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CBSE Class 12 Science Mathematics · Ch 2: Inverse Trigonometric Functions

CBSE Class 12 Science Mathematics · Ch 2: Inverse Trigonometric Functions is an online chapter test in the CBSE Class 12 Science pattern, covering Inverse 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.

30
Questions
20
Minutes
30
Marks
None
Negative marking
Unlock all 20 tests — ₹199Try English · Ch 1: The Last Lesson free →

Topics in this test

TopicQuestions
Inverse Trigonometric Functions30

Difficulty: 7 medium · 23 hard

Inverse Trigonometric Functions MCQ questions with answers

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

  1. Q1. The principal value of $\tan^{-1}(\sqrt{3}) - \sec^{-1}(-2)$ is:

    $\tan^{-1}(\sqrt{3}) - \sec^{-1}(-2)$ का मुख्य मान (principal value) है:

    • A. $-\frac{\pi}{3}$
    • B. $\frac{\pi}{3}$
    • C. $\pi$
    • D. $-\frac{2\pi}{3}$
    Solution

    Here $\tan^{-1}(\sqrt{3})=\frac{\pi}{3}$, and since the range of $\sec^{-1}$ is $[0,\pi]$, $\sec^{-1}(-2)=\pi-\frac{\pi}{3}=\frac{2\pi}{3}$, so the value is $\frac{\pi}{3}-\frac{2\pi}{3}=-\frac{\pi}{3}$.

    यहाँ $\tan^{-1}(\sqrt{3})=\frac{\pi}{3}$ है, और चूँकि $\sec^{-1}$ का परिसर (range) $[0,\pi]$ है, इसलिए $\sec^{-1}(-2)=\pi-\frac{\pi}{3}=\frac{2\pi}{3}$ होता है, अतः मान $\frac{\pi}{3}-\frac{2\pi}{3}=-\frac{\pi}{3}$ है।

  2. Q2. Three of the following expressions have the same value. Which one is the ODD ONE OUT?

    निम्नलिखित व्यंजकों में से तीन का मान समान है। इनमें से कौन-सा विषम (ODD ONE OUT) है?

    • A. $\sin^{-1}\frac{1}{2}$
    • B. $\tan^{-1}\frac{1}{\sqrt{3}}$
    • C. $\cos^{-1}\frac{1}{2}$
    • D. $\cos^{-1}\frac{\sqrt{3}}{2}$
    Solution

    $\sin^{-1}\frac{1}{2}$, $\tan^{-1}\frac{1}{\sqrt{3}}$ and $\cos^{-1}\frac{\sqrt{3}}{2}$ each equal $\frac{\pi}{6}$, while $\cos^{-1}\frac{1}{2}=\frac{\pi}{3}$.

    $\sin^{-1}\frac{1}{2}$, $\tan^{-1}\frac{1}{\sqrt{3}}$ और $\cos^{-1}\frac{\sqrt{3}}{2}$ प्रत्येक का मान $\frac{\pi}{6}$ है, जबकि $\cos^{-1}\frac{1}{2}=\frac{\pi}{3}$।

  3. Q3. The value of $\cos\left(\sin^{-1}\frac{3}{5}+\sin^{-1}\frac{4}{5}\right)$ is:

    $\cos\left(\sin^{-1}\frac{3}{5}+\sin^{-1}\frac{4}{5}\right)$ का मान है:

    • A. $\frac{24}{25}$
    • B. $0$
    • C. $-\frac{7}{25}$
    • D. $\frac{7}{25}$
    Solution

    Let the two angles be $\alpha,\beta$; then $\cos(\alpha+\beta)=\frac{4}{5}\cdot\frac{3}{5}-\frac{3}{5}\cdot\frac{4}{5}=0$, showing the two inverse sines add to $\frac{\pi}{2}$.

    मान लीजिए दोनों कोण $\alpha,\beta$ हैं; तब $\cos(\alpha+\beta)=\frac{4}{5}\cdot\frac{3}{5}-\frac{3}{5}\cdot\frac{4}{5}=0$, जो दर्शाता है कि दोनों प्रतिलोम ज्या (sine) का योग $\frac{\pi}{2}$ है।

Frequently asked questions

How many questions are in the CBSE Class 12 Science Mathematics · Ch 2: Inverse Trigonometric Functions?

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

Is there negative marking in the CBSE Class 12 Science Mathematics · Ch 2: Inverse Trigonometric Functions?

No — wrong answers are not penalised in this test.

Which topics does the CBSE Class 12 Science Mathematics · Ch 2: Inverse Trigonometric Functions cover?

Inverse Trigonometric Functions (30 questions).

Is the CBSE Class 12 Science Mathematics · Ch 2: Inverse Trigonometric Functions free?

It is part of the CBSE Class 12 Science Test Series 2027 — Chapter-wise + Full Tests (20 tests, ₹199). You can first try English · Ch 1: The Last Lesson for free.

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