MCQ and Introduction on Algebra

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Algebra is the branch of mathematics that deals with rules to manipulate variables in the formula. The rules help in explaining the relationship between the operations and also simplify the equation which helps in solving them. Variables, constants, numbers, equations, expressions, quadratic equations, and linear equations are the basics of algebra. It is the field of study that extends beyond math and helps further in understanding calculus and statistics. Algebraic equations solve unknown quantities.

The four different types of algebra are elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra.

Read more: Math Equations

Ques. Solve the value of( 61681 x 61681-31681 x 3168130000)

94362
93352
95362
93362
None of the above

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Ans. (d) 93362

Explanation: ( 61681 x 61681-31681 x 3168130000)

61681+31681x (61681+31681)30000

(93362 x 30000)/30000

= 93362

Ques. Solve the quadratic equation: 2 + √5 and 2- √5

x² + 4x + 1 = 0
x² – 4x – 1 = 0
x² – 4x + 1 = 0
x² + 4x + 1 = 0

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Ans. (b) x² – 4x – 1 = 0

Explanation: Let the roots of the equation be A and B

A = 2 + √5

B = 2- √5

A + B = 2 + √5 + 2- √5 = 4

A x B = ( 2 + √5)( 2- √5 )

= 4 – 5 = – 1

Thus, x² – 4x – 1 = 0

Ques. Calculate the value of k if one of the zeros of the quadratic polynomial (k-1)x² +kx +1 = -3.

2/3
-4/3
-2/3
4/3

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Ans. (d) 4/3

Explanation: Let p(x) = (k-1)x² + kx + 1

Given, X = -3 is one of its 0

Thus, p(x) at x = -3 becomes 0.

Therefore,

(k-1)(-3)² + k(-3) + 1 = 0

9k-9-3k+1=0
6k= 8
k = 4/3

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Relevant Concepts
Discriminant Formula	Linear Equation	Linear Algebra
Graphs	Line Graph	Set Formula

Ques. calculate the value of Q² if one root of the equation 5x² +2x + Q = 2 is reciprocal of another.

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Ans. (b) 49

Explanation: Let the roots of 5x² +2x + Q - 2 = 0 are a and b

a = 1/b

ab = 1

ax² +bx +c = 0

a = 5, b = 2, c=Q-2

(Q-2)/5 = 1
Q-2 = 5
Q = 7
Q² = 7² = 49

Ques. Find out the number if the sum of the consecutive numbers is 41

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Ans. (a) 21

Explanation: Let one of the numbers = x

The other number = x +1

as per the equation,

x +x + 1 = 41

2x +1 = 41

2x = 40

X = 20

Thus,

First number = 20

Second number = 20 + 1 = 21

Ques. Find the positive integral solution of a in 3x² – ax + 6 = ax² +2x + 2. The equation has only one solution.

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Ans. (c ) 2

Explanation: Given

3x² – ax +6 = ax² +2x + 2

3x² – ax² – ax – 2x + 6 – 2 = 0
(3-a)x² – (a +2)x + 4 = 0

D = B2 – 4AC = 0

(a+2)² – 4 (3-a)4 = 0

a² + 4a + 4 – 48 + 16a = 0

a² +20a – 44 = 0

a² +22a – 2a – 44 = 0

a(a+22) – 2(a+22) = 0

a = 2,-22

therefore, the positive integral solution of a = 2

Ques. Find the product of two consecutive numbers were four times the first time is 10 more than thrice the second number

156
210
182
306

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Ans. (c) 182

Explanation: Suppose the first number = a

Second number = a+1

According to the question

4a = 3 x (a +1 ) +10

a = 13

hence,

first number= 13

second number = 14

product = 13 x 14 = 182

Read more:

Relevant Concepts
Cardioid	Matrices	Vectors
Unit Vectors	Conic Sections	Trigonometry

Ques. What is the degree of the polynomial 2x⁵ + 2x³y³ + 4y⁴ + 5

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Ans. (b) 6

Explanation: Degree of polynomial in 2x⁵ = 5

Degree of polynomial in 2x³y³ = 6

Degree of polynomial in 4y⁴ = 4

Degree of polynomial in 5 = 0

Hence the greatest degree = 6

Therefore, the degree of polynomial = 6

Ques. If the value of x is given as 10+3, solve x³ – 1/x³

254
216
334
234

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Ans. (d) 234

Explanation: 1/x = 1/(10+3)

= (10-3 )/ (10+3) (10-3 )

=(10-3 )/(√10)² – (3)²

= 1/x = √10 – 3

= x- 1/x = 10+3 - 10+3 = 6 ….. (i)

By squaring both sides,

(x-1/x)² = (6)²
X²– 2x(1/x) + 1/x² = 36
X² – 2 +1/x² = 36
X² + 1/x² = 38 …. (ii)

Therefore, x³ – 1/x³ = (x-1/x)(x²+x 1/x + 1/x²)

X³ – 1/x³ = (x – 1/x)(x² + 1/x² +1 )
X³ – 1/x³ = 6 x (38 + 1)
X³ – 1/x³ = 234

Ques. The sum of the digit of a two-digit number is 10. If 18 is added to the number, then the digits are reversed. What is the number?

62
46
37
27
None of the above

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Ans. (b) 46

Explanation: Let the digit at ones place be y and the digit in ten’s place be x

the number = 10x + y

the sum of the digits = 10

x +y = 10

the digits are reversed when 18 is added,

new number = 10y +x

(10x +y) + 18 = 10y +x

9x +18 = 9y
X +2 = y

Therefore, x +y = 10

X + (x+2) = 10
2x +2 = 10
2x = 8
X =4

Therefore, y = 10-x = 10-4 = 6

The number is 10x +y = (10 x 4) + 6 = 46

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MCQ and Introduction on Algebra

CBSE X Related Questions

1.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

2.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

3.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

4.
Use graphical method to solve the system of linear equations : $x = -3$ and $5x - 2y = -5$.

5.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

6.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

Similar Mathematics Concepts

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MCQ and Introduction on Algebra

CBSE X Related Questions

1.Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

2.In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

3.A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

4.Use graphical method to solve the system of linear equations : $x = -3$ and $5x - 2y = -5$.

5.Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

6.Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent. Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

2.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

3.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

4.
Use graphical method to solve the system of linear equations : $x = -3$ and $5x - 2y = -5$.

5.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

6.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.