List of practice Questions

If an equilateral triangle \( \triangle ABC \) has one side of 12 cm, and another equilateral triangle \( \triangle DEF \) has one side of 6 cm, then what is the ratio of their areas?
In \( \triangle ABC \) and \( \triangle PQR \), which are similar triangles, \( AD \) is perpendicular to \( BC \) and \( PT \) is perpendicular to \( QR \). If \( AD = 9 \) cm and \( PT = 7 \) cm, then the ratio of the areas of triangles \( ABC \) and \( PQR \) is:
If one side of an equilateral triangle is 12 cm, then its height is:
The distance between two parallel tangents of a circle is 10 cm. Then the radius of the circle is:
If two circles touch each other externally, then what is the number of common tangents?
From an external point \( P \), two tangents \( PA \) and \( PB \) are drawn to a circle. If \( PA = 6 \) cm, then \( PB \) is:
If three points are collinear then what is the area of the triangle formed by them?
If \( A(-1,0) \), \( B(5,-2) \), and \( C(8,2) \) are the vertices of a triangle \( \triangle ABC \), then the coordinates of its centroid are:
If in \( \triangle ABC \), \( AD \) is the bisector of \( \angle BAC \) and \( AB = 10 \) cm, \( AC = 14 \) cm, \( BC = 6 \) cm, then the value of \( DC \) is:
In \( \triangle ABC \), \( DE \parallel BC \) such that \( \frac{AD}{DB} = \frac{3}{5} \). If \( AC = 5.6 \) cm, then \( AE \) is:
If the ratio of corresponding sides of two similar triangles is \( 5:6 \), then the ratio of their perimeters is:
In \( \triangle ABC \), \( AB = 6\sqrt{3} \) cm, \( AC = 12 \) cm, and \( BC = 6 \) cm, then \( \angle B \) is:
If \( P \left( \frac{a}{2}, 4 \right) \) is the midpoint of the line segment joining the points \( A(-6,5) \) and \( B(-2,3) \), then the value of \( a \) is:
At temperature \( T \) (K), the equilibrium constant \( K_c \) for the reaction: \[ A_2(g) \rightleftharpoons B_2(g) \] is 99.0. Two moles of \( A_2(g) \) were heated in a 1L closed flask to reach equilibrium. What are the equilibrium concentrations (in \( mol \ L^{-1} \)) of \( A_2(g) \) and \( B_2(g) \)?
Explain the advantages and disadvantages of modern mass media.
Write a note on the change and development of industrial society in India.
What is called ‘social survey’? State its main objectives.
Define the interview method and explain its main advantages.
What effect did globalisation have on employment opportunities? Clarify.
Discuss the changing forms of the means of mass communication.
Clarify the main reasons of women movement.
Describe the theory of demographic transition.
Discuss the government efforts made for the Divyangas.
“Indian society and structure provides us a social map.” Explain.
What do you understand by `colonialism`? Discuss its effects.