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- Question
For the inequation x^2?7x + 12 > 0, which one of the following is correct ?
Options- A. 3 < x < 4
- B. ?? < x < 3 only
- C. 4 < x < ? only
- D. ?? < x < 3 or 4 < x < ?
- Correct Answer
- ?? < x < 3 or 4 < x < ?
- 1. If cot A = [sin B/(1 ? cos B)], then what is the value of cot 2A?
Options- A. cot(B/2)
- B. cot 2B
- C. cot B
- D. tan B Discuss
- 2. If x3 ? y3 = 81 and x ? y = 3, then what is the value of x2 + y2 ?
Options- A. 18
- B. 21
- C. 27
- D. 36 Discuss
- 3. If (x + y + z) = 12, xy + yz + zx = 44 and xyz = 48, then what is the value of x3 + y3+ z3 ?
Options- A. 104
- B. 144
- C. 196
- D. 288 Discuss
- 4. If m n = 2 , mn = 15 , (m , n > 0) then the value of m2-n2m3-n3
Options- A. 1856
- B. 1658
- C. 1586
- D. 1568 Discuss
- 5. If 4(x+y) = 256 and (256)(x-y) = 4 , then what is the value of x and y?
Options- A. 17/8, 15/8
- B. 17/4, 15/4
- C. 9/17, 15/17
- D. 8/17, 8/15 Discuss
- 6. If tan x = 1, 0 < x < 90, then what is the value of 2 sin x cos x?
Options- A. 1/2
- B. 1
- C. ?3/2
- D. ?3 Discuss
- 7. What is the value of sin 46 cos 44+ cos 46 sin 44?
Options- A. 2
- B. sin 2
- C. 1
- D. 0 Discuss
- 8. Suppose 0 < ? < 90, then for every ? 4 sin2 ? + 1 is greater than or equal to ?
Options- A. 2
- B. 4 sin ?
- C. 4 cos ?
- D. 4 tan ? Discuss
- 9. Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30 deg, and the angle of elevation to the top of the tower at C is 45 deg. What is the ratio of the height of towers at B and C?
Options- A. 1:?3
- B. 1:3
- C. 1:2
- D. 1:2?3 Discuss
- 10. What is the value of tan 1° tan 2° tan 3°....... tan 89° ?
Options- A. 0
- B. 1
- C. 2
- D. infinity Discuss
Simplification problems
Search Results
Correct Answer: cot B
Correct Answer: 21
Correct Answer: 288
Correct Answer: 1568
Correct Answer: 17/8, 15/8
Correct Answer: 1
Explanation:
tan x = 1
then x = 45
2sin x. cos x = 2× 1/?2 x 1/?2 = 1
an x = 1
then
x = 45
o
2sin x. cos x =
2
×
Correct Answer: 1
Explanation:
sin 46. cos 44+ cos 46. sin 44
sin 46. sin (90 -44)+ cos 46. cos (90 -44)
= sin^2 46 + cos^2 46
= 1
Correct Answer: 4 sin ?
Explanation:
We know that,
Arithmetic mean ? Geometric mean
Correct Answer: 1:3
Explanation:
Let the side of regular hexagon be ?a?
Let height of the tower 1 be h1 and tower 2 be h2
Height of tower 1 = h1 = (distance between A and B)* (tan 30o)= a.1/?3
Distance between A and C = 2*?3.a/2= ?3a
Height of tower 2 = h2 = (distance between A and C)* (tan 45o) = ?3a.1 = ?3a
Ratio of height of towers at B and C respectively =a/?3/?3a = 1/3.
Correct Answer: 1
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