List of practice Questions

General Solution of the differential equation:
\(cos\,x(1+cos\,y)dx-sin\,y(1+sin\,x)dy=0\) is:

Area of the Region bounded by the curve y=√49-x2 and x-axis is .

Considering only the principal value of an inverse function, the set: A= { x ≥ 0, tan-1x + tan-16x = \(\frac{\pi}{4}\)}, then A is... 
 

If the line ax+by+c=0 is a normal to the curve xy=1, then 
 

The differential equation dy/dx=√1-y2/y determines a family of circles with

The number of solutions of tanx+secx=2cosx, n(0,2π) are?

The Points (1,3), (5,1) are Opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line y=2x+c, then one of the vertex on the other diagonal is? 
 
A particle is in uniform circular motion. Related to one complete revolution of the particle, which among the stataments is incorrect ?
When light propagates through a given homogeneous medium, the velocities of
 
'L' in the above sequence of reaction is/are(where L≠M≠N)
Five capacitors each of value 1 μF are connected as shown in the figure. The equivalent capacitance between A and B is
Five capacitors each of value 1 μF
In the following equation representing β- decay, the number of neutrons in the nucleus X is
\(_{83}^{210}\text{Bi}\rightarrow X+e^{-1}+\bar{v}\)
A parallel plate capacitor of capacitance C1 with a dielectric slab in between its plates is connected to a battery. It has a potential difference V1 across its plates. When the dielectric slab is removed, keeping the capacitor connected to the battery, the new capacitance and potential difference are C2 and V2 respectively. Then,
100 g of ice at 0 °C is mixed with 100 g of water at 100 °C. The final temperature of the mixture is
[Take Lf= 3.36 × 105 J kg-1 and Sw = 4.2 × 103 J kg-1 k-1]
Study the following information to answer the given question :
A, B, C, D, E, F, G and H are eight family members sitting around a circle facing towards the
centre.
(i)H is on the immediate left of A but is not the neighbour of E or D.
(ii)F is on the immediate right of B and G is the neighbour of E.
(iii) C is between E and F.
What is the position of D?

If nCr denotes the number of combinations of n distinct things taken r at a time, then the domain of the function g (x)= (16-x)C(2x-1)  is

A body of mass 10 kg is kept on a horizontal surface. The coefficient of kinetic friction between the body and the surface is 0.5. A horizontal force of 60N is applied on the body. The resulting acceleration of the body is about
Let F: R3 →R2 be the linear map defined by F(x, y, z) = (3x+2y-4z, x-5y+3z). The basis of R3 is S and basis of R2 is S', where S = {(1, 1, 1), (1, 1, 0), (1, 0, 0)} and S' = {(1, 3), (2, 5)}. Then the matrix of F in the bases of R3 and R2 is
For which toy category has there been a continuous increase in production over the years?
If A and B are events such that P(A)=\(\frac{1}{4}\), P(A/B)=\(\frac{1}{2}\) and P(B/A)=\(\frac{2}{3}\) then P(B) is
A variable force \(F=5x\) \(N\) acts on a body moving along x-axis. Find the work done by this force in displacing the body from \(x=2\) m to \(x=4\) m.
(K is constant)
The number of protons, neutrons and electrons in the ion \(^{32}_{16}S^{2-}\) respectively are
Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is:
Let f(x)=[x2]sinπx, x>0. Then

The area (in square units) of the region bounded by the curve y = |sin2x| and the X-axis in [0,2π] is