ALGEBRA QUESTION PAPER FOR PRACTISE.pdf

7/27/2019 ALGEBRA QUESTION PAPER FOR PRACTISE.pdf

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OMTEX CLASSES ALGEBRA ASSIGNMENT SSC

2013 - 2014

www.omtexclasses.com

PAPER NO. 1Q1. Attempt any six of the following sub questions:i. Find the first four terms of the sequence whose nth term is 3 + 1.ii. If one root of the quadratic equation 2 11 + = 0 is 9, then find the

value of k.

iii. What is sample spaceiv. Mohan has a hobby of solving problems everyday. He solved 2, 4, 3, 2, 4,

5, 1 problems in the last week. What is the mean number of problems

solved by Mohan per day?

v. Central angle = ?Total value of all the components

3600

vi. Find the value of discriminant for the following. 32 43 + 4 = 0.Q2. Attempt any five of the following sub questions:

i. Determine whether the given values of are the roots of the givenquadratic equation 62 2 = 0 . = 1

2, = 2

3, = 3

2

ii. Solve the simultaneous equations by using Graphical method. + 3 = 7;2 + + 1 = 0

iii. There are three boys and three girls. An environment committee of two isto be formed. Write the sample space S, the number of sample points

n(S). Also Event A and n(A). Where A is the event that the committee

should contain atleast one girl.iv. Without actually solving the simultaneous equation given, examine

whether it has unique solution, no solution or infinitely many solutions.

(i) + 3 + 4 = 0; 2x+ 6 y3 = 0v. A coin is tossed. Find the probability of the events. (i) Getting a head (ii)

Getting a tail.


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Q3. Attempt any four of the following sub questions

i. If the 10th term and the 18th term of an A.P. are 25 and 41 respectivelythey find the 38th term.

ii. How many terms are there in the A.P. 187, 194, 201, , 439? iii. Find the value of k for which given equation has real and equal roots.22 2 1 + 4 = 0iv. Find the value of k, if one root of the equation 52 + 6 + = 0 is 5 times

the other.

v. Below is given frequency distribution of Daily wages (in Rs.) of 130workers.

Daily wages (inRs.)

8084

8589

9094

9599

100104

105109

No. of workers10 20 25 40 30 5

Find modal wage of a worker.

Q4. Attempt any three of the folliwng sub questions:

i. If one root of the equation 2 10 + 2 = 0 is 5 3 , find k.ii. If

are the roots of the equation

2 +

+

= 0, Find the

value of + iii. What is the probability that an ordinary year has 53 Sundays?

Q5. Attempt any four of the following subquestions.

i. Solve 2166 7933 + 216 = 0.ii. Points (3,-1) and (6,1) lie on the line represented by the equation + = 9, find the values of and .iii. Following table shows frequency distribution of duration (in seconds)

of advertisements on TV.

Duration (in sec.) 2530 3035 3540 4045 4550 5055

No. of Advertisements 10 32 15 9 7 2


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Obtain mean duration of advertisement on TV by shift of origin and scale

method.

Iv. For an A.P.1

6,

1

4,

1

3, find 20 and 10 .


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PAPER NO 2.Q1. Attempt any six of the following sub questions:

i. Find the next four terms of the sequences: 2, 5, 8, 11 ii. Write the quadratic equation 7 4 2 = 0 in standard form 2 + + = 0.iii. If12 + 13 = 29 and 13 + 12 = 21, find + .iv. Two coins are tossed simultaneously. Write the sample space S and

the number of sample points n(s).

v. If one root of the quadratic equation 2 7 + = 0 is 4, then find thevalue of k.

vi. Find the modeQ2. Attempt any five of the following sub questions:

i. Find the first four terms of the sequence, whose nth term is tn = n22nii. Solve

2

17

+ 60 = 0 by factorisation method.

iii. Find the value of the determinant, 47 6355 2

5

iv. Form two digit number using the digits 0, 1, 2, 3 without repeating the

digits. Write sample space S, n(S), event P and n(P) where P is the

event that the number so formed is divisible by 3.

v. A die is thrown, find the probability of the eventsa.Getting a number less than 3, b. Getting a prime number.


i. How many three digit natural number are divisible by 4?ii. Determine the nature of the roots of the equation 22 + 5 3 = 0 from

its discriminanats.

iii. Solve the following simultaneous equations using graphical method. + 2 = 5, = 2 2.


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iv. Forty persons were examined for their Haemoglobin % in blood (in mgper 100 ml) and the results were grouped as below: Find Mode.

Haemoglobin %(mg/100ml)

13.114

14.115

15.116

16.117

17.118

No. Of persons8 12 10 6 4

Q4. Attempt any three of the folliwng sub questions:

1.The 11th term and 21st term of an A.P. are 16 and 29 respectively thenfind

a.The first term and the common differenceb.The 34th term c. n such that tn = 55.

2.Solve 2 2

+

1

2 9 +1

+ 14 = 0.3.Below is given frequency distribution of no. Of packages received at apost office per day. Find mean.

No. of Packages 1020 2030 3040 4050 5060 6070

No. of days2 8 16 24 30 20

Q5. Attempt any four of the following sub questions.

i. In winter the temperature at hill station from Monday to Friday is in A.P.The sum of the temperatures of Monday, Tuesday and Wednesday is zero

and the sum of the temperature of Thursday and Friday is 15. Find the

temperature of each of the five days.

ii.Solve the following simultaneous equations: 16+ + 2 = 1; 8+ 12 = 7iii.Two fair dice are thrown, find the probability of the following event that the

sum of the scores on their upper faces is less that 4.

iv.. If a card is drawn from a pack of 52 cards then find the probability ofgetting (i) a red card (ii) a face card.


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PAPER3Q1. Attempt any six of the following sub questions:

i. Find 11from the following A.P. 4, 9, 14, ii. Find the values of a, b, c for the following quadratic equation by

comparing with standard form. 2 + 2 + 1 = 0.iii. Say whether it is quadratic or not. 3 + 4 = 3.iv. If the value of the determinant

2

5 7is 31, find

.

v. What is the equation of Xaxis and Yaxis?vi. For a certain frequency distribution, Median = 156 and Mode = 180

obtain value of mean approximately.

Q2. Attempt any five of the following sub questions:

i. If are the roots of the equation 2 4 + 1 = 0 , finda.

2 +

2 b.

+

ii. Solve 32 26 + 2 = 0iii. Find three consecutive terms in a G.P. such that their sum is 38 andtheir product is 1728.

iv. 72+1 + 13+2 = 27; 132+1 + 7+2 = 33.

v. Find the value of if the given equation 42 3 + 1 = 0 has real andequal roots.


i. A box contains 36 cards marked with number 1 to 36. One card isdrawn from the box at random. What is the probability, that the

number on the ticket is either divisible by 3 or a perfect square.

ii. If (3,1) is the point of intersection of lines + = 7 and + = 5,find the values of a and b.

iii. Solve the following simultaneous equations: 1 + 1 = 12 ; 3 3 = 1

This Question Has been removed.


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iv. Determine the nature of the roots of the quadratic equation 22 7 3 = 0 from its discriminant.

Q4. Attempt any three of the following sub questions:

i. If one root of the equation 2 10 + 2 = 0 is 5 3 , find k.ii. If are the roots of the equation 2 + + = 0, Find thevalue of

+ iii. What is the probability that an ordinary year has 53 Sundays?

Q5. Attempt any four of the following sub questions.

i. Solve 216

6

793

3 + 216 = 0.

ii.

A card is drawn at random from a well shuffled pack of 52 cards. Findthe probability that the card drawn is a diamond card.

iii. Points (3,-1) and (6,1) lie on the line represented by the equation + = 9, find the values of and .iv. A game of change consists of spinning an arrow which comes to rest

pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are

equally likely outcomes. What is the probability that it will point at (a)

8 (b) an odd number (c) a number greater than 2?

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ALGEBRA QUESTION PAPER FOR PRACTISE.pdf