Mathematics - Algebraic Expressions
Exam Duration: 45 Mins Total Questions : 30
If x + y= 5,Y+ z = 7 and z + x = 12, what is the value of x + y + z?
- (a)
12
- (b)
2
- (c)
5
- (d)
24
How many auxiliary formulae can be formed from the expression in the box?
A=\(\frac { 1 }{ 2 } \)h(a+b)
- (a)
2
- (b)
3
- (c)
4
- (d)
1
A and B are polynomials and each is the additive inverse of the other. What does it mean?
- (a)
A = B
- (b)
A + B is a zero polynomial.
- (c)
A - B is a zero polynomial.
- (d)
A - B = B - A
If C=\(\frac { x-a }{ x-b } \) , find the value of x.
- (a)
\(\frac { bC-a }{ C-b } \).
- (b)
\(\frac { C-a }{ C-b } \).
- (c)
\(\frac { C+a }{ C+b } \).
- (d)
\(\frac { 1-C }{ a-bC } \).
Which of the following is true?
- (a)
The product of numbers p and q subtracted from 7 is 7 + pq.
- (b)
Y - y3 is a monomial.
- (c)
The coefficient of y2 in 2x2y + 7y2 is 7
- (d)
100z3 is a binomial
Simplify x2y3 - 1.5 x2y3 + 1.4x2y3.
- (a)
0.9x2y3
- (b)
-0.9x2y3
- (c)
0.9
- (d)
-0.9
What is the value of
(a3- 2a2+ 4a - 5) - (-a3- 8a + 2a2+ 5)?
- (a)
2a3+7a2+6a-10
- (b)
2a3+7a2+12a-10
- (c)
2a3-4a2+12a-10
- (d)
2a3-4a2+ 6a-10
By how much is x4- 4x2y2 less than x4+8x2y2+y4?
- (a)
-12x2y2
- (b)
12x2y2
- (c)
-12xy
- (d)
12xy
Simplify the following expression.
x (y - z) - y (z - x) - z (x - y)
- (a)
2x (y - z)
- (b)
2y (z - x)
- (c)
2x (z - y)
- (d)
2z(x - y)
The third term of the series 7n + 20 is 41. What is the 10th term?
- (a)
90
- (b)
56
- (c)
63
- (d)
87
Which expression gives the predecessor of a natural number 'n'?
- (a)
2n-1
- (b)
n+1
- (c)
n-1
- (d)
2n+1
From the sum of 7x - 2y - 3z and 3x + 5y - 8z, take away x - 3z.
- (a)
9x - 3y + 8z
- (b)
9x + 3y - 8z
- (c)
9x + 3y + 8z
- (d)
9x - 3y - 8z
If P+\(\frac { 5 }{ 4 } \)(4-2P)=-4, find P.
- (a)
-6
- (b)
6
- (c)
18
- (d)
-18
How is "4 is less than half of x" written in symbolic form?
- (a)
4>\(\frac { x }{ 2 } \) .
- (b)
\(\frac { x-4 }{ 2 } \).
- (c)
\(\frac { x }{ 2 } \)+4
- (d)
4<\(\frac { x }{ 2 } \) .
The length of a rectangle is 2(x + 6) ern, and its width is half its length. What is its perimeter?
- (a)
6(x - 3)cm
- (b)
6(x - 6) cm
- (c)
3(x + 6) cm
- (d)
(6x + 36) cm
The value of \((-5x^2y)\times(-\frac{2}{3}xy^2z)\times(\frac{8}{15}xyz^2)\times(-\frac{1}{4}z)\) is______.
- (a)
\(-\frac{4}{9}x^4y^4z^4\)
- (b)
\(\frac{4}{9}x^4y^4z^4\)
- (c)
\(-\frac{4}{9}x^3y^3z^3\)
- (d)
\(\frac{4}{9}x^3y^3z^3\)
Addition of \(\frac{a^2}{2}+\frac{b^3}{3}-\frac{c^3}{4},\frac{2a^2}{3}+\frac{3b^3}{4}-\frac{4c^3}{5}\) and a2+b3+c3 is_______.
- (a)
\(\frac{13}{6}a+\frac{25}{12}b^3-\frac{1}{20}c^3\)
- (b)
\(\frac{13}{6}a^2-\frac{1}{20}b^3+\frac{25}{12}c^3\)
- (c)
\(\frac{13}{6}a^2+\frac{25}{12}b^3-\frac{1}{20}c^3\)
- (d)
\(\frac{13}{6}a^2-\frac{25}{12}b^3+\frac{1}{20}c^3\)
Simplify \((2x+\frac{1}{3y})^2-(2x-\frac{1}{3y})^2.\)
- (a)
\(\frac{4x}{3y}\)
- (b)
\(2(4x^2+\frac{1}{9y^2})\)
- (c)
\(\frac{8x}{3y}\)
- (d)
\(\frac{4y}{3x}\)
The value of 9x2 + 49y2 - 42xy when x = 15 and y = 3 is_______.
- (a)
636
- (b)
576
- (c)
456
- (d)
386
The number of diagonals drawn from one vertex of a polygon of n sides is_________.
- (a)
n - 1
- (b)
n - 2
- (c)
n - 3
- (d)
n
By how much is a4 + 4a2b2 + b4 more than a4 - 8a2b2 + b4?
- (a)
12a2b2
- (b)
- 12a2b2
- (c)
2a4 + 2b4
- (d)
10a2b2
The degree of (6x7 -7x3 + 3x2 + 2x -1) is________.
- (a)
7
- (b)
6
- (c)
3
- (d)
5
If \(\frac{x}{y}=\frac{3}{4},\) then the value of \((\frac{6}{7}+\frac{y-x}{y+x})\) equals______.
- (a)
\(\frac{5}{7}\)
- (b)
\(1\frac{1}{7}\)
- (c)
1
- (d)
2
If x = - 2, y = 3 and z = 1, then the value of expression x3 + y3 + z3 - 3xyz is_________.
- (a)
38
- (b)
37
- (c)
-37
- (d)
-38
How many trinomials are there?
(i) 4y - 7z
(ii) x + y - xy
(iii) 7mn
(iv) z2 - 3z + 8
(v) 1 + x + x2
- (a)
2
- (b)
3
- (c)
4
- (d)
5
Rohan spends Rs x daily and saves Rs y per week. What is his income in 3 weeks?
- (a)
Rs (21x + 3y)
- (b)
Rs (3x + 9y)
- (c)
Rs (21x + 9y)
- (d)
Rs (7x + 3y)
A vacuum cleaner set costs Rs 154.25 k. Additional pipe costs Rs 15.2 k. What is the total cost of 3 vacuum cleaner sets and 5 additional pipes?
- (a)
Rs 400 k
- (b)
Rs 530.75 k
- (c)
Rs 538.75 k
- (d)
Rs 600 k
State 'T' for true and 'F' for false.
I. Expression with two unlike terms is called a monomial.
II. The sum of two unlike terms is a term with coefficient equal to the sum of coefficients of the two unlike terms.
III. The value of 3y2 - 5y + 3, when y = 1 is 1
- (a)
I II III T T F - (b)
I II III T F T - (c)
I II III F T F - (d)
I II III F F T
Match the following.
Column-I | Column-II |
(P) (x2 + 5)(x3 + 3) + 5 | (1) -x3 - 3x2+ 3x + 2 |
(Q) \((\frac{-10}{3}xy^3)\times(\frac{6}{5}x^3y)\) | (2) -x3 + x2+ 3x - 6 |
(R) (x3- x2- x - 2) -(2x3 + 2x2 - 4x - 4) | (3) x5 + 5x3+ 3x2 + 20 |
(S) (x3-x2-x-2) +(2x2 - 2x3 + 4x- 4) | (4) -4x4y4 |
- (a)
(P) \(\rightarrow\) (1), (Q) \(\rightarrow\) (2), (R) \(\rightarrow\) (3), (S) \(\rightarrow\) (4)
- (b)
(P) \(\rightarrow\) (3), (Q) \(\rightarrow\) (4), (R) \(\rightarrow\) (1), (S) \(\rightarrow\) (2)
- (c)
(P) \(\rightarrow\) (4), (Q) \(\rightarrow\) (1), (R) \(\rightarrow\) (3), (S) \(\rightarrow\) (2)
- (d)
(P) \(\rightarrow\) (3), (Q) \(\rightarrow\) (4), (R) \(\rightarrow\) (2), (S) \(\rightarrow\) (1)
Fill in the blanks.
(i) Any expression with one or more terms is called a____P_______.
(ii) Terms which have the same algebraic factors are____Q_____terms.
(iii) The___R____is the numerical factor in the term.
(iv) Algebraic expressions are formed from____S_____and____T_____.
- (a)
P Q R S T Binomial unlike term factors constants - (b)
P Q R S T Polynomial like term factors constants - (c)
P Q R S T Trinomial unlike coefficient variables constant - (d)
P Q R S T Polynomial like coefficient variables constants