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

1. 225 cm

2. 250 cm 

3. 150 cm 

4. 175 cm

Two convex lenses of focal lengths 10 cm and 30 cm are kept at a separation of 20 cm. Then the correct statement is:

A biconvex lens is cut into two halves along (i) XOX' and (ii) YOY' as shown in the figure. Let \(f\), \(f'\) \(f''\) be the focal lengths of the complete lens, of each half in case (i), and of each half in case (ii), respectively.
   
Choose the correct statement from the following:

A lens forms an image of a point object placed at distance 20 cm from it. The image is formed just in front of the object at a distance 4 cm from the object (and towards the lens). The power of the lens is:

1.  $-$2.25 D

2.  1.75 D

3.  $-$1.25 D

4.  1.4 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 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 P₁, P₂, and P₃ are powers of the three parts respectively, then:

Two convex lenses of focal length X and Y are placed parallel to each other. An object at infinity from the first lens forms its image at infinity from the second lens. The separation between the two lenses should be:

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 $1.5\times {10}^{11}$ $m$. What is the diameter of the sun's image on the paper?
1. \( 9.2 \times 10^{-4} \mathrm{~m} \)
2. \(6.5 \times 10^{-4} \mathrm{~m} \)
3. \(6.5 \times 10^{-5} \mathrm{~m} \)
4. \( 12.4 \times 10^{-4} \mathrm{~m}\)