of radius 1.75 m stands vertically. A small sphere of mass 1kg rolls on the inside of this ring without slipping. If it has a velocity of 10m/s at the bottom of the ring,then its velocity when it reaches the top is:(Take g=10 m/s²)

A series LCR circuit consists of a variable capacitor connected to an inductor of inductance 50 mH,resistor of resistance 100 Ω and an AC source of angular frequency 500 rad/s. The value of capacitance so that maximum current may be drawn into the circuit is: