# Algebra Shaalaa.com Model Set 1 2019-2020 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

Algebra [Shaalaa.com Model Set 1]
Date: March 2020
Duration: 2h

 1
 1.A | MCQs
 1.A.i

Find the correct answer from the alternatives given.

The persons of O - blood group are 40%. The classification of persons based on blood groups is to be shown by a pie diagram. What should be the measures of angle for the persons of O - blood group?

114°

140°

104°

144°

Concept: Concept of Pie Graph (Or a Circle-graph)
Chapter: [0.06] Statistics
 1.A.ii

Choose the correct alternative answer for the following question.

What is the probability of the event that a number chosen from 1 to 100 is a prime number ?

1/5

6/25

 1/4

13/50

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability
 1.A.iii

Choose the correct alternative answer for  the following question .
The sequence –10, –6, –2, 2,...

is an A.P.,Reason d = -16

is an A.P Reason d = 4

is an A.P.,Reason d = -4

is not an A.P.

Concept: Sum of First n Terms of an A.P.
Chapter: [0.03] Arithmetic Progression
 1.A.iv

Write the correct alternative for the following questions.

Rate of GST on brokerage is ...

5%

12%

18%

28%

Concept: GST on Brokerage Services
Chapter: [0.04] Financial Planning
 1.B
 1.B.i

Write the quadratic equation whose roots are ‒2 and ‒3.

 1.B.ii

If sumf_ix_i=75 and sumfi=15 , then find the mean x .

Concept: Median of Grouped Data
Chapter: [0.06] Statistics
 1.B.iii

Fill in the blanks with correct number$\begin{vmatrix}3 & 2 \\ 4 & 5\end{vmatrix}$ = 3 x ____ - ____ x 4 = ____ - 8 = ____

Concept: Linear Equation in Two Variables
Chapter: [0.01] Linear equations in two variables
 1.B.iv

Write the sample space for selecting a day randomly of the week.

Concept: Sample Space
Chapter: [0.05] Probability
 2
 2.A | Solve any 2 of the following
 2.A.i

If 12x +13y =29 and 13x +12y=21, find x + y.

Concept: Linear Equation in Two Variables
Chapter: [0.01] Linear equations in two variables
 2.A.ii

Solve the following quadratic equation for x: 4x^2 + 4bx – (a^2 – b^2) = 0

Concept: Solutions of Quadratic Equations by Completing the Square
 2.A.iii

Find the term t15 of an A.P. : 4, 9, 14, …………..

Concept: General Term of an Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
 2.B | Solve any 4 of the following
 2.B.i

Find the value of k for which the given simultaneous equations have infinitely many solutions:
kx + 4y = 10;
3x + 2y = 5.

Concept: Linear Equation in Two Variables
Chapter: [0.01] Linear equations in two variables
 2.B.ii

Solve the following quadratic equation by factorization method : x^2-5x+6=0

Concept: Solutions of Quadratic Equations by Factorization
 2.B.iii

State whether the following sequence is an Arithmetic Progression or not:
3, 6, 12, 24,......

Concept: Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
 2.B.iv

For a certain frequency distribution, the value of mean is 20 and mode is 11. Find the value of median.

Concept: Median of Grouped Data
Chapter: [0.06] Statistics
 2.B.v

For a certain frequency distribution, the values of mean and median are 72 and 78 respectively. Find the value of mode.

Concept: Median of Grouped Data
Chapter: [0.06] Statistics
 3
 3.A | Solve any 1 of the following
 3.A.i

How many three digit natural numbers are divisible by 5?

Concept: Introduction to Sequence
Chapter: [0.03] Arithmetic Progression
 3.A.ii

The market value of a mutual fund is 400 crore rupees. Which is divided into 8 crore units.

(a) Suppose you invest Rs. 10,000 in the units, how many units will you get ?
(b) While selling the units if their market value is increased by 10%, how much amount will you get by selling them ?

Concept: Mutual Fund - MF
Chapter: [0.04] Financial Planning
 3.B | Solve any 2 of the following
 3.B.i

The measurements (in mm) of the diameters of the head of the screws are given below:

 Diameter (in mm) No. of Screws 33 — 35 10 36 — 38 19 39 — 41 23 42 — 44 21 45 — 47 27

Calculate mean diameter of head of a screw by ‘Assumed Mean Method’.

Concept: Mean of Grouped Data
Chapter: [0.06] Statistics
 3.B.ii

Two digit numbers are formed using the digits 0, 1, 2, 3, 4, 5 where digits are not repeated.

P is the event that the number so formed is even.
Q is the event that the number so formed is greater than 50.
R is the event that the number so formed is divisible by 3.
Then write the sample space S and events P, Q, R using set notation.

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability
 3.B.iii

The marks scored by students in Mathematics in a certain Examination are given below:

 Marks Scored Number of Students 0 — 20 3 20 — 40 8 40 — 60 19 60 — 80 18 80 — 100 6

Draw histogram for the above data.

Concept: Graphical Representation of Data as Histograms
Chapter: [0.06] Statistics
 3.B.iv

In a certain race, there are three boys A, B, C. The winning probability of A is twice than B and the winning probability of B is twice than C. If P(A) + P(B) + P(C) = 1, then find the probability of win for each boy.

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability
 4 | Solve any 2 of the following
 4.A

Solve the following simultaneous equations: 7/(2X+1)+13/(Y+2)=27,13/(2X+1)+7/(Y+2)=33

Concept: Equations Reducible to a Pair of Linear Equations in Two Variables
Chapter: [0.01] Linear equations in two variables
 4.B

The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.

 4.C

Smt. Malhotra purchased solar panels for the taxable value of Rs. 85,000. She sold them for Rs. 90,000. The rate of GST is 5%. Find the ITC of Smt. Malhotra. What is the amount of GST payable by her?

Concept: GST - Computation and ITC
Chapter: [0.04] Financial Planning
 5 | Solve any 1 of the following
 5.A

On the first day of the sale of tickets of a drama, in all 35 tickets were sold. If the rates tickets were Rs. 20 and Rs. 40 per ticket and the total collection was Rs, 900, find the number of tickets sold of each rate.

Concept: Simple Situational Problems
Chapter: [0.01] Linear equations in two variables
 5.B

Solve the following quadratic equation by factorization method : 3x^2-29x+40=0

Concept: Solutions of Quadratic Equations by Factorization

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