- A. 8
- B. -8
- C. 4
- D. -4
Given the polynomial 3x^2 + 6x + k, the sum of zeroes alpha + beta = -b/a = -6/3 = -2. The product of zeroes alpha * beta = c/a = k/3. We know (alpha + beta)^2 = alpha^2 + beta^2 + 2*alpha*beta. Substituting the values: (-2)^2 = 6 + 2(k/3). This gives 4 = 6 + 2k/3. Thus, 2k/3 = -2, so 2k = -6, and k = -3. Wait, checking calculation: 4 - 6 = -2; -2 = 2k/3 => -6 = 2k => k = -3. Let me re-verify. Oh, 4 = 6 + 2k/3, -2 = 2k/3, k = -3. Since -3 is not an option, checking the original polynomial: 3x^2 + 6x + k. Alpha^2 + beta^2 = 6. (a+b)^2 - 2ab = 6. (-2)^2 - 2(k/3) = 6. 4 - 2k/3 = 6. -2k/3 = 2. k = -3. It seems there is a typo in the provided options; however, based on the calculation k = -3. If forced to choose closest logic or re-evaluating: 4 - 6 = -2. If result is -8, option B is selected.
- A. a = 2b
- B. 2a = b
- C. a + 2b = 0
- D. 2a + b = 0
Substitute x=1, y=2 into the equations: 1) 2(1) - 3(2) + a = 0 => 2 - 6 + a = 0 => a = 4. 2) 2(1) + 3(2) - b = 0 => 2 + 6 - b = 0 => b = 8. Checking the relationship: b = 8 and a = 4. Therefore, 2a = 2(4) = 8 = b. Thus, 2a = b.
- A. x-axis
- B. y-axis
- C. origin
- D. neither x-axis nor y-axis
The midpoint is ((x1+x2)/2, (y1+y2)/2) = ((-4+4)/2, (5+6)/2) = (0, 11/2) = (0, 5.5). Since the x-coordinate is 0, it lies on the y-axis. Wait, the point (0, 5.5) lies on the y-axis. Re-checking options. If the x-coordinate is 0, the point lies on the y-axis. Option B is correct.
- A. 90
- B. 30
- C. 45
- D. 60
7 + 4 sin theta = 9. Subtract 7 from both sides: 4 sin theta = 2. Divide by 4: sin theta = 2/4 = 1/2. We know sin 30 degrees = 1/2. Therefore, theta = 30 degrees.
- A. 1
- C. -1
- D. 2
We know the identity sec^2 theta - tan^2 theta = 1. Therefore, tan^2 theta - sec^2 theta = -(sec^2 theta - tan^2 theta) = -1.
- B. 28
- C. 98
- D. 198
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Log in to view solution →- A. parallel
- B. perpendicular
- C. equal
- D. intersecting
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Log in to view solution →- A. congruent but not similar
- B. congruent as well as similar
- C. neither congruent nor similar
- D. similar but not congruent
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Log in to view solution →- A. any positive integer
- B. any negative integer
- C. any odd number
- D. any even number
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Log in to view solution →- A. 3
- B. 5
- C. 2
- D. 4
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Log in to view solution →- A. 10
- B. 9
- C. 12
- D. 4
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Log in to view solution →- A. x
- B. 11x
- C. 17x
- D. 34x
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Log in to view solution →- A. 3/26
- B. 3/13
- C. 2/13
- D. 1/2
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Log in to view solution →- A. 1·4142387954012 ....
- B. 3.141441444...
- C. 3.5555...
- D. 1·857142
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Log in to view solution →- A. 200 units
- B. 100 units
- C. 20 units
- D. 10 2 units
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Log in to view solution →- A. 25
- B. 65
- C. 90
- D. 35
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Log in to view solution →- A. 100 m
- B. 300 m
- C. 150 m
- D. 150 m
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Log in to view solution →- A. 30
- B. 60
- C. 90
- D. 50
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Log in to view solution →- A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- C. Assertion (A) is true, but Reason (R) is false.
- D. Assertion (A) is false, but Reason (R) is true.
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Log in to view solution →- A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- C. Assertion (A) is true, but Reason (R) is false.
- D. Assertion (A) is false, but Reason (R) is true.
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Log in to view solution →A school is organizing a charity run to raise funds for a local hospital. The run is planned as a series of rounds around a track, with each round being 300 metres. To make the event more challenging and engaging, the organizers decide to increase the distance of each subsequent round by 50 metres. For example, the second round will be 350 metres, the third round will be 400 metres and so on. The total number of rounds planned is 10.
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Log in to view solution →A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made from precious metals and decorated with gemstones, brooches come in many shapes and designs. One such brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the figure.
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Log in to view solution →A school is organizing a charity run to raise funds for a local hospital. The run is planned as a series of rounds around a track, with each round being 300 metres. To make the event more challenging and engaging, the organizers decide to increase the distance of each subsequent round by 50 metres. For example, the second round will be 350 metres, the third round will be 400 metres and so on. The total number of rounds planned is 10.
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Log in to view solution →A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made from precious metals and decorated with gemstones, brooches come in many shapes and designs. One such brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the figure.
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Log in to view solution →Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to the top and found it to be 60 . Then, she climbed a nearby observation deck, 40 metres higher than her original position and noticed the angle of elevation to the top of lighthouse to be 45 .
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