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MARCH 2019

MATHEMATICS PART-I

General Instructions :

(1) All questions are compulsory.

(2) Use of calculator is not allowed.

(3) Figures to the right of questions indicate full marks.

Q 1. (A) Solve the following questions (Any four):

(i) Find the median of :

(ii) Multiply and write the answer in the simplest form :

(iii) If and , the find the value of .

(iv) Write the ratio of second quantity to first quantity in the reduced form :

(v) Write the following polynomial in coefficient form :

(vi) For computation of income tax which is the assessment year of financial year 01-04-2016 to ?

(B) Solve the following questions (Any two) :

(i) Find the value of the polynomial , when .

(ii) If , then find :

(1)

(2) .

(iii) Sangeeta’s monthly income is . She spent of her income and donated for socially useful causes. How much money did she save ?*

Solution 1.

(A) (i) Answer is not given due to the change in reduced syllabus.

(ii)

Ans.

On adding equation (i) and (ii), we get

(iv) Given, First quantity Dozen Pens Pens

Second quantity Pens

(v) Polynomial in coefficient form is :

(vi) Answer is not given due to the change in reduced syllabus.

(B) (i) Given,

(ii) Given,

(1)

(2)

(iii) Answer is not given due to the change in reduced syllabus.

Q 2. (A) Choose the correct alternative :

(i) In the A. P. 2, -2, -6, -10, common difference is :
(A) -4
(B) 2
(C) -2
(D) 4

(ii) For the quadratic equation , the values of are :
(A)
(B)
(C)
(D)

(iii) The tax levied by Central Government for trading within a state is :
(A) IGST
(C) SGST
(B) CGST
(D) UTGST

(iv) If a die is rolled, what is the probability that number appearing on upper face is less than 2 ?
(A)
(B)
(C) 1
(D)

(B) Solve the following questions (Any two) :

(i) First term and common difference of an A.P. are 12 and 4 respectively. If , find .

(ii) If , then find the value of .

(iii) Solve the following quadratic equation :

Solution 2.

(A) (i) (A) -4

(ii) (C)

(iii) Answer is not given due to the change in reduced syllabus.

(iv) (D)

(B) (i) Given, first term , common difference and .

According to the formula,

(ii) Given,

(iii) Given,

On splitting the middle term

and -5 are the roots of the given quadratic equation.

Q 3. (A) Complete the following activities (Any two) :

(i) Smita has invested to purchase shares of FV at a premium of . Find the number of shares she purchased. Complete the given activity to get the answer.

(ii) The following table shows the daily supply of electricity to different places in a town. To show the information by a pie diagram, measures of central angles of sectors are to be decided.

Complete the following activity to find the measures :

(iii) Two coins are tossed simultaneously. Complete the following activity of writing the sample space (S) and expected outcomes of the events :

(i) Event : to get at least one head.

(ii) Event B : to get no head.

Activity : If two coins are tossed simultaneously

(i) Event : at least getting one head.

(ii) Event B : to get no head.

(B) Solve the following questions (Any two) :

(i) Find the 19th term of the A.P. 7, 13, 19, 25,

(ii) Obtain a quadratic equation whose roots are -3 and -7 . *

(iii) Two numbers differ by 3 . The sum of the greater number and twice the smaller number is 15 . Find the smaller number.

Solution 3.

(A) (i) Answer is not given due to the change in reduced syllabus.

(ii) Answer is not given due to the change in reduced syllabus.

(iii) Activity : If two coins are tossed simultaneously.

(i) Event : at least getting one head.

(ii) Event B : to get no head.

(B) (i) Given, A. P. is 7, 13, 19, 25, …….. .

Here,

According to formula,

term is :

The term is 115 .

(ii) Answer is not given due to the change in reduced syllabus.

(iii) Let, the greater number be and the smaller number be .

From the given conditions

and

Now, multiplying equation (i) by 2 and adding both the equations, we get.

Now, substituting the value of in equation (i), we get.

The smaller number is 4 .

Ans.

[9]

Q 4. Solve the following questions (Any three) :

(i) Amit saves certain amount every month in a specific way, In the first month he saves , in the second month , in the third month and so on. How much will be his total savings in 17 months ?

Ans.

Given, Amit’s saving in first month is ₹ 200, in second month is ₹ 250, in third month is ₹ 300 and so on.

forms an A. P.

Here,

and

To find his total savings in 17 months, we have to find .

Amit’s total savings in 17 months will be .

(ii) A two digit number is to be formed using the digits . Repetition of the digits is allowed. Find the probability that a number so formed is a prime number.

Ans.

Sample space Two digit numbers formed out of , with repetition.

Event : Number formed is a prime number.

(iii) Smt. Malhotra purchased solar panels for the taxable value of . She sold them for ₹ 90,000 . The rate of GST is . Find the ITC of Smt. Malhotra. What is the amount of GST payable by her ?*

Ans.

Answer is not given due to the change in reduced syllabus.

(iv) Solve the following simultaneous equations graphically :

Ans.

Given, and .

Solution of given equations :

Q 5. (A) Solve the following questions (Any one):

(i) The following frequency distribution table shows marks obtained by 180 students in Mathematics examination :

Find the value of .

Also draw a histogram representing the above information.

Solution

Answer is not given due to the change in reduced syllabus.

(ii) Two taps together can fill a tank completely in minutes. The smaller tap takes 3 minutes more than the bigger tap to fill the tank. How much time does each tap take to fill the tank completely?

Solution

Let, the bigger tap alone fills the tanks in minutes.

Then, the smaller tap alone fills the tank in minutes.

Therefore, In one minute the bigger tap will fill part of the tank and in one minute smaller tap will fill part of the tank.
Both the taps together fill part of the tank in one minute.

But, both the taps together fill the tank in minutes minutes

But, the time cannot be negative

Bigger tap fills the tank in 5 minutes and smaller tap takes 8 minutes to fill the tank.

Q 6. Solve the following questions (Any one) :

(A) The co-ordinates of the point of intersection of lines and is . Find the values of and .

Solution

Given,

The point of intersection of equation (i) and (ii) is

Substituting the values of and in equations (i) and (ii), we get

Multiplying equation (iv) by 3 and adding to equation (iii), we get

Substituting the value of in equation (iii), We get

The values of is 4 and is 3 .

(B) The following frequency distribution table shows the distances travelled by some rickshaws in a day. Observe the table and answer the following questions :

(i) Which is the modal class? Why?

(ii) Which is the median class and why?
(iii) Write the cumulative frequency (C. F.) of the class preceding the median class. (iv) What is the class interval to calculate median?

Solution

Answer is not given due to the change in reduced syllabus.