A concave lens of focal length \(25~\text{cm}\) produces an image \(\frac{1}{10}\text{th}\)$$ of the size of the object. The distance of the object from the lens is:

A lens forms an image of a point object placed at distance \(20~\text{cm}\) from it. The image is formed just in front of the object at a distance \(4~\text{cm}\) from the object (and towards the lens). The power of the lens is:
1. \(-2.25~\text D\) 
2. \(1.75~\text D\) 
3. \(-1.25~\text D\) 
4. \(1.4~\text D\) 

In the diagram shown below, the image of the point object \(O\) is formed at \(l\) by the convex lens of focal length \(20~\text{cm},\)  where \(F_1\) and \(F_2\) are foci of the lens. The value of \(x'\) is:
        

A thin equiconvex lens of power \(P\) is cut into three parts \(A,B,\) and \(C\) as shown in the figure. If \(P_1,P_2\) and \(P_3\) are powers of the three parts respectively, then:
            

If the space between two convex lenses of glass in the combination shown in the figure below is filled with water, then:
               

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length \(10\) cm. The diameter of the sun is \(1.39\times 10^9~\text{m}\) and its mean distance from the earth is \(1.5\times 10^{11}~\text{m}.\) What is the diameter of the sun's image on the paper?
1. \( 9.2 \times 10^{-4}~\text{m} \)
2. \(6.5 \times 10^{-4}~\text{m} \)
3. \(6.5 \times 10^{-5}~\text{m} \)
4. \( 12.4 \times 10^{-4}~\text{m} \)