1)If U= {1,2,3,4………}’ P= {x: x is a composite number,
x<=13}, Q= {2,3,6,9,12,15} and R= {2,4,6,12,14,16} then
answer the following questions:
a. Write the set P in listing method.
b. Find (PQR)
c. Show the given information in Venn-diagram.
d. By constructed Venn-diagram, Verify the relation:
n(P)=no(P) + no (P inter Q) + no (PQR)
2)The monthly salary of a married person is Rs. 75,000.
He gets the festival allowance of one month’s salary in a
year. He pays a yearly insurance premium of Rs. 30,000
and donates Rs. 50,000 to charity in the year.1%upto
600000,10%upto 800000, 20%above 8,00,000.
a. What is his annual income?
b. Find the taxable income.
c. Calculate social security charge.
d. Find the total tax paid by the person
in the year.
3) The monthly salary of a salesperson is Rs. 35,000.
Commission of 2.5% is provided if the sales is more than
Rs. 2,50,000 per month.
a. Write the formula to calculate the commission rate.
b. Calculate the commission if the sales of the month is
Rs. 6,50,000.
c. What is his income of the month?
4.A cooperation decided to distribute 15% dividend of the
net profit earned in the year. It has distributed 12000
shares receive.
a. The cooperation earned net profit of Rs. 22,00,000 in a
year.
What dividend does a person with 250 shares receive?
b. What should be the net profit of the cooperation so that
each
share should receive Rs. 35 at the same dividend?
5) A triangular plot of land having sides 18m, 26m, and 30
m then
a. Find the area of land.
b. Write the relation between Aana and paisa.
c. Express the area of plot in Ropani-Aana-Paisa-Daam
format.
(1 Aana = 31.80 sq. m)
6) A square room is 9ft high.196sq.ft. carpet is required for
the floor.
a. Find the length of room.
b. Calculate the area of 4 walls and ceiling.
7) The length of a hall is three times its breadth and 5m
high. It contains three windows of size 2m * 1.5m and two
doors of size 1m * 2.5m.
a. Write the formula to calculate area of 4 walls.
b. Find its length if the cost of painting its 4 walls at the
rate of
Rs. 120 per sq. m is Rs. 46,320.
c. Find the cost of tiling its floor at the rate of Rs. 125 per
sq. m.
8) If 2^x(x+1) *4^x+1/(2 ^ x+1 )^x-1 *8^x is algebraic
fraction.
a. Write the law of negative index.
b. Prove that the given algebraic fraction is equal to 8.
9)p^3+8, p^2 +p-2, and 4p^2-p-18 are three expressions
then,
a. Write the factors of first expression.
b. If one of the factors of second expression is p-1, find the
other
factors.
c. Find the H.C.F of the given expressions.
10) 2m^3n+16n, m^4-12m^2 and 3m^3+6m^2+12m are
three expressions then,
a. Find the factors of first expression.
b. Factorize second expression.
c. Find the L.C.M of given expressions.
11) Study the given figure and answer the following
questions.
a. If AP I BC, write the relation between [BAP AND [CAP.
b. Find the size of unknown angles.
c. Verify experimentally that the sum of any two sides
of a triangle is always greater than the third side by
drawing
two triangles of different measurement.
12) In the given figure, PQR-PMN.
a. Write the corresponding side of MP.
b. Find the value of x.
13) Study the given figure and answer the following
questions.
a. State any one condition of similarity of
two triangles.
b. Show that ABC – APQ.
c. Prove that: AC. PQ = AP. BC
14) Study the table of marks obtained by the students in
an
examination and answer the following questions.
Marks
No. of students
0-10 10-20 20-30 30-40 40-50
4
3
5
6
2
a. How many students are there who obtain less than 20
marks?
b. Represent the given data in histogram.
c. Draw the frequency polygon over the histogram.
d. Write a difference between frequency polygon and
ogive.
15) Observe the following information.
Marks
22
34 45
Frequency
3
5
6
53
56
68
8
7
2
a. What is the mean of the given data?
b. Construct the less than c.f. table.
c. Calculate the first and third quartiles of the given data.
d. By how much percent, third quartiles of the given
data.
16) Solve the following problems:
a. Name the trigonometrical ratio of perpendicular to
hypotenuse
of right-angled triangle with respect to<. A
b. Find the value of sin30-cos60.
c. Find cos< from the given figure.
d. Find the value of x.
4cm