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Question 1 of 5
1. Question
For what value of k is (x-5) a factor of x3-3x2+kx-10?
Correct
Ans: a
Let
p(x) = x3—3x2+kx-10
Then, (x-5) is a factor of p(x)
\p(/5)=0
53-3(5)2+k ´5 -10=0
125-75+5k-10=0
40+5k=0
K=-8
Hence, the value of k is -8
Incorrect
Ans: a
Let
p(x) = x3—3x2+kx-10
Then, (x-5) is a factor of p(x)
\p(/5)=0
53-3(5)2+k ´5 -10=0
125-75+5k-10=0
40+5k=0
K=-8
Hence, the value of k is -8
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Question 2 of 5
2. Question
The expression
X3q2-x3pt+4x2pt-4x2q2+3xq2-3xpt
Is divisible by
Correct
Ans: c
x3q2-x3pt+4x2q2-4x2q2+3xq2-3xpt
=x3q2-x3pt-4x2q2+4x2pt+3xq2-3xpt
=x3(q2-pt)-4x2(q2-pt)+3x(q2-pt)
=(x3-4×2+3x)(q2-pt)=x(x2-4x+3)(q2-pt)
=x(x2-3x-x+3)(q2-pt)
= x[x(x-3)-1(x-3)](q2-pt)=x(x-3)(x-1)(q2-pt)
Hence, the given expression is divisible by (x-1)and(x-3)
Incorrect
Ans: c
x3q2-x3pt+4x2q2-4x2q2+3xq2-3xpt
=x3q2-x3pt-4x2q2+4x2pt+3xq2-3xpt
=x3(q2-pt)-4x2(q2-pt)+3x(q2-pt)
=(x3-4×2+3x)(q2-pt)=x(x2-4x+3)(q2-pt)
=x(x2-3x-x+3)(q2-pt)
= x[x(x-3)-1(x-3)](q2-pt)=x(x-3)(x-1)(q2-pt)
Hence, the given expression is divisible by (x-1)and(x-3)
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Question 3 of 5
3. Question
If x+y+z=0, then x3+y3+z3-3xyz is equal to
Correct
Ans: a
Because x3+y3+z3-3xyz=(x+y+z)
(x2+y2+z2-xy-yz-zx)
Given, x+y+z=0
∴x3+y3+z3-3xyz=0
Hence, the value of x3+y3+z3-3xyz is zero.
Incorrect
Ans: a
Because x3+y3+z3-3xyz=(x+y+z)
(x2+y2+z2-xy-yz-zx)
Given, x+y+z=0
∴x3+y3+z3-3xyz=0
Hence, the value of x3+y3+z3-3xyz is zero.
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Question 4 of 5
4. Question
If ax+by-2=0 and axby =1, Where a ¹0, b¹0 then what is (a2x+b2y)equal to?
Correct
Ans: a
Given, ax+by-2=0
ax+by=2
Squaring on both sides, we get
(ax+by)2=(2)2
⇒a2x2+b2y2+2axby=4
⇒a2x2+b2y2+2=4
a2x2+b2y2=2
a2x2=1 and b2y2=1
ax=1 and by =1 ⇒ x=1/a and y=1/b
∴a2x+b2y=a2.(1/a)+b2.(1/b)=a+b
Incorrect
Ans: a
Given, ax+by-2=0
ax+by=2
Squaring on both sides, we get
(ax+by)2=(2)2
⇒a2x2+b2y2+2axby=4
⇒a2x2+b2y2+2=4
a2x2+b2y2=2
a2x2=1 and b2y2=1
ax=1 and by =1 ⇒ x=1/a and y=1/b
∴a2x+b2y=a2.(1/a)+b2.(1/b)=a+b
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Question 5 of 5
5. Question
What is the value of 3 x0.3 x0.03x 0.003x 0.0003 x 30?
Correct
Ans: b
3 x0.3 x0.03x 0.003x 0.0003 x 30
=3 x 3x 10-1 x 3 x 10-2 x3 x10-3 x 3 x 10-4x 3x 10
=(3)6 (10)-9 = (32)3 (10-3)3
=(9)3 1/(1000)3 = (9/1000)3 = (0.009)3
Incorrect
Ans: b
3 x0.3 x0.03x 0.003x 0.0003 x 30
=3 x 3x 10-1 x 3 x 10-2 x3 x10-3 x 3 x 10-4x 3x 10
=(3)6 (10)-9 = (32)3 (10-3)3
=(9)3 1/(1000)3 = (9/1000)3 = (0.009)3
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