List of top Questions asked in KEAM- 2021

A bag contains 5 yellow, 3 green, 2 blue and 7 white balls. If 4 balls are chosen at random, then the probability that none of them are white is

If $sin\alpha +sin \beta = \frac{\sqrt6}2$ and $cos \alpha + cos\beta = \frac{\sqrt2}2$ then $coas(\alpha - \beta)$ is equa; to

Let $f(x)=6\sqrt{x^5}^3$. If $f'(x)=ax^p$, where a and p are constants, then the value of p is equal to

The radius of a circular plate is 1.05 m. Its area (in $m^2$) up to correct significant figures is

For any two positive rational numbers m and n, a binary operation * is defined by $m*n=\frac{m+n}{3}$, then $\frac{7}{2}*\frac{5}{2}$ is equal to

The term independent of x in the binomial expansion of $(x+\frac{2}{x^3})^{20}$ is

When a body is strained, energy stored per unit volume is (Y-Young's modulus)

If one cell is connected wrongly in a series combination of four cells each of e.m.f. 1.5 V and internal resistance of 0.5 Ω, then the equivalent internal resistance of the combination is

The general solution of the differential equation 4xy+12x+(2x²+3)y' = 0 is

If $B_c$ is the magnetic induction at the ceflte ofa circular coit carrying curreflt, then the magnetic induction at a poitrt oo the axis of the coil at a distance equal to the radius of the coil is

"No two electrons in an atom can have the same set of four quantum numbers." This is known as

The first ionisation enthalpy is the least in

If $\frac{z}{i}=11-13i$, then $z+\bar z$ is equal to

Let X be the set {1, π, {42, √2}, {1,3}}. Which of the following statement(s) is/are true? Ρ : π ∈X , Q :{1,3} ⊆ X , R : {1,7} ⊆ X 

The X and Y coordinates of the three particles of masses m, 2m and 3m are respectively (0,0), (1,0) and (-2,0). The X-coordinate of the centre of mass of the system is

A hammer is dropped into a mine. Its velocities at depths d, 2d and 3d are in the ratio

The apparent depth of a needle lying in a water beaker is found to be 9 cm. If water is replaced by a liquid of refractive index 1.5, then the apparent depth of needle will be (μ of water is 4/3)

The solution set of the inequality 5(4x+6) <25x+10 is

The matrix $\begin{bmatrix} -2&1&0\\3&4&1\\-4&\lambda&0 \end{bmatrix}$ is non-singular for $\lambda\ne$

Let $\begin{vmatrix} x-1&2&1\\2&x-1&2\\1&x+2&x-1 \end{vmatrix}=ax^3+bx^2+cx+d$, where a,b,c and d are constants. Then the value of d is

If the inequality -13 ≤ x ≤ 5 is expressed in the form |x-a|≤b, then the values of a and b are respectively

Let $A+B=\begin{bmatrix} 4&1&4\\1&4&4 \end{bmatrix}$and $B=\begin{bmatrix} 1&0&-2\\-1&3&0 \end{bmatrix}$, then A=

If x²² is in the (r+1)th term of the binomial expansion of (3x³-x²)⁹, then the value of r is equal to

If $\begin{vmatrix} 1&2&1\\0&x&-3\\2&-1&x \end{vmatrix}=0$, then the value of x are

The value of the determinant $\begin{vmatrix} 4&4^2&4^3\\3&3^2&3^3\\2&2^2&2^3 \end{vmatrix}$is