List of top Questions asked in KEAM- 2023

The minimum of \(f(x)=\sqrt{(10-x^2)}\) in the interval \([-3,2]\) is

For any real number \(x\), the least value of \(4cosx-3sinx+5\) is ?

A six faced fair die is rolled for a large number of times. Then, the mean value of the outcome is 
Suppose the point \(P(1,1)\) is translated to \(Q\) in the direction of y = 2x. If \(PQ = 1\),then Qis
A thin particle moves from \((0,1)\) and gets reflected upon hitting the x-axis at \((√3,0)\). Then the slope of the reflected line is ?

Let \(S=\){\(n∈NIn^3+3n^2+5n+3\) is not divisible by \(3\)}.Then, which of the following statements is true about \(S\)

If the median of the observations \(4,6,7,x,x+2,12,12,13\) arranged in an increasing order is 9,then the variance of these observations is 
If\( \dfrac{1+sinx}{1-sinx}=\dfrac{(1+siny)^3}{(1-siny)^3}\) for some real values \(x\) and \(y\) ,then \(\dfrac{sinx}{siny}\)=
Let \(a,b,c,d \) be an increasing sequence of real numbers,which are in geometric progression .If \(a+d=112\) and \(b+c=48\) ,then the value of \(\dfrac{a+c+8}{b}\) is 
In a linear programming problem ,the restrictions under which the objective function is to be optimized are called as?
The correct order of variation of first ionisation enthalpies is:
The number of S-S bonds and the number of lone pairs in S8 molecule,respectively,are:
Consider the Linear Programming Problem:
Minimize 3x1+4x2 +2x3
subject to
x1+x2+x3≤6
x1+2x2+x3≤10
x1,x2,x3≥0.
Then, the number of basic solutions are
Let the probability distribution of random variable X be
X-2-1123
P(X=x)k2k2kk3k

Then, the value of E(X2) is
The value of \(cos^{-1}(cos(\dfrac{7\pi}{4}))\) is 

A horizontal force is exerted on a 20 kg box to slide it up on an inclined plane with an angle of 30°. The frictional force retarding the motion is 80 N. If the box moves with a constant speed, then the magnitude of the force is:(Take g=10 ms-2)

If the \(XZ\)-plane divides the straight line joining the points \((2,4,7)\) and \((3,-5,8)\)  in the ratio \(α:1\),then the value of \(α\) is ? 
For any \(n≥0\) the value of \(\sum_{r=0}^n \dfrac{(4r+3).(nC_r)^2}{(2n+3)}\) is 
The set of points of the form(t^2+t+1,t^2-t+1),where t is a real number, represents a/an
A wheel is rolling on a plane surface. A point on the rim of the wheel at the same level as the Centre has a speed of 4m/s. The speed of the Centre of the wheel is:
The domain of the real valued function \(f(x)=\dfrac{√(x2−7x+6)}{√(​x2−4​+1)}\)  is

A projectile is thrown at a speed V and at an angle with the horizontal. If the speed at its maximum height is \(\frac{V}{3}\),then the value of tan θ is: 

\(\text{The value of    } cosec20°tan60°-sec20° \text{is }\)
Let \(k\) be a real number such that \(\sin \dfrac{3π}{14} \cos \dfrac{3π}{14} = k \cos \dfrac{π}{14}\).Then the value of \(4k\) is 
The number of electrons in one mole of methane: