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प्र: In how many ways the letters of the word 'DESIGN' can be arranged so that no consonant appears at either of the two ends? 1276 0

उत्तर : 3. "48"
व्याख्या :
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

प्र: How many words can be formed with or without meaning by using three letters out of k, l, m, n, o without repetition of alphabets. 1276 0

उत्तर : 1. "60"
व्याख्या :
Answer: A) 60 Explanation: Given letters are k, l, m, n, o = 5 number of letters to be in the words = 3 Total number of words that can be formed from these 5 letters taken 3 at a time without repetation of letters = 5P3 ways. ⇒ 5P3 = 5 x 4 x 3 = 60 words.

प्र: A number is 2 more than thrice the second number and 4 times the smaller number is 5 more than the greater number. What is greater number ? 1276 0

उत्तर : 2. "23"
व्याख्या :
Answer: B) 23 Explanation: Let the greater and smaller number be p and q respectively. 4q = p + 5 ------ (I) p = 3q+2 ------- (II) From equation (I) and (II) q = 7 p = 23

प्र: A contractor undertake to finish a certain work in 124 days and employed 120 men. After 64 days, he found that he had already done 2/3 of the work. How many men can be discharged so that the work may finish in time ? 1274 0

उत्तर : 4. "56"
व्याख्या :
Answer: D) 56 Explanation: Days remaining 124 – 64 = 60 days Remaining work = 1 - 2/3 = 1/3 Let men required men for working remaining days be 'm' So men required = (120 x 64)/2 = (m x 60)/1 => m = 64 Men discharge = 120 – 64 = 56 men.

प्र: 3/4 divided by 2 is 1271 0

उत्तर : 4. "3/8"
व्याख्या :
Answer: D) 3/8 Explanation: 3/4 divided by 2 = 3/4/2 = 3/4x2 = 3/8. Hence, 3/4 divided by 2 is equal to 3/8.

प्र: In How many ways can the letters of the word 'CAPITAL' be arranged in such a way that all the vowels always come together? 1270 0

उत्तर : 1. "360"
व्याख्या :
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

प्र: The price of 2 oranges, 3 bananas and 4 apples is Rs. 15. The price of 3 oranges, 2 bananas and 1 apple is Rs. 10. What will be price of 4 oranges, 4 bananas and 4 apples ? 1269 0

उत्तर : 3. "Rs. 20"
व्याख्या :
Answer: C) Rs. 20 Explanation: Let the Oranges be 'O', Bananas be 'B' and Apples be 'A' From the given data, 2O + 3B + 4A = 15 ...... (I) 3O + 2B + A = 10 ..... (II) On adding (I) and (II), 5O + 5B + 5A = 25 O + B + A = 5 4O + 4B + 4A = 20.

प्र: Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32 , then p lies in the interval ? 1268 0

उत्तर : 3. "[1, 1/2]"
व्याख्या :
Answer: C) [1, 1/2] Explanation: Probability of atleast one failure= 1 - no failure > 31/32= 1 - P5 > 31/32= P5<1/32= p < 1/2Also p > 0Hence p lies in [0,1/2].

प्र: In how many ways the letters of the word 'DESIGN' can be arranged so that no consonant appears at either of the two ends? 1276 05b5cc7b4e4d2b41977750892

उत्तर : 3. "48" व्याख्या :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

प्र: How many words can be formed with or without meaning by using three letters out of k, l, m, n, o without repetition of alphabets. 1276 05b5cc6abe4d2b4197774d058

प्र: A number is 2 more than thrice the second number and 4 times the smaller number is 5 more than the greater number. What is greater number ? 1276 05b5cc6c9e4d2b4197774df9c

उत्तर : 2. "23" व्याख्या :Answer: B) 23 Explanation: Let the greater and smaller number be p and q respectively. 4q = p + 5 ------ (I) p = 3q+2 ------- (II) From equation (I) and (II) q = 7 p = 23

प्र: A contractor undertake to finish a certain work in 124 days and employed 120 men. After 64 days, he found that he had already done 2/3 of the work. How many men can be discharged so that the work may finish in time ? 1274 05b5cc6cce4d2b4197774e16c

उत्तर : 4. "56" व्याख्या :Answer: D) 56 Explanation: Days remaining 124 – 64 = 60 days Remaining work = 1 - 2/3 = 1/3 Let men required men for working remaining days be 'm' So men required = (120 x 64)/2 = (m x 60)/1 => m = 64 Men discharge = 120 – 64 = 56 men.

प्र: 3/4 divided by 2 is 1271 05b5cc666e4d2b4197774bed0

उत्तर : 4. "3/8" व्याख्या :Answer: D) 3/8 Explanation: 3/4 divided by 2 = 3/4/2 = 3/4x2 = 3/8. Hence, 3/4 divided by 2 is equal to 3/8.

प्र: In How many ways can the letters of the word 'CAPITAL' be arranged in such a way that all the vowels always come together? 1270 05b5cc7b4e4d2b41977750897

उत्तर : 1. "360" व्याख्या :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

प्र: The price of 2 oranges, 3 bananas and 4 apples is Rs. 15. The price of 3 oranges, 2 bananas and 1 apple is Rs. 10. What will be price of 4 oranges, 4 bananas and 4 apples ? 1269 05b5cc6c9e4d2b4197774df5a

उत्तर : 3. "Rs. 20" व्याख्या :Answer: C) Rs. 20 Explanation: Let the Oranges be 'O', Bananas be 'B' and Apples be 'A' From the given data, 2O + 3B + 4A = 15 ...... (I) 3O + 2B + A = 10 ..... (II) On adding (I) and (II), 5O + 5B + 5A = 25 O + B + A = 5 4O + 4B + 4A = 20.

प्र: Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32 , then p lies in the interval ? 1268 05b5cc71ee4d2b4197774f5c7

उत्तर : 3. "[1, 1/2]" व्याख्या :Answer: C) [1, 1/2] Explanation: Probability of atleast one failure= 1 - no failure > 31/32= 1 - P5 > 31/32= P5<1/32= p < 1/2Also p > 0Hence p lies in [0,1/2].

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प्र: In how many ways the letters of the word 'DESIGN' can be arranged so that no consonant appears at either of the two ends? 1276 0

उत्तर : 3. "48"
व्याख्या :
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

प्र: How many words can be formed with or without meaning by using three letters out of k, l, m, n, o without repetition of alphabets. 1276 0

प्र: A number is 2 more than thrice the second number and 4 times the smaller number is 5 more than the greater number. What is greater number ? 1276 0

उत्तर : 2. "23"
व्याख्या :
Answer: B) 23 Explanation: Let the greater and smaller number be p and q respectively. 4q = p + 5 ------ (I) p = 3q+2 ------- (II) From equation (I) and (II) q = 7 p = 23

प्र: A contractor undertake to finish a certain work in 124 days and employed 120 men. After 64 days, he found that he had already done 2/3 of the work. How many men can be discharged so that the work may finish in time ? 1274 0

उत्तर : 4. "56"
व्याख्या :
Answer: D) 56 Explanation: Days remaining 124 – 64 = 60 days Remaining work = 1 - 2/3 = 1/3 Let men required men for working remaining days be 'm' So men required = (120 x 64)/2 = (m x 60)/1 => m = 64 Men discharge = 120 – 64 = 56 men.

प्र: 3/4 divided by 2 is 1271 0

उत्तर : 4. "3/8"
व्याख्या :
Answer: D) 3/8 Explanation: 3/4 divided by 2 = 3/4/2 = 3/4x2 = 3/8. Hence, 3/4 divided by 2 is equal to 3/8.

प्र: In How many ways can the letters of the word 'CAPITAL' be arranged in such a way that all the vowels always come together? 1270 0

उत्तर : 1. "360"
व्याख्या :
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

प्र: The price of 2 oranges, 3 bananas and 4 apples is Rs. 15. The price of 3 oranges, 2 bananas and 1 apple is Rs. 10. What will be price of 4 oranges, 4 bananas and 4 apples ? 1269 0

उत्तर : 3. "Rs. 20"
व्याख्या :
Answer: C) Rs. 20 Explanation: Let the Oranges be 'O', Bananas be 'B' and Apples be 'A' From the given data, 2O + 3B + 4A = 15 ...... (I) 3O + 2B + A = 10 ..... (II) On adding (I) and (II), 5O + 5B + 5A = 25 O + B + A = 5 4O + 4B + 4A = 20.

प्र: Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32 , then p lies in the interval ? 1268 0

उत्तर : 3. "[1, 1/2]"
व्याख्या :
Answer: C) [1, 1/2] Explanation: Probability of atleast one failure= 1 - no failure > 31/32= 1 - P5 > 31/32= P5<1/32= p < 1/2Also p > 0Hence p lies in [0,1/2].