All questions
- Let Ui = 1 Xi for i ∈ 50 = Ui = 1 for i ∈ n Yi = T, where each Xi contains 10 elements and each Yi contains 5 elements. Correct answer is 30 EXplaination: n(X_i) = 10. U_(i = 1 )X_i for i ∈ 50 = T, n (T) = 500 each element of T belongs to exactly 20 elements o... 1
- A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. Answer is 36 Note**then x cannot be: C > person like coffee T > Person like Tea n(C)=73 n(T) =65 n(C U T) ≤ 100 n(C)+n(T) -n(C ∩ T) ≤ 100 73... 1
- Set A has m elements and Set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets Correct answer is 28 Explaination: No. of subsets of A=2m No. of subsets of B=2n 2^m=2ⁿ+112 2^m−2ⁿ=112 2ⁿ(2^(m−n)−1)=112 2ⁿ(2^(m−n)−1)=2⁴(2³... 1
- In a college of 300 students, every student read 5 newspaper and every newspaper is read by 60 students. Correct option is C) Exactly 25 Let the number of newspapers be x. If every student reads one newspaper, the number of students would be x (... 1
- 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... 1
- 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... 1
- 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) =... 1
- 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... 1
- 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 1
- 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.... 1
- 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 ∪... 1
- 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 ∴... 1
- 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... 1
- 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 2
- 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 2
- 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 2
- 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 2
- 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 1
- 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 1
- 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 2
- Measures of some angles in the figure are given. Prove that APPB = AQQC Proof in this video https://youtu.be/UCQKZkO2w6A 1
- 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 2
- 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 2
- 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 1