All questions

• If A = [(x, y) : x2 + y2 = 25] and B = [(x, y) : x2 + 9y2 = 144], then A ∩ B contains _______ points. A = Set of all values (x, y) : x2 + y2 = 25 = 52 B = [x2 / 144] + [y2 / 16] = 1 i.e., [x2 / (12)2] + [y2 / (4)2] = 1. Clearly, A ∩ B consist... SETS, RELATIONS AND FUNCTIONS 1 answer
• Let A = {θ : tanθ + secθ = √2secθ} and B = {θ : secθ - tanθ = √2tanθ} be two sets then. (a) A = B (b) A ⊂ B (c) A ≠ B (d) B ⊂ A Correct option is A) A=B Explaination: tan θ + sec θ = √2 sec θ sin θ = √2 – 1 sec θ – tan θ = √2 tan θ sin θ = 1 / (√2 + 1) sin θ = √2 – 1... SETS, RELATIONS AND FUNCTIONS 1 answer
• In a certain town 30% families own a scooter and 40% on a car 50% own neither a scooter nor a car 2000 families The correct option (d) 1 and 3 Explanation: Suppose x families live in the town A = {families have scooter} B = {families have car} ∴ n(A) =... SETS, RELATIONS AND FUNCTIONS 1 answer
• Let X = {x, y, z} / x, y, z ∈ N, x + y + z = 10, {x < y < z } and Y = {(x, y, z) / x, y, z ∈ N, y = | x - z |} then X ∩ Y is equal to The correct option (d) {(2, 3, 5), (1, 4, 5)} Explanation: X = {(1, 2, 7), (1, 3, 6), (1, 4, 5), (2, 3, 5)} element of X which belong to Y a... SETS, RELATIONS AND FUNCTIONS 1 answer
• If two sets A and B are having 43 elements in comman, then the number of elements common to each of the sets A x B and B x A is The correct option (a) 43² Explanation: n((A x B) ∩ (B x A)) = n((A ∩ B) x (B ∩ A)) = n(A ∩ B) . n(B ∩ A) = 43 x 43 = 43² SETS, RELATIONS AND FUNCTIONS 1 answer
• If X ∪ {3, 4} = {1, 2, 3, 4, 5, 6}  the which of the following is true  (a) Smallest set X = {1, 2, 5, 6}  (b) Smallest set X = {1, 2, 3, 5, 6}  (a) Smallest set X = {1, 2, 5, 6} EXplaination: X ∪ {3, 4} = {1, 2, 3, 4, 5, 6} Then the Smallest set of X will be X ∪ {3, 4} – {3, 4} i.e.... SETS, RELATIONS AND FUNCTIONS 1 answer
• A survey shows that 70% of the Indian like mango where 82% like apple. If x% of Indian like both mango and apples then The correct option (b) 52 ≤ x ≤ 70 Explanation: n(A) = 70 n(B) = 82 n(A ∩ B) = x n(A ∪ B) = n(A) + n(B) – n(A ∩ B) ⇒ n(A ∩ B) = 152 – n(A ∪... SETS, RELATIONS AND FUNCTIONS 1 answer
• Two finite sets have m and n element respectively. The total number of subsets of first set is 112 more than the total number of sub sets of the second set. (c) 7, 4 No. of subset of first set – No of subset of second set = 112 ∴ 2^m – 2ⁿ = 112 ∴ 2ⁿ(2^(m–n) – 1) = 112 ∴ 2ⁿ(2^(m–n) – 1) = 2⁴ × 7 ∴... SETS, RELATIONS AND FUNCTIONS 1 answer
• If aN = {ax/x ∈ N} and bN ∩ cN = dN Where b, c ∈ N are relatively prime then (a) d = bc aN = {ax/x ∈ N} bN = {bx/x ∈ N} = the set of positive integers multiple of b cN = {cx/x ∈ N} = the set of positive integers multi... SETS, RELATIONS AND FUNCTIONS 1 answer
• In ∆ABC, ray BD bisects ∠ABC and ray CE bisects ∠ACB. If seg AB = seg AC, then prove that ED || BC Watch complete video and understand https://youtu.be/MGVjoeMgblM Similarity 2 answers
• In the adjoining figure, X is any point in the interior of triangle. Point X is joined to vertices of triangle. Seg PQ || seg DE, seg QR || seg EF. Watch till end and understand topic https://youtu.be/GKMhr5NSd8U Similarity 2 answers
• In ∆ABC,seg BD bisects ∠ABC. If AB = x,BC x+ 5, AD = x – 2, DC = x + 2, then find the value of x. x=10 https://youtu.be/qmV-xkI5hlQ Similarity 2 answers
• In ∆LMN, ray MT bisects ∠LMN. If LM = 6, MN = 10, TN = 8, then find LT. Correct Answer is LT=4.8 units https://youtu.be/V6lBZ3c0Hjw Similarity 2 answers
• In the adjoining figure, if AB || CD || FE, then find x and AE. Correct answer is x=6 and AE=18 units https://youtu.be/40WyRKKZ-P0 Similarity 1 answer
• Find QP using given information in the figure. geometry 10th similarity ex 1.2 q6 Answer is 22.4 units https://youtu.be/jUVX-PkzvP4 Similarity 1 answer
• In trapezium ABCD, side AB || side PQ || side DC, AP = 15, PD = 12, QC = 14, find BQ. Answer is 17.5 units https://youtu.be/CcaZK-Xttpg Similarity 2 answers
• Measures of some angles in the figure are given. Prove that APPB = AQQC Proof in this video https://youtu.be/UCQKZkO2w6A Similarity 1 answer
• In ∆MNP, NQ is a bisector of ∠N. If MN = 5, PN = 7, MQ = 2.5, then find QP. QP= 3.5 units https://youtu.be/4AH6mOn1r0I Similarity 2 answers
• In ∆PQR PM = 15, PQ = 25, PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason. it is prooved by Converse of Basic propertionality theorem https://youtu.be/eUKCnwjkNEc Similarity 2 answers
• Given below are some triangles and lengths of line segments. Identify in which figures, ray PM is the bisector of ∠QPR Answer:: Yes , NO , Yes Solution:: https://youtu.be/wo9-RFWTlo8 Similarity 1 answer
• In adjoining figure PQ ⊥ BC, AD ⊥ BC then find following ratios. Q5 All Question is solved https://youtu.be/nxzNVLMMEl8 Similarity Notes :: https://drive.google.com/file/d/13YAVLNHcjPc5z6tYxvFIr0L1SzAw8i6R/vi... Similarity 1 answer
• In adjoining figure, AP ⊥ BC, AD || BC, then find A(ΔABC) : A (ΔBCD) Correct answer is 1:1 https://youtu.be/usckRy2WdA0 Similarity 2 answers
• In adjoining figure 1.14 seg PS ⊥ seg RQ , seg QT ⊥ seg PR. If RQ = 6, PS = 6 and PR = 12, then find QT. Correct answer is 3 Similarity 1 answer
• If figure 1.13 BC ⊥ AB, AD ⊥ AB, BC = 4, AD = 8, then find A(△ ABC)/A(△ADB) Correct answer is 1/2 or 1:2 https://youtu.be/SW96gvgg-fo Similarity Notes :: https://drive.google.com/file/d/13YAVLNHcjPc5z6tYxvFIr0L1SzAw8... Similarity 1 answer