List of top Questions asked in KEAM

The angle of minimum deviation for a prism of apex angle 60° and refractive index of \(\sqrt{2}\) is:

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 ?

Suppose \(A=\begin{bmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{bmatrix}\) is an adjoint of the matrix \(\begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{bmatrix}\). Then the value of \(\frac{a_!+b_2+c_3}{b_1a_2}\) 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

An average frictional force of 80N is required to stop an object at a distance of 25m. If the initial speed of the object is 20m/s,the mass of the object 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

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

\(∫\dfrac{x+5}{x^{2}+1}dx=\)

Let α and β be such that α+β=π. If \(\cos\alpha=\frac{1}{\sqrt2}\), then the value of cot (β-α) is

If f(z)=zⁿ+a_n-1z^n-1 +......+a₁zⁿ+a₀ ∈ R[z] is a polynomial in z with no root over R,then deg(f)is

An inductor coil with an internal resistance of 50 Ω stores magnetic field energy 180 mJ and dissipates energy as heat at the rate of 200 W when a constant current 9 passed through it. The inductance of the coil will be:

If \(x\) is a real number such that \(tanx+cotx=2\),then \(x=\)?

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:

In a Zener regulated power supply circuit as shown in figure below,a Zener diode with V_z=1OV is used for regulation. The load current,Zener current and unregulated input V_in are 5mA,35mA and 20V,respectively. The value of R is:

A car moving with a velocity of 10m/s can be stopped by the application of a constant force F in a distance of 20m. If the velocity of the car is 30m/s. It can be stopped by this force in

The value of a(≠0) for which the equation \(\frac{1}{2}(x-2)^2+1=\sin(\frac{a}{x})\) holds is/are

If \( α,β,γ\) are the cube roots of \(-2\) ,then the value of \(xα+yβ+zγ/xβ+yγ+zα\) is (\(x,y,z\) are variables)

A billiard ball of mass ‘M’ moving with velocity ‘v₁’ collides with another ball of the same mass but at rest. If the collision is elastic the angle of divergence after the collision is

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

A Simple pendulum experiment is performed for the value of 'g',the acceleration due to the earth's gravity. The measured value of length of the pendulum is 25 cm with an accuracy of 1 mm and the measured time for 100 oscillations is found to be 100 sec with an accuracy of 1 sec. The percentage uncertainty in the determination of 'g' is:

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

\(∫sin^2 πx dx =\)?

Let \(f:R→R\) be a function defined by
\(f(x) = \begin{cases} 3e^x & \quad \text {if}\ {x<0}\\ x^2+3x+3 & \quad \text {if}\ 0≤x<1 \\ x^2-3x-3 & \quad \text {if} \ x≥1\end{cases}\)

Let \(f(x)=\dfrac{x-1}{x+1}\) ,Let \(S ={x∈R \text{ Iff } -1(x)=x \text{ does not hold} }\).The cardinality of S is

If\( \dfrac{1+sinx}{1-sinx}=\dfrac{(1+siny)^3}{(1-siny)^3}\) for some real values \(x\) and \(y\) ,then \(\dfrac{sinx}{siny}\)=

List of top Questions asked in KEAM

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