Consider the following two statements. Assertion (A): The equation $\sin x = 2$ has no real solution. Reason (R): For every real $x$, the value of $\sin x$ lies in the interval $[-1, 1]$. Which of the following is correct?

Both A and R are true, and R is the correct explanation of A

Both A and R are true, but R is not the correct explanation of A

Chapter testMathematicsIncluded in the seriesTest 15 of 36

CBSE Class 11 Science Mathematics · Ch 3: Trigonometric Functions

CBSE Class 11 Science Mathematics · Ch 3: Trigonometric Functions is an online chapter test in the CBSE Class 11 Science pattern, covering Trigonometric Functions. Attempt it on SeatBeat with a timer like the real exam, then see a detailed solution for every question and your score and weak-topic analysis.

Questions

Minutes

Marks

None

Negative marking

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Topics in this test

Topic	Subject	Questions
Trigonometric Functions	Mathematics	30

Difficulty: 7 medium · 23 hard

Trigonometric Functions MCQ questions with answers

The first 3 of 30 questions. Unlock the series for the rest, each with a solution.

Q1. If $A + B = 45^\circ$, then the value of $(1 + \tan A)(1 + \tan B)$ is
यदि $A + B = 45^\circ$, तो $(1 + \tan A)(1 + \tan B)$ का मान है
- A. $1$
- B. $\sqrt{2}$
- C. $2$
- D. $0$
Solution
Since $\tan(A+B) = 1$ gives $\tan A + \tan B = 1 - \tan A\tan B$, expanding $(1+\tan A)(1+\tan B) = 1 + (\tan A + \tan B) + \tan A\tan B = 1 + 1 = 2$.
चूँकि $\tan(A+B) = 1$ से $\tan A + \tan B = 1 - \tan A\tan B$ प्राप्त होता है, $(1+\tan A)(1+\tan B) = 1 + (\tan A + \tan B) + \tan A\tan B = 1 + 1 = 2$ का प्रसार करने पर।
Q2. Consider the following two statements. Assertion (A): The equation $\sin x = 2$ has no real solution. Reason (R): For every real $x$, the value of $\sin x$ lies in the interval $[-1, 1]$. Which of the following is correct?
निम्नलिखित दो कथनों पर विचार कीजिए। अभिकथन (A): समीकरण $\sin x = 2$ का कोई वास्तविक हल नहीं है। कारण (R): प्रत्येक वास्तविक $x$ के लिए, $\sin x$ का मान अंतराल $[-1, 1]$ में स्थित होता है। निम्नलिखित में से कौन-सा सही है?
- A. A is false but R is true / A असत्य है परन्तु R सत्य है
- B. Both A and R are true, and R is the correct explanation of A / A और R दोनों सत्य हैं, और R, A की सही व्याख्या है
- C. A is true but R is false / A सत्य है परन्तु R असत्य है
- D. Both A and R are true, but R is not the correct explanation of A / A और R दोनों सत्य हैं, परन्तु R, A की सही व्याख्या नहीं है
Solution
The range of the sine function is $[-1,1]$, so $\sin x = 2$ is impossible; thus both are true and R correctly explains A.
ज्या (साइन) फलन का परिसर $[-1,1]$ है, अतः $\sin x = 2$ असंभव है; इस प्रकार दोनों सत्य हैं और R, A की सही व्याख्या करता है।
Q3. The value of $2\sin 75^\circ \cos 15^\circ$ is
$2\sin 75^\circ \cos 15^\circ$ का मान है
- A. $\frac{\sqrt{3}}{2}$
- B. $\frac{\sqrt{3}+1}{2}$
- C. $\frac{2+\sqrt{3}}{2}$
- D. $\frac{2-\sqrt{3}}{2}$
Solution
Using $2\sin A\cos B = \sin(A+B) + \sin(A-B)$, it becomes $\sin 90^\circ + \sin 60^\circ = 1 + \tfrac{\sqrt{3}}{2} = \tfrac{2+\sqrt{3}}{2}$.
$2\sin A\cos B = \sin(A+B) + \sin(A-B)$ का उपयोग करने पर, यह $\sin 90^\circ + \sin 60^\circ = 1 + \tfrac{\sqrt{3}}{2} = \tfrac{2+\sqrt{3}}{2}$ बन जाता है।

Frequently asked questions

How many questions are in the CBSE Class 11 Science Mathematics · Ch 3: Trigonometric Functions?

30 questions for 30 marks, to be answered in 20 minutes.

Is there negative marking in the CBSE Class 11 Science Mathematics · Ch 3: Trigonometric Functions?

No — wrong answers are not penalised in this test.

Which topics does the CBSE Class 11 Science Mathematics · Ch 3: Trigonometric Functions cover?

Trigonometric Functions (30 questions).

Is the CBSE Class 11 Science Mathematics · Ch 3: Trigonometric Functions free?

It is part of the CBSE Class 11 Science Test Series 2027 — Chapter-wise + Full Tests (36 tests, ₹199). You can first try Biology · Ch 1: The Living World for free.

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