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Mathematics

The document outlines a mathematics examination for St. Mary's Classes, covering topics in differentiation and trigonometric equations with a total of 30 marks. It includes multiple-choice questions, problem-solving sections, and proofs related to trigonometric identities and differentiation. Students are required to solve specific problems and provide proofs, demonstrating their understanding of the material.

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ASHISH BEEDKAR
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10 views2 pages

Mathematics

The document outlines a mathematics examination for St. Mary's Classes, covering topics in differentiation and trigonometric equations with a total of 30 marks. It includes multiple-choice questions, problem-solving sections, and proofs related to trigonometric identities and differentiation. Students are required to solve specific problems and provide proofs, demonstrating their understanding of the material.

Uploaded by

ASHISH BEEDKAR
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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St.

Mary’s Classes
Mathematics Marks – 30
Topics: Differentiation and Trigonometric Equations
Q.1 Multiple Choice Questions 8 Marks
1. In ∆ ABC if a = 13, b = 14, c = 15 then value of cos A is?
A. 4/5 B. 33/65 C. 65/33 D. 5/4

dy
2. If x y = y x then dx = …

x(x logy−y) y(y logx−x) y2 (1−logx) y(1− logx)


A. B. C. D.
y(y logx−x) x(x logy−y) x2 (1−logy) x(1− logy)

3. The principal solution of equation cot θ = √3 is


π 7π π 5π π 8π 7π π
A. 6 , 6
B. 6 ,6
C. 6 , 6
D. ,
6 6

dy
4. If y = √tanx + √tanx + √tanx + ⋯ ∞ then value of dx =

sec2 x secx .tanx 2y−1 2y−1


A. 2y−1
B. 2y−1
C. sec2 x D. secx .tanx

Q.2 Solve any FOUR of the following 8 Marks


1. Differentiate the following with respect to x
2x
sin−1 ( )
1 + x2
2. State and Prove Cosine Rule (with Diagram).

3. If f(x) = √7 g(x) − 3 , g (3) =4 and g’(3) = 5, find f’(3).


3 3π
4. A. Find the Cartesian co-ordinate of the point whose polar co-ordinate is (4 , 4
)

B. Find the polar co-ordinate for the point whose Cartesian co-ordinate is (1, - √3)
dy
5. If, y = (4)log2 (sinx) + (9)log3 (sinx) find dx

A B C [A(∆ ABC)]2
6. In ∆ ABC prove that sin 2 sin 2 sin 2 = abcs

Q.3 Solve any FOUR of the following 12 Marks


B−C b−c A
1. In ∆ ABC, prove that sin ( 2
) =( a
) cos 2
dy 1−y2
2. If √1 − x 2 + √1 − y 2 = a (x – y) then show that = √
dx 1−x2

3. Prove the following.


A. tan−1 1 + tan−1 2 + tan−1 3 = π
4 12 33
B. cos−1 5 + cos−1 13 = cos−1 65

4. Find the derivate of 7x with respect tox 7 .


5. Find the general solution of the following

A. √3 cosecθ + 2 = 0
B. cot 4θ = - 1
2θ
C. tan 3
= √3

Q.4 Find the principal solution of the following 2 Marks


1 2
A. cos θ = B. sec θ =
2 √3

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