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Mathematics Trigonometric functions and their properties MCQ Questions for Class 11 General

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Trigonometric functions and their properties Practice Questions

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Question 171/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि (x) तीसरे चतुर्थांश में है और \(\tan x=\frac{9}{40}\), तो \(\sec x\) का मान क्या है?

If (x) is in the third quadrant and \(\tan x=\frac{9}{40}\), what is the value of \(\sec x\)?

Explanation opens after your attempt
Correct Answer

B. \(-\frac{41}{40}\)

Explanation

Simple Explanation

\(\sec^2 x=1+\tan^2 x\) से \(|\sec x|=\frac{41}{40}\) मिलता है। तीसरे चतुर्थांश में \(\sec x\) ऋणात्मक होता है। / From \(\sec^2 x=1+\tan^2 x\), \(|\sec x|=\frac{41}{40}\). In the third quadrant, \(\sec x\) is negative.

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Question 172/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि (x) चौथे चतुर्थांश में है और \(\cos x=\frac{15}{17}\), तो \(\sin x\) का मान क्या है?

If (x) is in the fourth quadrant and \(\cos x=\frac{15}{17}\), what is the value of \(\sin x\)?

Explanation opens after your attempt
Correct Answer

C. \(-\frac{8}{17}\)

Explanation

Simple Explanation

पहचान से \(|\sin x|=\frac{8}{17}\) मिलता है। चौथे चतुर्थांश में \(\sin x\) ऋणात्मक होता है। / The identity gives \(|\sin x|=\frac{8}{17}\). In the fourth quadrant, \(\sin x\) is negative.

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Question 173/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि (x) दूसरे चतुर्थांश में है और \(\cot x=-\frac{3}{4}\), तो \(\cosec x\) का मान क्या है?

If (x) is in the second quadrant and \(\cot x=-\frac{3}{4}\), what is the value of \(\cosec x\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{5}{4}\)

Explanation

Simple Explanation

\(\cosec^2 x=1+\cot^2 x\) से \(|\cosec x|=\frac{5}{4}\) मिलता है। दूसरे चतुर्थांश में \(\cosec x\) धनात्मक होता है। / From \(\cosec^2 x=1+\cot^2 x\), \(|\cosec x|=\frac{5}{4}\). In the second quadrant, \(\cosec x\) is positive.

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Question 174/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

\(\frac{\sec^2 x-1}{\tan^2 x}\) का सरल मान क्या है?

What is the simplified value of \(\frac{\sec^2 x-1}{\tan^2 x}\)?

Explanation opens after your attempt
Correct Answer

B. (1)

Explanation

Simple Explanation

\(\sec^2 x-1=\tan^2 x\) होता है। इसलिए पूरा भिन्न (1) के बराबर है। / \(\sec^2 x-1=\tan^2 x\). Therefore, the whole fraction equals (1).

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Question 175/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

\(\frac{\cosec^2 x-1}{\cot^2 x}\) का सरल मान क्या है?

What is the simplified value of \(\frac{\cosec^2 x-1}{\cot^2 x}\)?

Explanation opens after your attempt
Correct Answer

C. (1)

Explanation

Simple Explanation

\(\cosec^2 x-1=\cot^2 x\) होता है। इसलिए अनुपात (1) है। / \(\cosec^2 x-1=\cot^2 x\). Hence the ratio is (1).

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Question 176/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\(\sec x-\tan x\)\(\sec x+\tan x\)) का सरल मान क्या है?

What is the simplified value of (\(\sec x-\tan x\)\(\sec x+\tan x\))?

Explanation opens after your attempt
Correct Answer

D. (1)

Explanation

Simple Explanation

यह \(\sec^2 x-\tan^2 x\) बनता है। पहचान के अनुसार इसका मान (1) है। / It becomes \(\sec^2 x-\tan^2 x\). By identity, its value is (1).

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Question 177/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

(\(\cosec x-\cot x\)\(\cosec x+\cot x\)) का सरल मान क्या है?

What is the simplified value of (\(\cosec x-\cot x\)\(\cosec x+\cot x\))?

Explanation opens after your attempt
Correct Answer

A. (1)

Explanation

Simple Explanation

यह \(\cosec^2 x-\cot^2 x\) बनता है। मानक पहचान से इसका मान (1) है। / It becomes \(\cosec^2 x-\cot^2 x\). By the standard identity, its value is (1).

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Question 178/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\sin x+\cos x=1\), तो \(\sin x\cos x\) का मान क्या है?

If \(\sin x+\cos x=1\), what is the value of \(\sin x\cos x\)?

Explanation opens after your attempt
Correct Answer

B. (0)

Explanation

Simple Explanation

वर्ग करने पर \(1+2\sin x\cos x=1\) मिलता है। इसलिए \(\sin x\cos x=0\)। / Squaring gives \(1+2\sin x\cos x=1\). Therefore, \(\sin x\cos x=0\).

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Question 179/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\sin x-\cos x=0\), तो \(\tan x\) का मान क्या है?

If \(\sin x-\cos x=0\), what is the value of \(\tan x\)?

Explanation opens after your attempt
Correct Answer

C. (1)

Explanation

Simple Explanation

\(\sin x=\cos x\) होने पर \(\frac{\sin x}{\cos x}=1\) होगा। इसलिए \(\tan x=1\)। / When \(\sin x=\cos x\), \(\frac{\sin x}{\cos x}=1\). Hence \(\tan x=1\).

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Question 180/346 Medium Mathematics Trigonometric Functions Trigonometric functions and their properties Class 11 Level 70

यदि \(\sin^2 x=\frac{1}{4}\) और (x) प्रथम चतुर्थांश में है, तो \(\cos x\) का मान क्या है?

If \(\sin^2 x=\frac{1}{4}\) and (x) is in the first quadrant, what is the value of \(\cos x\)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{\sqrt{3}}{2}\)

Explanation

Simple Explanation

\(\cos^2 x=1-\frac{1}{4}=\frac{3}{4}\) होगा। प्रथम चतुर्थांश में \(\cos x=\frac{\sqrt{3}}{2}\) लिया जाता है। / \(\cos^2 x=1-\frac{1}{4}=\frac{3}{4}\). In the first quadrant, \(\cos x=\frac{\sqrt{3}}{2}\) is taken.

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