Chapter 4 : Determinants
Q. If a, b, c are in A.P, then the determinant
∣ ∣x+2x+3x+2ax+3x+4x+2bx+4x+5x+2c∣ ∣ is
1. 0
2. 1
3. x
4. 2x
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Q. Evaluate the determinants
(i)∣ ∣312001350∣ ∣ (ii)∣ ∣345112231∣ ∣

(iii)∣ ∣012103230∣ ∣ (iv)∣ ∣212021350∣ ∣
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Q. Let A=1sinθ1sinθ1sinθ1sinθ1, where 0θ2π. Then |A| lies between
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Q.
Prove that:

∣ ∣ ∣sinαcosαcos(α+δ)sinβcosβcos(β+δ)sinγcosγcos(γ+δ)∣ ∣ ∣=0
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Q. If x218x=623x6, then x is equal to
1. 6
2. ±6
3. 6
4. 0
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Q.
If true Enter 1 else 0.
∣ ∣xyx+yyx+yxx+yxy∣ ∣=2(x+y)(x2+y2xy)
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Q. If x, y, z are non zero real numbers, then the inverse of matrix A= x000y000z is
1. x1000y1000z1
2. xyzx1000y1000z1
3. 1xyzx000y000z
4. 1xyz100010001
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Q. Prove that ∣ ∣11+p1+p+q23+2p4+3p+2q36+3p10+6p+3q∣ ∣ =1
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Q. Let A=1sinθ1sinθ1sinθ1sinθ1, where 0θ2π. Then
1. Det(A)=0
2. Det(A)(2, )
3. Det(A)(2, 4)
4. Det(A)[2, 4]
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Q. If A=112213549, find |A|.
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Q. Evaluate ∣ ∣1xy1x+yyx+yxy∣ ∣
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Q.
Using properties of determinant, prove that:

∣ ∣3aa+ba+cb+a3bb+cc+ac+b3c∣ ∣ =3(a+b+c)(ab+bc+ca)
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Q. Find the value of determinant.
(i) cosθsinθsinθcosθ
(ii) x2x+1x1x+1x+1
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Q. If A=101012004 then show that |3A|=27|A|
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Q. Find the value of determinant 2451.
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Q. If A=1242, then show that |2A|=4|A|
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Q. Find the values of x, if
(i)2451=2x46x (ii)2345=x32x5
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Q.
Using properties of determinant, prove that:

∣ ∣ ∣xx21+px3yy21+py3zz21+pz3∣ ∣ ∣=(1+pxyz)(xy)(yz)(zx)
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Q. Using the property of determinants and without expanding, prove that
∣ ∣xax+ayby+bzcz+c∣ ∣=0
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Q.
Using the property of determinants and without expanding, find

∣ ∣abbccabccaabcaabbc∣ ∣=0
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