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For all x, x2 + 2ax + (10 − 3a) > 0, then the interval in which a lies, is?

  • a)
    a < -5

  • b)
    a > 5

  • c)
    -5 < a < 2

  • d)
    2 < a < 5

  • e)
    a < -2

Correct answer is option 'C'. Can you explain this answer?
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For all x,x2+ 2ax + (10 − 3a) > 0, then the interval in which...
In f(x) = ax2 + bx + c
When a > 0 and D < 0
Then f(x) is always positive.
x2 + 2ax + 10 − 3a > 0, ∀x ∈ R
⇒ D < 0
⇒ 4a2 − 4(10 − 3a) < 0
⇒ a2 + 3a − 10 < 0
⇒ (a+5)(a−2) < 0
⇒ a ∈ (−5,2)
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For all x,x2+ 2ax + (10 − 3a) > 0, then the interval in which...
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Directions: Study the following information and answer the given questions.In a numeric series, all the even numbers are represented as the sum of digits of its square and if the sum consists of more than 1 digit then again add the digits (For Ex. 8 square is 64 then the sum is 10 hence, 8 is coded as 1 (1 + 0)). All the odd numbers are represented as consecutive 5th alphabet of the alphabetical series starting from E (For ex. 1 is coded as E, 3 is coded as J)In coded language:“42765” is coded as - 74T9ONow following operations are to be applied to the coded number:I. If the number formed by adding all the digits in the coded number is divisible by 3 then all the digits must be again coded as the corresponding alphabets of all those digits.II. If there is any prime number in the coded form then they are to be coded as $.III. If there is more than 1 vowel in the coded number then all those vowels must be replaced with the next alphabet.IV. If the coded form starts and ends with a consonant then they must be interchanged.If the coded form does not satisfy the conditions given above then it should be kept as it is.If both the conditions, I and II are satisfied then directions given in condition I must be followed and accept this if any two or three conditions are satisfied at the same time then the directions given in all the conditions must be followed.Q. How many consonants will be there in the coded form of “68581247818” after applying the given conditions?

Directions: Study the following information and answer the given questions.In a numeric series, all the even numbers are represented as the sum of digits of its square and if the sum consists of more than 1 digit then again add the digits (For Ex. 8 square is 64 then the sum is 10 hence, 8 is coded as 1 (1 + 0)). All the odd numbers are represented as consecutive 5th alphabet of the alphabetical series starting from E (For ex. 1 is coded as E, 3 is coded as J)In coded language:“42765” is coded as - 74T9ONow following operations are to be applied to the coded number:I. If the number formed by adding all the digits in the coded number is divisible by 3 then all the digits must be again coded as the corresponding alphabets of all those digits.II. If there is any prime number in the coded form then they are to be coded as $.III. If there is more than 1 vowel in the coded number then all those vowels must be replaced with the next alphabet.IV. If the coded form starts and ends with a consonant then they must be interchanged.If the coded form does not satisfy the conditions given above then it should be kept as it is.If both the conditions, I and II are satisfied then directions given in condition I must be followed and accept this if any two or three conditions are satisfied at the same time then the directions given in all the conditions must be followed.Q. What will be the coded form of “762147” after applying the given conditions?

Directions: Study the following information and answer the given questions.In a numeric series, all the even numbers are represented as the sum of digits of its square and if the sum consists of more than 1 digit then again add the digits (For Ex. 8 square is 64 then the sum is 10 hence, 8 is coded as 1 (1 + 0)). All the odd numbers are represented as consecutive 5th alphabet of the alphabetical series starting from E (For ex. 1 is coded as E, 3 is coded as J)In coded language:“42765” is coded as - 74T9ONow following operations are to be applied to the coded number:I. If the number formed by adding all the digits in the coded number is divisible by 3 then all the digits must be again coded as the corresponding alphabets of all those digits.II. If there is any prime number in the coded form then they are to be coded as $.III. If there is more than 1 vowel in the coded number then all those vowels must be replaced with the next alphabet.IV. If the coded form starts and ends with a consonant then they must be interchanged.If the coded form does not satisfy the conditions given above then it should be kept as it is.If both the conditions, I and II are satisfied then directions given in condition I must be followed and accept this if any two or three conditions are satisfied at the same time then the directions given in all the conditions must be followed.Q. Which of the following number will be coded as “P$T$P” after applying the given conditions?

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For all x,x2+ 2ax + (10 − 3a) > 0, then the interval in whichalies, is?a)a < -5b)a > 5c)-5 < a < 2d)2 < a < 5e)a < -2Correct answer is option 'C'. Can you explain this answer?
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For all x,x2+ 2ax + (10 − 3a) > 0, then the interval in whichalies, is?a)a < -5b)a > 5c)-5 < a < 2d)2 < a < 5e)a < -2Correct answer is option 'C'. Can you explain this answer? for Banking Exams 2024 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about For all x,x2+ 2ax + (10 − 3a) > 0, then the interval in whichalies, is?a)a < -5b)a > 5c)-5 < a < 2d)2 < a < 5e)a < -2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Banking Exams 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For all x,x2+ 2ax + (10 − 3a) > 0, then the interval in whichalies, is?a)a < -5b)a > 5c)-5 < a < 2d)2 < a < 5e)a < -2Correct answer is option 'C'. Can you explain this answer?.
Solutions for For all x,x2+ 2ax + (10 − 3a) > 0, then the interval in whichalies, is?a)a < -5b)a > 5c)-5 < a < 2d)2 < a < 5e)a < -2Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Banking Exams. Download more important topics, notes, lectures and mock test series for Banking Exams Exam by signing up for free.
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