State the reasons for the following.
(i) A square is a special kind of a rectangle.
(ii) A rhombus is a special kind of a parallelogram.
(iii) A rhombus and a kite have one common property.
(iv) A square and a rhombus have one common property.

Let P ,Q ,R and S be the points on the plane with position vectors -2i-j ,4i ,3i+3ja n d-3j+2j , respectively. The quadrilateral P Q R S must be a Parallelogram, which is neither a rhombus nor a rectangle Square Rectangle, but not a square Rhombus, but not a square

State which of the following sets are empty and which are not? (i) The set of lines passing through a given point. (ii) Set of odd natural numbers divisible by 2. (iii) {x : x is a natural number, x lt 5 and x gt 7} (iv) {x : x is a common point to any two parallel lines} (v) Set of even prime numbers.

Which of the following are reasons for Mendel's success ? (i) Usage of pure lines or pure breeding varieties (ii) Consideration of one character at a time (iii) Maintenance of statistical records of experiments (iv) Knowledge of linkage and incomplete dominance

Which of the following statements, support the view that elaborate sexual reproductive process appeared much later in the organic evolution ? (i) Lower groups of organisms have simpler body design. (ii) Asexual reproduction is common in lower groups. (iii) Asexual reproduction is common in higher groups of organisms. (iv) The high incidence of sexual reproduction in angiosperms and vertebrates. Choose the correct answer given below.

Four Tamil Nadu State transport buses take the following routes. The first is a one - way journey, and the rest are round trips. Find the places on the map, put points on them and connect them by lines to draw the routes. The places connecting four different routes are given as follows. (i) Nagercoil, Tiruneveli, Virudhnagar, Madurai (ii) Sivagangai, Puthukottai, Thanjavur, Dindigul (iii) Erode, Coimbatore, Dharmapuri, karur (iv) Chennai, Cuddalore, Krishnagiri, Vellore You will get the following shapes. Label the vertices with city names, draw the shapes exactly as they are shown on the map without rotations.

If S = {square, rectangle, circle, rhombus, triangle}, list the elements of the following subset of S. The set of shapes which have 5 sides.

mn squares of equal size are arranged to form a rectangle of dimension m by n, where m and n are natural numbers. Two square will be called neighbors if they have exactly one common side. A number is written in each square such that the number written in any square is the arithmetic mean of the numbers written in its neighboring squares. Show that this is possible only if all the numbers used are equal.