Practice Question and Answer
8Q: In a plane 8 points are colliner out of 12 points, then the number of triangles we get with those 12 points is 1208 05b5cc7b4e4d2b419777508ab
5b5cc7b4e4d2b419777508ab- 120false
- 2160false
- 3164true
- 4220false
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Answer : 3. "164"
Explanation :
Answer: C) 164 Explanation: For a triangle, we need 3 non-collinear points. So with 12 points (when all the 12 are such that any three non-collinear is12C3. But among them 8 points are collinear. If all these 8 points are different we get 8C3 triangles as they are collinear. In 12C3 triangles, we do not get 8C3 triangles Therefore, The number of triangles we get = 12C3-8C3 = 164
Q: If A1, A2, A3, A4, ..... A10 are speakers for a meeting and A1 always speaks after, A2 then the number of ways they can speak in the meeting is 1672 05b5cc7b4e4d2b419777508a6
5b5cc7b4e4d2b419777508a6- 19!false
- 29!/2false
- 310!false
- 410!/2true
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Answer : 4. "10!/2"
Explanation :
Answer: D) 10!/2 Explanation: As A1 speaks always after A2, they can speak only in 1st to 9th places and A2 can speak in 2nd to 10 the places only when A1 speaks in 1st place A2 can speak in 9 places the remaining A3, A4, A5,...A10 has no restriction. So, they can speak in 9.8! ways. i.e when A2 speaks in the first place, the number of ways they can speak is 9.8!. When A2 speaks in second place, the number of ways they can speak is 8.8!. When A2 speaks in third place, the number of ways they can speak is 7.8!. When A2 speaks in the ninth place, the number of ways they can speak is 1.8! Therefore,Total Number of ways they can speak = (9+8+7+6+5+4+3+2+1) 8! = 92(9+1)8! = 10!/2
Q: The number of ways that 7 teachers and 6 students can sit around a table so that no two students are together is 1502 05b5cc7b4e4d2b419777508a1
5b5cc7b4e4d2b419777508a1- 17! x 7!false
- 27! x 6!true
- 36! x 6!false
- 47! x 5!false
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Answer : 2. "7! x 6!"
Explanation :
Answer: B) 7! x 6! Explanation: The students should sit in between two teachers. There are 7 gaps in between teachers when they sit in a roundtable. This can be done in 7P6ways. 7 teachers can sit in (7-1)! ways. Required no.of ways is = 7P6.6! = 7!.6!
Q: The number of ways that 8 beads of different colours be strung as a necklace is 2423 05b5cc7b4e4d2b4197775089c
5b5cc7b4e4d2b4197775089c- 12520true
- 22880false
- 34320false
- 45040false
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Answer : 1. "2520"
Explanation :
Answer: A) 2520 Explanation: The number of ways of arranging n beads in a necklace is (n-1)!2=(8-1)!2=7!2 = 2520 (since n = 8)
Q: In How many ways can the letters of the word 'CAPITAL' be arranged in such a way that all the vowels always come together? 1294 05b5cc7b4e4d2b41977750897
5b5cc7b4e4d2b41977750897- 1360true
- 2720false
- 3120false
- 4840false
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Answer : 1. "360"
Explanation :
Answer: A) 360 Explanation: CAPITAL = 7 Vowels = 3 (A, I, A) Consonants = (C, P, T, L) 5 letters which can be arranged in 5P5=5! Vowels A,I = 3!2! No.of arrangements = 5! x 3!2!=360
Q: In how many ways the letters of the word 'DESIGN' can be arranged so that no consonant appears at either of the two ends? 1295 05b5cc7b4e4d2b41977750892
5b5cc7b4e4d2b41977750892- 1240false
- 272false
- 348true
- 436false
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Answer : 3. "48"
Explanation :
Answer: C) 48 Explanation: DESIGN = 6 letters No consonants appear at either of the two ends. = 2 x 4P4 = 2 x 4 x 3 x 2 x 1= 48
Q: Using numbers from 0 to 9 the number of 5 digit telephone numbers that can be formed is 1474 05b5cc7b4e4d2b4197775088d
5b5cc7b4e4d2b4197775088d- 11,00,000false
- 259,049false
- 33439true
- 46561false
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Answer : 3. "3439"
Explanation :
Answer: C) 3439 Explanation: The numbers 0,1,2,3,4,5,6,7,8,9 are 10 in number while preparing telephone numbers any number can be used any number of times. This can be done in 105ways, but '0' is there So, the numbers starting with '0' are to be excluded is 94 numbers. Total 5 digit telephone numbers = 105- 94 = 3439
Q: The Kulu Valley is situated between 8120 05b5cc7b4e4d2b41977750888
5b5cc7b4e4d2b41977750888- 1Ladakh and Pirpanjalfalse
- 2Ranjoti and Nag Tibbafalse
- 3Lesser Himalayas Siwalikfalse
- 4Dhauladar and Pirpanjaltrue
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Answer : 4. "Dhauladar and Pirpanjal"
Explanation :
Answer: D) Dhauladar and Pirpanjal Explanation: