Q1. What is the remainder when (4x^3-3x^2+2x-1) is divided by (x+2)?
(a) 48
(b) 49
(c) –49
(d) –48
( f(x)=4x^3-3x^2+2x-1
Put x=-2
Then, remainder f(-2)=4(-2)^3-3(-2)^2+2(-2)-1
=-32-12-4-1
=-49 )
Q2. If (x + 6) is a factor of f(x)=x^3+3x^2+4x+P, find the value of P.
(a) 42
(b) 132
(c) 192
(d) 82
(Since, (x + 6) is a factor of f(x), therefore
f(-6)=0
⇒(-6)^3+3(-6)^2+4(-6)+P=0
⇒-216+108-24+P=0
⇒P=132)
Q3. Factorize the expression a^2 b^3+a^3 b^2-
(a) a^2 b^2 (a+b)
(b) ab (ab+ab)
(c) ab(a+b)
(d) a^3 b^3
(a^2 b^3+a^3 b^2=a^2 b^2.b+a^2.a.b^2
=a^2 b^2 (b+a)
=a^2 b^2 (a+b) )
Q4. Solve the expression (2x + 3y + 4z)^2-
(a) 4x^2+9y^2+16z^2+12xy-24yz-16xz
(b) 4x^2+9y^2+16z^2+12xy+24yz-16xz
(c) 4x^2+9y^2+16z^2+12xy-24yz+16xz
(d) None of these
((a+b-c)〗^2=a^2+b^2+c^2+2ab-2bc-2ca
Putting a=2x,b=3y,c=4z, we get
∴(2x+3y-4z)^2=4x^2+9y^2+16z^2+12xy-24yz-16xz )
Q5. The expression f(x)=a_0 x^n+a_1 x^(n-1)+a_2 x^(n-2)+⋯+a_(n-1) x is a polynomial of degree n-
(a) If n is a negative integer and a_n≠0
(b) If n is a positive integer and a_0≠0
(c) If n is any integer
(d) Only when n is positive integer
(The given expression is a degree of n, if n is a positive integer and a_0≠0)
Q6. If – 3a+2b+5c is subtracted from 2a+b-8c, what will be the result?
(a) 5a-b+13c
(b) 5a+b-13c
(c) 5a+b+13c
(d) 5a-b-13c
( required result
=(2a+b-8c)-(-3a+2b+5c)
=2a+b-8c+3a-2b-5c
=5a-b-13c )
Q7. Find the value of (-14a^4 b^3 c)÷(-7abc)-
(a) -2a^3 b^2 c
(b) -2a^3 b^2
(c) 2a^3 b^2
(d) 2abc
( (-14 a^4 b^3 c)/(-7abc)=2a^(4-1) b^(3-1) c^(1-1)=2a^3 b^2)
Q8. A system of two simultaneous linear equations in two variables has a unique solution, if their graphs-
(a) Are parallel
(b) Are coincident
(c) Intersect at one point
(d) None of the above
(Two lines intersect at one point. )
Q9. A number is three times the another number. If sum of both the numbers be 20, find them.
(a) 5, 15
(b) 4, 12
(c) 4, 16
(d) 6, 18
( Let second number = x
And first number = 3x
According to the question,
x + 3x = 20
⇒ 4x = 20
⇒ x = 5
∴ 3x = 3 × 5 = 15)
Q10. If a, b and c are three natural numbers in ascending order, then-
(a) c^2-a^2=b^2
(b) c^2-a^2<b^2
(c) c^2+b^2=a^2
(d) c^2-a^2>b
(If three natural numbers a, b and c are in ascending order then the difference of the square of third number and square of first number will certainly be greater than the second number.
As for example, a = 2, b = 3, c = 4
⇒ c^2-a^2>b
⇒(4)^2-(2)^2>3
⇒16-4>3
⇒12>3 (True))
