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CBSE Class 12 Science Mathematics · Ch 4: Determinants

CBSE Class 12 Science Mathematics · Ch 4: Determinants is an online chapter test in the CBSE Class 12 Science pattern, covering Determinants. 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
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Topics in this test

TopicQuestions
Determinants30

Difficulty: 7 medium · 23 hard

Determinants MCQ questions with answers

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

  1. Q1. The area of the triangle whose vertices are $(3, 8)$, $(-4, 2)$ and $(5, -1)$ is:

    उस त्रिभुज का क्षेत्रफल जिसके शीर्ष $(3, 8)$, $(-4, 2)$ और $(5, -1)$ हैं, है:

    • A. $37$ square units / $37$ वर्ग इकाई
    • B. $\frac{75}{2}$ square units / $\frac{75}{2}$ वर्ग इकाई
    • C. $75$ square units / $75$ वर्ग इकाई
    • D. $150$ square units / $150$ वर्ग इकाई
    Solution

    Area $=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)| = \frac{1}{2}\times75=\frac{75}{2}$ square units.

    क्षेत्रफल $=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)| = \frac{1}{2}\times75=\frac{75}{2}$ वर्ग इकाई।

  2. Q2. In the determinant $\begin{vmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{vmatrix}$, if $M_{21}$ denotes the minor of $a_{21}$, then the cofactor $C_{21}$ is given by:

    सारणिक $\begin{vmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{vmatrix}$ में, यदि $M_{21}$, $a_{21}$ का उपसारणिक (minor) है, तो सहखंडज (cofactor) $C_{21}$ दिया जाता है:

    • A. $C_{21} = -M_{21}$
    • B. $C_{21} = M_{12}$
    • C. $C_{21} = -M_{12}$
    • D. $C_{21} = M_{21}$
    Solution

    The cofactor is defined as $C_{ij} = (-1)^{i+j}M_{ij}$. For $i=2, j=1$, $(-1)^{3} = -1$, so $C_{21} = -M_{21}$.

    सहखंडज को $C_{ij} = (-1)^{i+j}M_{ij}$ के रूप में परिभाषित किया जाता है। $i=2, j=1$ के लिए, $(-1)^{3} = -1$, इसलिए $C_{21} = -M_{21}$।

  3. Q3. If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$, then $|A^{-1}|$ is equal to:

    यदि $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$ है, तो $|A^{-1}|$ बराबर है:

    • A. $-\frac{1}{2}$
    • B. $\frac{1}{2}$
    • C. $2$
    • D. $-2$
    Solution

    Since $|A^{-1}| = \frac{1}{|A|}$ and $|A| = 1\times4 - 2\times3 = -2$, we get $|A^{-1}| = -\frac{1}{2}$.

    चूँकि $|A^{-1}| = \frac{1}{|A|}$ है और $|A| = 1\times4 - 2\times3 = -2$ है, इसलिए $|A^{-1}| = -\frac{1}{2}$ प्राप्त होता है।

Frequently asked questions

How many questions are in the CBSE Class 12 Science Mathematics · Ch 4: Determinants?

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

Is there negative marking in the CBSE Class 12 Science Mathematics · Ch 4: Determinants?

No — wrong answers are not penalised in this test.

Which topics does the CBSE Class 12 Science Mathematics · Ch 4: Determinants cover?

Determinants (30 questions).

Is the CBSE Class 12 Science Mathematics · Ch 4: Determinants free?

It is part of the CBSE Class 12 Science Test Series 2027 — Chapter-wise + Full Tests (46 tests, ₹199). You can first try English · Ch 1: The Last Lesson for free.

More tests in the CBSE Class 12 Science Test Series 2027 — Chapter-wise + Full Tests

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