12th Math chapter 6 Bihar board with NCERT-Details & Highlights
| name of content | 12th Math chapter 6 full solution |
| content | Math objective type MCQ question with answer |
| name of subjects | class 12 Math |
| important for exam | Bihar board & other state board |
| pattern & Level | NCERT & State level question |
12th Math chapter 6 all objective solutions – download PDF
Question 1. The radius of a cylinder is increasing at the rate of 3 m/s and its height is decreasing at the rate of 4 m/s. The rate of change of volume when the radius is 4 m and height is 6 m, is
-
- (a) 80π cu m/s
(b) 144π cu m/s
(c) 80 cu m/s
(d) 64 cu m/s
- (a) 80π cu m/s
Answer: (a) 80π cu m/s
Question 2. The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases, when the side is 10 cm, is
-
- (a) √3 cm2/s
(b) 10 cm2/s
(c) 10√3 cm2/s
(d) 103√ cm2/s
- (a) √3 cm2/s
Answer: (c) 10√3 cm2/s
Question 3. A particle is moving along the curve x = at2 + bt + c. If ac = b2, then particle would be moving with uniform
-
- (a) rotation
(b) velocity
(c) acceleration
(d) retardation
- (a) rotation
Answer: (c) acceleration
Question 4. The distance ‘s’ metres covered by a body in t seconds, is given by s = 3t2 – 8t + 5. The body will stop after
-
- (a) 1 s
(b) 34 s
(c) 43 s
(d) 4 s
- (a) 1 s
Answer: (c) 43 s
Question 5. The position of a point in time ‘t’ is given by x = a + bt – ct2, y = at + bt2. Its acceleration at time ‘t’ is
-
- (a) b – c
(b) b + c
(c) 2b – 2c
(d) 2b2+c2−−−−−−√
- (a) b – c
Answer: (d) 2b2+c2−−−−−−√
Question 6. The function f(x) = log (1 + x) – 2x2+x is increasing on
-
- (a) (-1, ∞)
(b) (-∞, 0)
(c) (-∞, ∞)
(d) None of these
- (a) (-1, ∞)
Answer: (a) (-1, ∞)
Question 7. f(x)=(e2x−1e2x+1) is
-
- (a) an increasing function
(b) a decreasing function
(c) an even function
(d) None of these
- (a) an increasing function
Answer: (a) an increasing function
Question 8. The function f(x) = cot-1 x + x increases in the interval
-
- (a) (1, ∞)
(b) (-1, ∞)
(c) (0, ∞)
(d) (-∞, ∞)
- (a) (1, ∞)
Answer: (d) (-∞, ∞)
Question 9. The function f(x) = xlogx increases on the interval
-
- (a) (0, ∞)
(b) (0, e)
(c) (e, ∞)
(d) none of these
- (a) (0, ∞)
Answer: (c) (e, ∞)
Bihar Board most mcq solution 12th math chapterb 6
Question 10. The length of the longest interval, in which the function 3 sin x – 4sin3x is increasing, is
-
- (a) π3
(b) π2
(c) 3π2
(d) π
- (a) π3
Answer: (a) π3
Question 11. 2x3 – 6x + 5 is an increasing function, if
-
- (a) 0 < x < 1
(b) -1 < x < 1
(c) x < -1 or x > 1
(d) -1 < x < −12
- (a) 0 < x < 1
Answer: (c) x < -1 or x > 1
Question 12. If f(x) = sin x – cos x, then interval in which function is decreasing in 0 ≤ x ≤ 2π, is
-
- (a) [5π6,3π4]
(b) [π4,π2]
(c) [3π2,5π2]
(d) None of these
- (a) [5π6,3π4]
Answer: (d) None of these
Question 13. The function which is neither decreasing nor increasing in (π2,3π2) is
-
- (a) cosec x
(b) tan x
(c) x2
(d) |x – 1|
- (a) cosec x
Answer: (a) cosec x
Question 14. The function f(x) = tan-1 (sin x + cos x) is an increasing function in
-
- (a) (π4,π2)
(b) (−π2,π2)
(c) (0,π2)
(d) None of these
- (a) (π4,π2)
Answer: (d) None of these
Question 15. The function f(x) = x3 + 6x2 + (9 + 2k)x + 1 is strictly increasing for all x, if
-
- (a) k>32
(b) k<32
(c) k≥32
(d) k≤32
- (a) k>32
Answer: (a) k>32
Question 16. The point on the curves y = (x – 3)2 where the tangent is parallel to the chord joining (3, 0) and (4, 1) is
-
- (a) (−72,14)
(b) (52,14)
(c) (−52,14)
(d) (72,14)
- (a) (−72,14)
Answer: (d) (72,14)
Question 17. The slope of the tangent to the curve x = a sin t, y = a{cot t + log(tan t2)} at the point ‘t’ is
-
- (a) tan t
(b) cot t
(c) tan t2
(d) None of these
- (a) tan t
Answer: (a) tan t
Question 18. The equation of the normal to the curves y = sin x at (0, 0) is
-
- (a) x = 0
(b) x + y = 0
(c) y = 0
(d) x – y = 0
- (a) x = 0
Answer: (b) x + y = 0
Question 19. The tangent to the parabola x2 = 2y at the point (1, 12) makes with the x-axis an angle of
-
- (a) 0°
(b) 45°
(c) 30°
(d) 60°
- (a) 0°
Answer: (b) 45°
BSEB 12th math chapter 6 mcq solution
Question 20. The two curves x3 – 3xy2 + 5 = 0 and 3x2y – y3 – 7 = 0
-
- (a) cut at right angles
(b) touch each other
(c) cut at an angle π4
(d) cut at an angle π3
- (a) cut at right angles
Answer: (a) cut at right angles
Question 21. The distance between the point (1, 1) and the tangent to the curve y = e2x + x2 drawn at the point x = 0
-
- (a) 15√
(b) −15√
(c) 25√
(d) −25√
- (a) 15√
Answer: (c) 25√
Question 22. The tangent to the curve y = 2x2 -x + 1 is parallel to the line y = 3x + 9 at the point
-
- (a) (2, 3)
(b) (2, -1)
(c) (2, 1)
(d) (1, 2)
- (a) (2, 3)
Answer: (d) (1, 2)
Question 23. The tangent to the curve y = x2 + 3x will pass through the point (0, -9) if it is drawn at the point
-
- (a) (0, 1)
(b) (-3, 0)
(c) (-4, 4)
(d) (1, 4)
- (a) (0, 1)
Answer: (b) (-3, 0)
Question 24. Find a point on the curve y = (x – 2)2. at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).
-
- (a) (3, 1)
(b) (4, 1)
(c) (6,1)
(d) (5, 1)
- (a) (3, 1)
Answer: (a) (3, 1)
Question 25. Tangents to the curve x2 + y2 = 2 at the points (1, 1) and (-1, 1) are
-
- (a) parallel
(b) perpendicular
(c) intersecting but not at right angles
(d) none of these
- (a) parallel
Answer: (b) perpendicular
Question 26. If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is
-
- (a) 1%
(b) 2%
(c) 3%
(d) 4%
- (a) 1%
Answer: (a) 1%
Question 27. If there is an error of a% in measuring the edge of a cube, then percentage error in its surface area is
-
- (a) 2a%
(b) a2 %
(c) 3a%
(d) None of these
- (a) 2a%
Answer: (b) a2 %
Question 28. If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximating error in calculating its volume.
-
- (a) 2.46π cm3
(b) 8.62π cm3
(c) 9.72π cm3
(d) 7.46π cm3
- (a) 2.46π cm3
Answer: (c) 9.72π cm3
Question 29. Find the approximate value of f(3.02), where f(x) = 3x2 + 5x + 3
-
- (a) 45.46
(b) 45.76
(c) 44.76
(d) 44.46
- (a) 45.46
Answer: (a) 45.46
Important mcq notes 12th math chapter 6
Question 30. f(x) = 3x2 + 6x + 8, x ∈ R
-
- (a) 2
(b) 5
(c) -8
(d) does not exist
- (a) 2
Answer: (d) does not exist
Question 31. Find all the points of local maxima and local minima of the function f(x) = (x – 1)3 (x + 1)2
-
- (a) 1, -1, -1/5
(b) 1, -1
(c) 1, -1/5
(d) -1, -1/5
- (a) 1, -1, -1/5
Answer: (a) 1, -1, -1/5
Question 32. Find the local minimum value of the function f(x) = sin4x + cos4x, 0 < x < π2
-
- (a) 1√2
(b) 12
(c) √32
(d) 0
- (a) 1√2
Answer: (b) 12
Question 33. Find the points of local maxima and local minima respectively for the function f(x) = sin 2x – x , where
−π2≤x≤π2
-
- (a) −π6, π6
(b) π3, −π3
(c) −π3, π3
(d) π6, −π6
- (a) −π6, π6
Answer: (d) π6, −π6
Question 34. If y=ax−b(x−1)(x−4) has a turning point P(2, -1), then find the value of a and b respectively.
-
- (a) 1, 2
(b) 2, 1
(c) 0, 1
(d) 1, 0
- (a) 1, 2
Answer: (d) 1, 0
Question 35. sinp θ cosq θ attains a maximum, when θ =
-
- (a) tan−1pq−−√
(b) tan−1(pq)
(c) tan−1q
(d) tan−1(qp)
- (a) tan−1pq−−√
Answer: (a) tan−1pq−−√
Question 36. Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x2.
-
- (a) 25
(b) 43
(c) 62
(d) 49
- (a) 25
Answer: (d) 49
Question 37. If y = x3 + x2 + x + 1, then y
-
- (a) has a local minimum
(b) has a local maximum
(c) neither has a local minimum nor local maximum
(d) None of these
- (a) has a local minimum
Answer: (c) neither has a local minimum nor local maximum
Question 38. Find both the maximum and minimum values respectively of 3x4 – 8x3 + 12x2 – 48x + 1 on the interval [1, 4].
-
- (a) -63, 257
(b) 257, -40
(c) 257, -63
(d) 63, -257
- (a) -63, 257
Answer: (c) 257, -63
Question 39. It is given that at x = 1, the function x4 – 62x2 + ax + 9 attains its maximum value on the interval [0, 2]. Find the value of a.
-
- (a) 100
(b) 120
(c) 140
(d) 160
- (a) 100
Answer: (b) 120
12th math chapter 6 important mcs solution
Question 40. The function f(x) = x5 – 5x4 + 5x3 – 1 has
-
- (a) one minima and two maxima
(b) two minima and one maxima
(c) two minima and two maxima
(d) one minima and one maxima
- (a) one minima and two maxima
Answer: (d) one minima and one maxima
Question 41. The coordinates of the point on the parabola y2 = 8x which is at minimum distance from the circle x2 + (y + 6)2 = 1 are
-
- (a) (2, -4)
(b) (18, -12)
(c) (2, 4)
(d) none of these
- (a) (2, -4)
Answer: (a) (2, -4)
Question 42. The distance of that point on y = x4 + 3x2 + 2x which is nearest to the line y = 2x – 1 is
-
- (a) 35√
(b) 45√
(c) 25√
(d) 15√
- (a) 35√
Answer: (d) 15√
Question 43. The function f(x) = x + 4x has
-
- (a) a local maxima at x = 2 and local minima at x = -2
(b) local minima at x = 2, and local maxima at x = -2
(c) absolute maxima at x = 2 and absolute minima at x = -2
(d) absolute minima at x = 2 and absolute maxima at x = -2
- (a) a local maxima at x = 2 and local minima at x = -2
Answer: (b) local minima at x = 2, and local maxima at x = -2
Question 44. The combined resistance R of two resistors R1 and R2 (R1, R2 > 0) is given by 1R=1R1+1R2. If R1 + R2 = C (a constant), then maximum resistance R is obtained if
-
- (a) R1 > R2
(b) R1 < R2
(c) R1 = R2
(d) None of these
- (a) R1 > R2
Answer: (c) R1 = R2
Question 45. Find the height of a cylinder, which is open at the top, having a given surface area, greatest volume and of radius r.
-
- (a) r
(b) 2r
(c) r2
(d) 3πr2
- (a) r
Answer: (a) r
Question 46. Find the height of the cylinder of maximum volume that can be is cribed in a sphere of radius a.
-
- (a) 2a3
(b) 2a3√
(c) a3
(d) a3
- (a) 2a3
Answer: (b) 2a3√
Question 47. Find the volume of the largest cylinder that can be inscribed in a sphere of radius r cm.
-
- (a) πr333√
(b) 4πr2h33√
(c) 4πr3
(d) 4πr333√
- (a) πr333√
Answer: (d) 4πr333√
Question 48. The area of a right-angled triangle of the given hypotenuse is maximum when the triangle is
-
- (a) scalene
(b) equilateral
(c) isosceles
(d) None of these
- (a) scalene
Answer: (c) isosceles
Question 49. Find the area of the largest isosceles triangle having perimeter 18 metres.
-
- (a) 9√3
(b) 8√3
(c) 4√3
(d) 7√3
- (a) 9√3
Answer: (a) 9√3
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| SL.N. | Subject name with solutions |
| 01 | Physics |
| 02 | Chemistry |
| 03 | Biology |
| 04 | Math |
| 05 | Hindi |
| 06 | English |