12th Mathematics - Book Back Answers - Chapter 7 - English Medium Guides

  

 

Plus Two / 12th Mathematics - Book Back Answers - Chapter 7 - English Medium

Tamil Nadu Board 12th Standard Mathematics - Chapter 7: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 7 from the Tamil Nadu State Board 12th Standard Mathematics textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.

    We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.

    By going through this material, you’ll gain a strong understanding of Chapter 7 along with the corresponding book back questions and answers (PDF format).

Question Types Covered:

• 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following 
• 2 Mark Questions: Answer briefly 
• 3, 4, and 5 Mark Questions: Answer in detail

All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.

All the best, Class 12 students! Prepare well and aim for top scores. Thank you!

 

I. Multiple Choice Questions

1. The volume of a sphere is increasing in volume at the rate of 3𝞹 cm³ / sec .
The rate of change of its radius when radius is $\frac{\mathbf{1}}{\mathbf{2}}$ cm
(1) 3 cm/s 
(2) 2 cm/s 
(3) 1 cm/s 
(4) $\frac{\mathbf{1}}{\mathbf{2}}$ cm/s
Answer Key:
(1) 3 cm/s 

 
2. A balloon rises straight up at 10 m/s. An observer is 40 m away from the spot where the
balloon left the ground. The rate of change of the balloon’s angle of elevation in radian per
second when the balloon is 30 metres above the ground.
(1) $\frac{\mathbf{3}}{\mathbf{25}}$ radians/sec 
(2) $\frac{\mathbf{4}}{\mathbf{25}}$ radians/sec 
(3) $\frac{1}{5}$ radians/sec 
(4) $\frac{1}{3}$ radians/sec
Answer Key:
(2) $\frac{\mathbf{4}}{\mathbf{25}}$ radians/sec

 
3. The position of a particle moving along a horizontal line of any time t is given by
s(t) = 3t² − 2t −8 2 . The time at which the particle is at rest is
(1) t = 0 
(2) t = $\frac{1}{3}$
(3) t =1 
(4) t = 3
Answer Key:
(2) t = $\frac{1}{3}$

$\frac{\mathrm{ }}{}$
4. A stone is thrown up vertically. The height it reaches at time t seconds is given by x = 80t −16t² .
The stone reaches the maximum height in time t seconds is given by
(1) 2 
(2) 2.5 
(3) 3 
(4) 3.5
Answer Key:
(2) 2.5 

 
5. The point on the curve 6y = x³ + 2 at which y-coordinate changes 8 times as fast as x-coordinate
is
(1) (4,11) 
(2) (4,−11) 
(3) (−4,11) 
(4) (−4,−11)
Answer Key:
(1) (4,11) 

 
6. The abscissa of the point on the curve f (x) = $\sqrt{\mathbf{8}\mathbf{-}\mathbf{2}\mathbf{x}}$ at which the slope of the tangent is
−0.25?
(1) −8 
(2) −4 
(3) −2 
(4) 0
Answer Key:
(2) −4

 
7. The slope of the line normal to the curve f (x) = 2cos 4x at x = $\frac{\mathbf{\pi }}{\mathbf{12}}$ is
(1) −4$\sqrt{\mathbf{3}}$
(2) −4
(3) $\frac{\sqrt{\mathbf{3}}}{\mathbf{12}}$
(4) 4$\sqrt{\mathbf{3}}$
Answer Key:
(3) $\frac{\sqrt{\mathbf{3}}}{\mathbf{12}}$

$\frac{\mathbf{ }}{}$
8. The tangent to the curve y² − xy  + 9 = 0 is vertical when
(1) y = 0 
(2) y = ±$\sqrt{\mathbf{3}}$ 
(3) y = $\frac{\mathbf{1}}{\mathbf{2}}$
(4) y = ±3
Answer Key:
(4) y = ±3

 
9. Angle between y² = x and x² = y at the origin is
(1) tan^-1$\frac{\mathbf{3}}{\mathbf{4}}$
(2) 

(3) $\frac{\mathit{\pi }}{\mathbf{2}}$
(4) $\frac{\mathit{\pi }}{\mathbf{4}}$
Answer Key:
(3) $\frac{\mathit{\pi }}{\mathbf{2}}$

$\frac{\mathbf{ }}{}$
10. The value of the $\underset{\mathbf{x}\mathbf{\to }\mathbf{0}}{\mathbf{lim}}$  is
(1) 0 
(2) 1 
(3) 2 
(4) ∞
Answer Key:
(1) 0

 
11. The function sin⁴x cos⁴x is increasing in the interval
(1)

(2) 
(3) 
(4) 

Answer Key:
(3) 

${\mathrm{<math\; xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo> </mo></mrow></math>}}^{}$
12. The number given by the Rolle’s theorem for the function x³ − 3x² , x ∈ [0,3] is
(1) 1 
(2) $\sqrt{\mathbf{2}}$ 
(3) $\frac{\mathbf{3}}{\mathbf{2}}$
(4) 2
Answer Key:
(4) 2

 
13. The number given by the Mean value theorem for the function x∈[1, 9] is
(1) 2 
(2) 2.5 
(3) 3 
(4) 3.5
Answer Key:
(3) 3

 
14. The minimum value of the function | 3− x | + 9 is
(1) 0 
(2) 3 
(3) 6 
(4) 9
Answer Key:
(4) 9

 
15. The maximum slope of the tangent to the curve y = e^x sin x, x∈[0,2] is at
(1) x =
(2) x =
(3) x =
(4) x =$\frac{\mathbf{3}\mathbf{\pi }}{\mathbf{2}}$
Answer Key:
(2) x =

16. The maximum value of the function x²e^-2x, x>0 is
(1) $\frac{\mathbf{1}}{\mathbf{e}}$
(2) $\frac{\mathbf{1}}{\mathbf{2}\mathbf{e}}$
(3) $\frac{\mathbf{1}}{{\mathbf{e}}^{\mathbf{2}}}$
(4) $\frac{\mathbf{4}}{{\mathbf{e}}^{\mathbf{4}}}$
Answer Key:
(3) $\frac{\mathbf{1}}{{\mathbf{e}}^{\mathbf{2}}}$

$\frac{{\mathbf{ }}^{}}{}$
17. One of the closest points on the curve x² − y²  = 4 to the point (6,0) is
(1) (2,0) 
(2) ($\sqrt{\mathbf{5}}$,1) 
(3) (3, $\sqrt{\mathbf{5}}$) 
(4) ( $\sqrt{\mathbf{13}}$, -$\sqrt{\mathbf{3}}$)
Answer Key:
(3) (3, $\sqrt{\mathbf{5}}$) 

 
18. The maximum value of the product of two positive numbers, when their sum of the squares is
200, is
(1) 100 
(2) 25$\sqrt{\mathbf{7}}$
(3) 28 
(4) 24$\sqrt{\mathbf{14}}$
Answer Key:
(1) 100 

 
19. The curve y = ax⁴ + bx² with ab > 0
(1) has no horizontal tangent 
(2) is concave up
(3) is concave down 
(4) has no points of inflection
Answer Key:
(4) has no points of inflection

 
20. The point of inflection of the curve y = (x −1)³ is
(1) (0,0) 
(2) (0,1) 
(3) (1,0) 
(4) (1,1)
Answer Key:
(3) (1,0) 

 

II.Short Answer Questions.

12th Mathematics

III. Long Answer Questions.

12th Mathematics

IV. Exercise.

12th Mathematics