TextBook Solutions
- Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b): | a – b | is even} A = {1, 2, 3, 4, 5} and R = {(a, b): | a – b | is even} R = {(1, 3), (1, 5), (3, 5), (2, 4), (3, 1), (5, 1), (5, 3), (4, 2)} (a) (i) Let us... 1
- Show that the relation R in the set A = [x ∈ Z : 0 ≤ x ≤ 12}, given by (i) R = {(a, b): | a – b | is a multiple of 4} The set A = {x ∈ Z : 0 ≤ x ≤ 12} = {0, 1, 2, ………, 12} (i) R = {(a, b): | a – b | is a multiple of 4} |a – b | = 4k or b = a + 4k. ∴ R = {(1,... 2
- Give examples of relations which are (i) Symmetric but neither reflexive nor transitive. (ii) Transitive but neither Let A = set of straight lines in a plane. (i) R : {(a, b): a is perpendicular to b] Let a and b be two perpendicular lines. (a) If line a is... 2
- Show that the relation R in the set A of points in a plane, given by R: {(P, Q): Let O be the origin, then the relation R = {(P, Q): OP = OQ} (i) R is reflexive. Take any distance OP. We know OP = OP. ∴ R is reflexive. (i... 1
- Show that the relation R, defined in the set A of all triangles as R = {(T1, T2) : T1 is similar to T2} (i) In a set of triangles, R = {(T1, T2): T1 is similar to T2}, (a) A triangle T1 is similar to itself. R is reflexive. (b) If triangle T1 i... 1
- Show that the relation R, defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 Let n be the number of sides of a polygon P1. R = {(P1, P2): P1 and P2 are n sided polygons}. (i) (a) Any polygon P1 has n sides ⇒ R is refl... 1
- Let L be the set of all the lines in XY-plane and R be the relation in L defined as R = {(L1, L2) L = Set of all the lines in XY-plane. R = {(L1, L2): L1 is parallel to L2} (i) (a) L1 is parallel to itself ⇒ R is reflexive. (b) L1 is para... 1
- Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1,1), (4,4), (1,3), (3, 3), (3, 2)} (b) R is reflexive and transitive but not symmetric. Explanation:: Let R be the relation with set {1,2, 3,4}, given by R = {(1,2), (2,2), (1... 1
- Let R be the relation in the set N given by R = {(a, b): a = b – 2, b > 6}. (C) (6, 8) ∈ R Explanation: According to given condition b>6 {.: option a cannot be answer and a is smaller than b therefore option d is als... 1
- The speed of light in a vacuum is 299,792,458 meters per second.
- The number of chromosomes in the shoot tip cells of a maize plant is 20. The number of chromosomes (a) 20 correct option is (a) 20 2
- Which of the following is a post-fertilisation event in flowering plants? (b) Embryo development 2
- There are various types of reproduction. The type of reproduction adopted by an organism depends on d) the organisms habitat, physiology and genetic makeup. 2
- There is no natural death in single celled organisms like Amoeba and bacteria because (c) parental body is distributed among the offspring 2
- Appearance of vegetative propagules from the nodes of plants such as sugarcane and ginger is mainly because (b) nodes have meristematic cells 2
- The male gametes of rice plant have 12 chromosomes in their nucleus. The chromosome number in the female gamete (c) 12, 24, 24 2
- The term ‘clone’ cannot be applied to offspring formed by sexual reproduction because (a) offspring do not possess exact copies of parental DNA 2
- The wall of the ovary forms (a) pericarp (b) fruit wall (c) fruit (d) both (a) and (b). (d) both (a) and (b). 2
- In which of the following plants, sepals do not fall off after fertilisation and remain attached to the fruit? (a) Brinjal is the correct option 2
- In flowering plants, both male and female gametes are non-motile. The method to bring them together c) pollination 2
- If a butterfly has chromosome number 360 in its meiocyte (2n). What will be the chromosome number in its gametes? (b) 190 is correct option 2
- In maize, a meiocyte has 20 chromosomes. What will be the number of chromosomes in its somatic cell? (c) 20 is correct option 2
- Which of the following organisms has the highest number of chromosomes? (c) Ophioglossum 2
- A diploid parent plant body produces ________ gametes and a haploid parent plant body produces ________ gametes. (d) haploid, haploid 2