Mathematics Questions and Answers – Determinant – 1

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Determinant – 1”.

1. Evaluate \(\begin{vmatrix}2&5\\-1&-1\end{vmatrix}\).
a) 3
b) -7
c) 5
d) -2
View Answer

Answer: a
Explanation: Expanding along R1, we get
∆=2(-1)-5(-1)=-2+5
=3.
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2. Evaluate \(\begin{vmatrix}5&-4\\1&\sqrt{3}\end{vmatrix}\).
a) 4\(\sqrt{3}\)+4
b) 4\(\sqrt{3}\)+5
c) 5\(\sqrt{3}\)+4
d) 5\(\sqrt{3}\)-4
View Answer

Answer: c
Explanation: Evaluating along R1, we get
∆=5(\(\sqrt{3}\))-(-4)1=5\(\sqrt{3}\)+4.

3. Evaluate \(\begin{vmatrix}-sinθ&-1\\1&sin⁡θ\end{vmatrix}\).
a) cos2⁡θ
b) -cos2⁡θ
c) cos⁡2θ
d) cos⁡θ
View Answer

Answer: a
Explanation: Expanding along R1, we get
∆=-sinθ(sinθ)-(-1)1=-sin2⁡θ+1=cos2⁡θ.
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4. Evaluate \(\begin{vmatrix}i&-1\\-1&-i\end{vmatrix}\).
a) 4
b) 3
c) 2
d) 0
View Answer

Answer: d
Explanation: Expanding along R1, we get
∆=-i(i)-(-1)(-1)=-i2-1=-(-1)-1=0.

5. Evaluate \(\begin{vmatrix}1&1&-2\\3&4&5\\-1&2&1\end{vmatrix}\).
a) -6
b) -34
c) 34
d) 22
View Answer

Answer: b
Explanation: ∆=\(\begin{vmatrix}1&1&-2\\3&4&5\\-1&2&1\end{vmatrix}\)
Expanding along the first row, we get
∆=1\(\begin{vmatrix}4&5\\2&1\end{vmatrix}\)-1\(\begin{vmatrix}3&5\\-1&1\end{vmatrix}\)-2\(\begin{vmatrix}3&4\\-1&2\end{vmatrix}\)
=1(4-5(2))-1(3-5(-1))-2(6-4(-1))
=(4-10)-(3+5)-2(6+4)
=-6-8-20=-34.
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6. Evaluate \(\begin{vmatrix}5&4&3\\3&4&1\\5&6&1\end{vmatrix}\).
a) 4
b) -24
c) -8
d) 8
View Answer

Answer: c
Explanation: Expanding along the first row, we get
∆=5\(\begin{vmatrix}4&1\\6&1\end{vmatrix}\)-4\(\begin{vmatrix}3&1\\5&1\end{vmatrix}\)+3\(\begin{vmatrix}3&4\\5&6\end{vmatrix}\)
=5(4-6)-4(3-5)+3(18-20)
=5(-2)-4(-2)+3(-2)=-10+8-6=-8.

7. Evaluate \(\begin{vmatrix}8x+1&2x-2\\x^2-1&3x+5\end{vmatrix}\).
a) -2x3-26x2+45x+3
b) -2x3+26x2+45x+3
c) -2x3+26x2+45x-3
d) -2x3-26x2-45x+3
View Answer

Answer: b
Explanation: Expanding along the first row, we get
∆=8x+1(3x+5)-(2x-2)(x2-1)
=(24x2+43x+5)-(2x3-2x2-2x+2)
=-2x3+26x2+45x+3.
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8. If A=\(\begin{bmatrix}2&5&9\\6&1&3\\4&8&2\end{bmatrix}\), find |A|.
a) 352
b) 356
c) 325
d) 532
View Answer

Answer: a
Explanation: Given that, A=\(\begin{bmatrix}2&5&9\\6&1&3\\4&8&2\end{bmatrix}\)
⇒|A|=\(\begin{vmatrix}2&5&9\\6&1&3\\4&8&2\end{vmatrix}\)
Evaluating along the first row, we get
∆=2\(\begin{vmatrix}1&3\\8&2\end{vmatrix}\)-5\(\begin{vmatrix}6&3\\4&2\end{vmatrix}\)+9\(\begin{vmatrix}6&1\\4&8\end{vmatrix}\)
∆=2(2-24)-5(12-12)+9(48-4)
∆=2(-22)-0+9(44)
∆=-44+9(44)=44(-1+9)=352

9. Evaluate \(\begin{vmatrix}\sqrt{3}&\sqrt{2}\\-1&2\sqrt{3}\end{vmatrix}\).
a) 6-3\(\sqrt{2}\)
b) 6-\(\sqrt{2}\)
c) 6+3\(\sqrt{2}\)
d) 6+\(\sqrt{2}\)
View Answer

Answer: d
Explanation: ∆=\(\begin{vmatrix}\sqrt{3}&\sqrt{2}\\-1&2\sqrt{3}\end{vmatrix}\)
∆=(\(\sqrt{3}\)×2\(\sqrt{3}\))+\(\sqrt{2}\)
∆=6+\(\sqrt{2}\).
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10. Find the value of x if \(\begin{vmatrix}3&x\\2&x^2 \end{vmatrix}\)=\(\begin{vmatrix}5&3\\3&2\end{vmatrix}\).
a) x=1, –\(\frac{1}{3}\)
b) x=-1, –\(\frac{1}{3}\)
c) x=1, \(\frac{1}{3}\)
d) x=-1, \(\frac{1}{3}\)
View Answer

Answer: a
Explanation: Given that \(\begin{vmatrix}3&x\\2&x^2 \end{vmatrix}\)=\(\begin{vmatrix}5&3\\3&2\end{vmatrix}\)
⇒3x2-2x=5(2)-3(3)
⇒3x2-2x=1
Solving for x, we get
x=1, –\(\frac{1}{3}\).

Sanfoundry Global Education & Learning Series – Mathematics – Class 12.

To practice all areas of Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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