Simplification problems
- 1. If cosec2 ? = 625/576 , then what is the value of [(sin ? ? cos ?)/(sin ? + cos ?)]?
Options- A. 1
- B. 31/17
- C. 17/31
- D. 14/25 Also asked in: Bank Exams
Correct Answer: 17/31
- 2. What is the value 32cos 39sin 51-sin239 + sin251
Options- A. 1/2
- B. 5/2
- C. 0
- D. Both 1/2 and 5/2 Also asked in: Bank Exams
Correct Answer: Both 1/2 and 5/2
- 3. What is (x-y)3+y-23+z-x33x-yy-zz-x =?
Options- A. 1
- B. 0
- C. 1/3
- D. 3 Also asked in: Bank Exams
Correct Answer: 1
- 4. If ax= by= cz and b2= ac , then what is 1x+1z equal to ?
Options- A. 1/y
- B. -1/y
- C. 2/y
- D. -2/y Also asked in: Bank Exams
Correct Answer: 2/y
- 5. If p and q are the roots of the equation x2 ?15x + r = 0 and p ?q = 1, then what is the value of r ?
Options- A. 55
- B. 56
- C. 60
- D. 64 Also asked in: Bank Exams
Correct Answer: 56
Explanation:
In the below equation,
x2?15x + r = 0
sum of roots = p + q = -(-15)/1 = 15 (sum of roots for equation ax2+ bx + c is -b/a)
product of roots = pq = r/1 = r (product of roots for equation ax2+ bx + c is c/a)
given p ?q = 1
also we know that p+q = 15
subtracting the squares of both
(p+q)2 + (p-q)2 = 15^2?1
p2 + q2 + 2pq ?p2 ?q2 +2pq = 225 -1
4pq = 224
4r = 224
r = 56
- 6. If 3 tan ? = cot ? where 0 < ? < ?/2 , then what is the value of ? ?
Options- A. ?/6
- B. ?/4
- C. ?/2
- D. 1 Also asked in: Bank Exams
Correct Answer: ?/6
Explanation:
3tan ? = cot ?
3tan ? = 1/tan ?
tan2? = 1/3
tan ? = 1/?3
? = ?/6
- 7. What is the value of sin225°+ sin265° ?
Options- A. 0
- B. 1
- C. 2
- D. 4 Also asked in: Bank Exams
Correct Answer: 1
- 8. What is the value of sin6? + cos6? + 3 sin2? cos2? ?1 ?
Options- A. 0
- B. 1
- C. 2
- D. 4 Also asked in: Bank Exams
Correct Answer: 0
- 9. Consider the following for real numbers ?, ?, ? and ? ? 1) sec ? = 1/4 2) tan ? = 20 3) cosec ? = 1/2 4) cos ? = 2 How many of the above statements are not possible?
Options- A. one
- B. two
- C. three
- D. four Also asked in: Bank Exams
Correct Answer: three
Explanation:
Sec of any number can never be less than 1
tan can take any value from -? to + ?
cosec of any number can never be less than 1
cos of any number can never be greater than 1
so option 1,3,4 are not possible
- 10. For x = 462+3, what is the value of x+22x-22+x+23x-23
Options- A. 1
- B. ?2
- C. ?3
- D. 2 Also asked in: Bank Exams
Correct Answer: 2
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