TEST PAPER - 1
1) The shadow of a flag post 25m high is 25√2m. Find the angle of elevation of the Sun.
2) A conical tent has a circular base area 0.375 hectares. if its height is 20m, finds its capacity.
3) The sum of two radii of two circles is 18.5cm and the difference of their circumference is 22cm. Find the radius of the bigger circle.
4) OX and OY are the co-ordinate axes. AB = 6cm.
The point A slides along OX and point B slides along OY. Find the locus of the mid point of AB.
5) in the given figure
AB || CD and O is the centre of the circle. If angle BED= 35°, find angle ACD.
6) a) The line x - y = 3 divides the join of (3,4) and (8,3) in the ratio m: n. Find the ratio.
7) If A=2 0 & B= 14 0
-3 4. 45 44
find the value of scalar factors x and y, such that xA²+ yA= B.
8) 4x³- 12x²+ ax + b has x -3 is a factor but when it is divided by x+ 2 the reminder is -755. Find a and b.
9) A's income is Rs 140 more than B's and C's income is Rs 80 more than D's. If the ratio of A's and C's income is 2:3 and the ratio of B's and D's income is 1:2, find the income of each.
10) Three numbers are in continued proportion. Their sum is 38 and the sum of their squares is 532. Find the numbers.
11)Mrs. Mehta plans to invest Rs 8456 in shares. She partly invests in 17% shares at Rs 140 and the remaining amount in 9% share at Rs 112. Her income from the second investment is Rs 58 more than the first invesr. How much did she invest in shares at Rs 112?
Section II
12) If the loan is returned after one year, a person would have to pay Rs6240 only. If it is returned after 2 years he would have to pay Rs 6489.60 with compound interest. Calculate the amount of loan and the rate of interest.
13) Mrs. Bhagat deposits Rs 1500 every month for 36 months in a bank and receives Rs 65655 at the end of 36 months. Find the rate of simple interest paid by the bank on the recurring deposit.
14) Solve the equation and represent it on the number line
x/2 + 3 ≤ x/3 + 4 < 4x -7, x belongs to R.
15) From the following table, find the frequency distribution and calculate the mean marks:
Marks no of students
less than 8 4
Less than 16 10
less than 24 22
Less than 32 41
less than 40 50
16) Find the values of x and y if the matrices
A= x+ y y & B= 2 & C= 3
2x x- y -1 2 with the relation AB = C.
17) Prove: sin⁶x + cos⁶x = 1 - 3 sin²x + 3 sin⁴x.
18) Two spheres of the same metal weight 1kgf and 7kgf. The radius of the smaller sphere is 2.5cm. The spheres are melted to form a single big sphere . Find the diameter of bigg sphere.
19) MT and NT are tangents to two circles . Prove that M,B,N and T are concyclic points.
(Use alternate segment property and prove that angle MBN + Angle T = 180°)
20) ∆ ABC and ∆ PQR are similar and their areas are 1089cm² and 2304 cm² respectively. If AB= 22cm, find PQ.
21) If A(3,2), B(-2,4) and C(3,-2) are the vertices of ∆ ABC, find the equation of the line perpendicular to AB and passing through the mid-point of BC.
22) The difference between the reciprocals of two consecutive multiples of 3 is 1/468. Find the numbers.
23) A man borrowed a certain sum of money. He can pay Rs 242000 after 2 years or pay Rs 292820 after 4 years to clear the debt alongwith compound interest. Find
a) the rate percent per annum.
b) the sum borrowed.
TEST PAPER -2
1) From the adjoining histogram,
estimate the mode. Also construct the corresponding frequency distribution. Hence find the mean.
2) Find the values of x which satisfy the inequation:
-3+ x ≤ x/2 - 1/2 ≤ 5/6 + x; x belongs to N
graph solution set on the number line.
3) In the adjoining figure,
PQ is a tangent at Y, angle APQ=10°, angle BAY= 30° and XY is a diameter of the circle, Calculate the angles ABX, AXB, BYQ.
4) A hemispherical bowl of internal radius 18cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 6cm and height 12cm. How many bottles can be filled to empty the bowl?
5) In a cricket match Sanjay took 3 wickets less than twice the number of wickets taken by Anshu. If the product of the number of wickets taken by them is 20, find the number of wickets taken by each.
6) Evaluate: {(1+ sin30)/cos30 + cos30/(1+ sin30)}²{sin²60/(1- cos²60 tan²60)}.
7) From the following frequency distribution, draw an accurate ogive:
Marks no. of students
1-10 10
11-20 40
21-30 80
31-40 140
41-50 170
51-60 130
61-70 100
71-80 40
81- 90 20
From the ogive find
a) What percent of the candidate pass the examination, if the pass marks is 40 ?
b) What should the pass mark be, if it is decided to 80% of the candidates to pass ?
If scholarship are awarded to the top 15% of the students , what should be the lowest marks to gain a scholarship ?
8) The boundary of the shaded region in the given diagram consist of four half circles and two quarter circles,
if OP= PQ= OR= OS= 7cm, and the straight lines PQ and RS are perpendicular to each other, find
a) the length of the boundary.
b) the area of the shaded region .
9) A company with 15000 shares of nominal value of Rs 100, declares annual dividend of 10% to the shareholders.
a) find the total dividend paid by the company.
b) Mukesh had bought 250 shares of the company at Rs 125 per share . Calculate the dividend he receives and the percentage return on his investment.
10) A(7,6) and B(-5,-6) are the opposite vertices of a rhombus . Find the equations of its diagonals.
11) Using ruler and compass only , draw a circle of radius 3cm, Extend AB, a diameter of this circle to C, so that BC= 3cm.
Construct a circle to touch AB at C and to touch the circle externally .
12) If the matrices
A= 4 1 3 & B= 3 2 4 & C= 1 & D= x
0 -1 -3 -6 1 -3 3 y
-2
With the relation (3A - 2B)C= D then find x and y.
13) A model of a gas cylinder is made to a scale of 1:100. The gas cylinder consists of a cylindrical part and two hemispherical parts, as shown in the adjoining model.
a) The length of the model is 5 cm. Calculate the length of the cylinder in m.
b) The area of the gas cylinder is 10π m². Calculate the area of the model.
c) Calculate the volume of the gas cylinder in π litres.
TEST PAPER -3
1) The cost price of an article is Rs 2400 which is 20% below the marked price. It is sold at a discount of 16% on the marked price. Find
a) the marked price.
b) the selling price.
c) the profit percent.
2) A man invests Rs 15000 for two years at compound interest. After one year his money amounts to Rs 16800. Find
a) the rate of interest.
b) the intrest for the second year.
c) in what time will it amount to Rs 18816?
3) Draw a neat diagram, showing the lines of symmetry and name each figure in the following cases:
a) a quadrilateral with two diagonals as lines of symmetry.
b) a quadrilateral which has just one line of symmetry.
c) a triangle with only one line of symmetry.
d) ABCD is a rhombus. Prove that AC is a line of symmetry of the Rhombus.
4) In the adjoining figure,
RT is the tangent at S, Prove that :
a) angle PSR= angle OQS.
b) the triangle PSR and SQT are similar.
c) PR. QT = RS. ST
d) If PS= 9cm and PQ= 15cm, Write down the value of (PR. RS)/(QT. ST).
5) A(0,4), B(3,0) are the two vertices of ∆ AOB.
a) Write down the coordinates of A', the reflection of A in the x-axis, of B' the reflection ofB in the y-axis.
b) Assign special name to the figure ABA'B'.
c) If C is the midpoint of AB, write down the coordinates of C', the reflection of C in the origin.
d) assign special name to the quadrilateral ABA'C'.
6) A copper wire when bent in the form of square encloses an area of 121cm². If the same wire is bent into form of a a circle, find the area of the circle.
7) A(2,3), B(4,5) and C(7,2) are the vertices of ∆ ABC.
a) Write down the coordinates of A', B' and C', if ∆ A'B'C' is the image of ∆ ABC when reflected in the origin.
b) Write down the coordinates of A"B" and C", if ∆ A"B"C" is the image of ∆ A'B'C' when reflected in the y-axis.
c) Assign special name to the quadrilateral BCC"B".
d) Hence find its area.
8) A tradesman marks his goods at 50% above the cost price. if he allows two successive discounts of 20% and 10%, and GST is 5%. Find the cost price for the customer.
9) From the adjoining ∆ ABC,
prove that ∆ ABC and ∆ ABD are similar.
Hence prove that AB²= BC. BD.
If AB= 6cm, BD= 4cm and AC= 8cm, calculatethe AD.
10) The compound interest on a sum of money for 2 years is Rs 410 and the simple intrest on the same sum for the same period and at the same rate is Rs400. Find the sum and the rate of interest.
11) The diagram represents the wiper of a car with the dimensions given in the diagram. Calculate
a) the shaded area swept by the wiper.
b) the perimeter of the shaded area.
12) A man invests Rs 4000 in shares. He invests Rs 800 in 7%(Rs 100) shares at Rs 80, Rs 11400 in 8%(Rs 100) shares at Rs 70 and the remainder in 9%(Rs 100) shares. If the total yield from his investment is 10.25% at what price did he buy the 9% shares ? Also find the yield from the investment in 9% shares.
13) The annual salaries of a group of employees are given in the following table :
Salaries number of persons
45 3
50 5
55 8
60 7
65 9
70 4
75 7
Calculate the mean salary. Also calculate the median salary.
14) solve the following inequation and represent the solution set on a number line
x -3< 2x - 2 ≤ 9 - x, x belongs to N.
15) In cyclic quadrilateral ABCD,
AB|| DC, the bisectors of angle A meets CD at E and the circle at F. Prove that
a) EF= CF.
b) ∆ BCF ≡ ∆ DEF.
16) From a solid cylinder of height 12cm and base radius 5cm, a conical cavity of the same height and base is hollowed out. Find
a) the volume, of the remaining solid.
b) the surface, of the remaining solid.
17) A well is to be dug with 6m inside diameter and 20m in depth . Find the volume of the earth to be excavated. The earth taken out is spread all around to a width of 3 m to form an embankment . Find the height of the embankment .
18) Find the value of :
(Sun⁴30+ 2 sin²30 cos²30+ cos⁴30)(Sin²90+ cos²90+ tan²45)².
19) For the following distribution, calculate the mean:
Class frequency
10-16 2
16-22 20
22-28 10
28-34 6
34-40 12
Draw a histogram for the above data and estimate the mode.
20) A(2,5), B(4,1) and C(2,3) are the vertices of the ∆ ABC. Calculate:
a) the equation of the median AD.
b) the equation of the attitude AM.
c) the equation of AC.
d) the coordinates of E, if E is the fourth vertex of the parallelogram ABEC.
21) used ruler and compass only
a) construct a circle on AB = 8cm as diameter
b) to construct another circle of radius 3cm to touch the circle in (a) above externally and the diameter AB produced.
22) If A= 1 2 0 & B= 1 3 -1 & C= 2 & D= x
2 -1 3 2 -3 4 0 y
-1
With the relation (4A - 2B)C= D , then the value of x and y.
23) If A= 2 -1 & B= 2
4 3 -3
Find a matrix X such that AX= B.
Test paper - 4
1) Ashok sells a watch to Bhushan at a gain 20% and Bhushan sells it to Chetan at a loss of 10% while Chetan sells to Dhiraj at 20% profit. If Dhiraj pays Rs 2592 for the watch, find the cost price of Ashok .
2) Anshu gave some money at simple interest to Anuj. At the end of 16 years he received 3 times of his loan from Anuj. Find the rate of interest.
3) The y-axis is a line of symmetry for a figure ABCD containing the point A(3,6) and B(-3,4). State the coordinates of C and D.
4) From the adjoining figure, prove that ∆ XYZ ~ ∆ ABC. Hence prove that
XZ/AC = √{XY/AB . YZ/BC}
Assign a special name to quadrilateral APXR.
5) in a plane, what is the locus of the point equidistant from two intersecting lines ?
In space, what is the locus of points equidistant from the vertices of a square ?
6) Plot the points P(2,7), Q(4,-1) and R(-2,6) on a graph paper. Find the distance PR.
Draw the reflection of this triangle in the y-axis. Write down the coordinates of P'Q' and R' the images of P,Q,R respectively.
7) The boundary of the shaded region in the given diagram consists of three sem circular areas. Calculate
a) the length of the boundary.
b) the area of the shaded region.
8) If (-3,2),(1,-2) and (5,6) are the midpoint of the sides of the triangle, find the coordinates of the vertices of the triangle.
9) A profit at 20% is made on goods when a discount of 10% is given on the marked price. What profit percent will be made, when a discount of 20% is given on the marked price ?
10) in adjoining figure, M is the midpoint of the side CD of a parallelogram ABCD. prove that EL= 2BL.
11) A sum of Rs 32800 is borrowed to be paid back in two years by two equal annual installments, allowing 5% compound interest. Find the annual payment.
12) A point P(-3,4) is reflected in the line x= 2, find its image P'. Hence find the equation of the perpendicular bisector of PP'.
13) A man transfers his Rs 100 shares from 10% at 75 to 16% at 80 and thereby increase his annual income by Rs 2000. Find the number of original shares held by him.
14) In the adjoining figure, the incircle of ∆ABC touches sides BC, CA and AB at D,E,F respectively. Show that
a) AF+ BD+ CE = AE+ BF+ CD.
15) The number of words in 70 sentences of a book were counted and grouped as follows:
No of words CF
1-7 22
8-14 47
15-21 57
22-28 66
29-35 70
Find the mean number of the words in a sentence.
16) Find the values of x, which satisfy the inequation:
2+ x ≤ 3x - 3 ≤ 5+ x; x belongs to I.
Graph the solution set on the number line.
17) Two circles cut at AB and a straight line PAQ cuts the circles at P and Q. If O is the centre of the circle through PAB and the tangents at P and Q meets in T.
Prove that
a) angle TPA= angle ABP
b) P,B,Q,T are concyclic.
18) A solid cone is of height 12cm and the base radius 6cm. Find the radius of the circular section cut from the cone by a plane parallel to the base and 3cm from it. Hence find the volume of the remaining solid .
19) The area of a right angled triangle is 30 sq. units. If the difference between the sides containing right angle is 7 units, find the perimeter of the triangle.
20) In the adjoining diagram, ABCD is a rectangular slab 2m by 5m. What is the height of D above the ground ?
21) For the following frequency distribution, draw an ogive, hence find
Wt in kg no of students
40-45 4
45-50 10
50-55 14
55-60 12
60-65 6
65-70 4
a) median
b) the quartiles.
22) Find the equation of the line through the origin perpendicular to the line joining the points A(-1,-4) and B(7,2).
Find also the equation of the line through (3,4) and parallel to AB.
23) Draw AB= 5cm and BC= 7.5cm such that angle ABC= 90°. Find a point P which is equidistant from B and C and 5cm from A.
also construct a circle touching AB and BC and having its centre R, equidistant from B and C.
24) find the value of a and b from the matrix equation. Where
A= 3 2 & B= a 1 & C= 4 5
4 1 5 b -3 5
With the relation AB= C
in general, if AB = AC, A≠ 0, does it imply B= C ?
25) From the adjoining diagram, write down:
i) tan+90- x)
ii) tan(90- y)
in terms of a, b and h.
Hence show that
BC= h(90- x) - tan(90- y)
If x= 30° , y= 45° and h= 10m, find BC .
26) For the adjoining model of a solid which is drawn to a scale of 1: 200, calculate:
a) the surface area in π m²
b) the volume of litres.
Test paper - 5
1) Rajesh sold was 20% profit. if it had been solved 20% loss, then the selling price would have been Rs 100 less. Find the cost price of the watch.
2) The population of a city has been increasing at the rate of 10% every 5 years. The present population is 48400. What was it 10 years ago?
3) lines l and m are lines of symmetry quadrilateral EFGH. Prove that EFGH is a rectangle.
4) In the adjoining figure MP= NP, RT perpendicular to PN and RS perpendicular to PM
Prove that RT. RM = NR. RS.
5) in a plane, what is the locus of points equidistant from the sides of an angle?
What is the locus of points equidistant from two perpendicular lines ?
6) state the coordinates of the points (4,3) after reflection in the x-axis, followed by reflection in the line x= -2.
State true or false: 'Under reflection, lines which are parallel to the mirror line, have images which are also parallel to the mirror line '.
7) A horse is teethered to one corner of a square plot of side 42m, by a rope 35m long. Find
a) what area it can graze ?
b) what area will be left ungrazed ?
8) if the following pair of lines are perpendicular, find the value of k.
x/3+ y/7= 0 and ky = 3x + 5.
9) A shopkeeper allows 20% discount on his advertised price and then makes a profit of 25% on his outlay. What is the advertise price on which he gains Rs 8000?
10) In the adjoining figure. AD is the bisector of angle A. Prove that
BD/DC = AB/AC.
11) A and B each borrow equal sums for 3 years at 10% simple interest and compound interest respectively. At the time of repayment B has to pay Rs 125.50 more than A. Find the sum borrowed and the interest paid by each.
12) O(0,0), A(4,3) and B(5,0) are the vertices of a ∆ OAB. Find the image A' of A under reflection in the line OB.
a) Show that OA= OB= 5.
b) Assign special name to OABA'.
C) What is the relation between angle AOB and angle A'OB ?
13) Mr Harshad invest Rs 20000. He invests Rs 9000 in 12%, 100 rupees share at Rs 75, Rs 7000 in 10% ten rupees shares at Rs 7 and the remainder in 8%, 100 rupees shares . if the total income from his investment is 14.2%, find at what price did he buy 8% shares ?
14) Find i) the mean ii) the median iii) the mode, for the following numbers, which represent the weights (in kg) of 10 new-born babies:
3.2, 3.4, 3.8, 4.7, 3.7, 4.2, 3.8, 3, 3.5.
15) Find the value of x, satisfy the inequation: 3x - 2> x +4≤ 9; x belongs to R.
Graph the solution set on the number line.
16) A spherical lead shell of external diameter 18cm is melted into a conical vessel 14cm in radius and 31/7 cm high. Find the inner diameter of the shell.
17) x articles cost Rs (3x +20) and (x +4) similar articles cost Rs (5x -4). Find x.
18) Given that AB= 6, BC= 8, angle B= angle M= 90°, find
a) tan angle ABM
b) sin angle ABM.
19) For the following distribution draw an ogive:
Mark frequency
5-9 6
10-14 15
15-19 25
20-24 31
25-29 27
30-34 20
35-39 16
From the ogive obtain the semiinterquartile
20) Find the equation of a line parallel to the line y - 3x = 5 and bisecting the segment joining (-1,2) and (5,7).
21) Construct the rhombus ABCD in which each of the four equal sides= 3.4cm and the diagonal AC= 5.8cm using straight edge and compass only, construct:
a) the circle circumscribed to the triangle ACD,
b) the centre P, of the largest circle that can be drawn within the ∆ ACD to touch the sides of the ∆ ACD.
22) If X= 1 2 & Y= 2 0 & C= 1 2 & D= 7
0 1 0 2 0 1 3
a) Find the matrix A and B if
a) XA= Y
b) CB = D.
23) The angle of depression of two boats at B and C on a river from the top of a tree on the bank of the river at 30° and 45°. The height of the tree is 20m and the boats are in line with the tree and on the same side of it
Find the distance BC between the boats.
24) For the adjoining model of a rocket, which is drawn to scale of 1:1500, calculate:
a) the total surface area in π m².
b) the total volume of the rocket in m³.
Test paper - 6
1) A sales a watch to B at a gain of 20% and B sales it to C at a loss of 10%. If C pays Rs 432, what did it cost to A ?
2) The amount of a certain sum with simple interest at a certain rate of interest are Rs 520 in 3 years and Rs 600 in 5 years. Find the sum and the rate of interest.
3) Draw all the lines of symmetry of the adjoining regular hexagon.
What is the image of P under a clockwise rotation of 180° above O ?
What is the magnitude of angle POS
4) In the adjoining diagram, AP= 3, PQ= 4, BC= 6 and PQ is parallel to BC. Calculate
a) PB
b) PQ/BC . AM/AN
5) a) State the locus of the centre of a circle of radius 2cm touching a fixed circle of radius 3cm, Centre A.
b) State the locus of the centre of a circle of varying radius touching two arms of angle ABC.
6) A point P is reflected in the origin. Coordinates of its image are (-3,2).
a) find the coordinates of P.
b) Find the coordinate of the image P under the reflection the y-axis.
7) Calculate the area of the shaded part of the semicircle in the adjoining diagram, given BC= 20cm. AC =12cm π= 3.142).
8) Points A, B and C have coordinates (1,2), (1,0), (4,0). If ABCD is a parallelogram. Find the coordinates of D.
9) Vishal marks his goods at such a price that he can reduce 20% for cash and yet makes 28% profit. What is the marked price of the article, which cost him Rs 250?
10) In the adjoining diagram, AB, CD and EF are parallel lines. Given that AB= 9cm, CD= y cm, EF= 15cm, AC= 6 cm and CF= x cm, calculate
a) x b) y. c) BC. BE d) BD: DF.
11) A sum of money lent out at simple interest amounts to Rs 7000 in 5 years and to Rs 7800 in 7 years. Find the sum and the rete percent .
12) A and B have coordinates (4,3) and (0,0). Find :
a) the image A' of A under reflection in the y-axis.
b) the image B' of B under reflection in the line AA'.
c) Calculate the length of A'B'.
13) A man invests Rs 8000 in a company paying 8% p.a, when a share of face value of Rs 100 is selling at Rs 60 premium.
a) what is annual income ?
b) what percentage does he get on his money ?
14) From the adjoining diagram, calculate:
a) angle DCA b) angle ACB
15) Calculate the mean and the medium for the following distribution:
number frequency
10 20
15 12
20 8
25 10
30 9
35 1
16) Find the values of x, which satisfy the inequation:
x - 5/2≤ 1+ x/3 ≤ x + 1/3, x belongs to W
graph the solution set on the number line.
17) In the diagram, ABCD is a parallelogram and AB is a diameter. If angle BCE=50°, Calculate
a) angles BED, ABD, AID.
18) water flows through a circular pipe of internal radius 7cm per second. if the pipe is always half full, find the number of litres discharged in 10 minutes.
19) a man buys a identical articles for a total cost Rs 20. If the price of each article was increased by Rs 2, he would be able to buy two less than the original number for Rs 18. Obtain on equation for x and solve it.
20) a) Evaluate sin 60 + cos 30 + tan²30 sin 90.
b) verify : tan60= (2 tan39)/(1 - tan²30).
21) using the data given below construct the cumulative frequency table and draw the ogive. From the ogive determine.
a) the median
b) the interquartile range
Mass no of packets
60-70 2
70-80 5
80-90 12
90-100 10
100-110 8
110-120 3
22) The coordinates of P,Q,R. the vertices of a triangle PQR are (1,1),(5,4),(4,0). if the altitude through P meets QR in X, find
a) the gradient of PX
b) the equation of PX.
23) If A= 2 12 & B= 4 x
0 1 0 1
find the value of x that A²= B.
24) If A= 2 1 & B= x & C= 6
-4. 3 y 8 with the relation AB= C.
25) From the adjoining figure, calculate the height of the tower, correct to the nearest cm.
Test paper -7
Section - A
1) The cost price of 30 eggs is equal to the selling price of 20 eggs. Find the profit percent.
2) The amount of a certain sum with simple interest at a certain rate of interest is Rs 520 in 3 years and 600 in 5 years. Find the sum and the rate of interest.
3) PQRSTU is a regular hexagon with Centre O.
a) What is the image of P under the reflection in the line RU ?
b) also draw all its lines of symmetry.
c) does the hexagon have a point symmetry ?
d) write down the magnitude of angle POT.
4) for the adjoining trapezium,
AB= 4cm , DC= 6cm, PC= 7.5 cm, find
a) AP b) DP: PB c) AD: BC
5) P is a moving point in the plane of ∆ ABC. State the locus of P in the following cases:
a) PA= PC
b) P is equidistant from AB and BC.
c) P is equidistant from AB and AC
Assign special name to a point P, satisfying koci in (b) and (c(.
6) Find the coordinates of the image of (3,1) under reflection in the x-axis followed by reflection in the line x= 1.
7) ABCD represents a flower bed if OA= 28 m and OD= 21m,
find
a) the area of the flower bed.
b) the perimeter of the flower bed .
8) The lines represented by 2x + 5y= 1 and px + 2y= 2 are perpendicular. Find the value of p.
9) A shopkeeper makes his goods at such a price that after allowing a discount of 25/2% for cash payment, he still make a profit of 10%. Find the marked price of an article which cost him Rs 45.
10) If N is the midpoint of AB in the diagram, and triangle ABC has an area 20cm²,
find:
a) the area of ∆ AMN.
b) The area of ∆ NMC.
11) A certain sum amounts to Rs 4640 in 2 years and Rs 4960 in 3 years . Find the principal and the rate percent at SI.
12) A frustum of a cone has diameter of 6cm and 18cm and a slant height of 10cm.
Calculate the height of the cone of which the frustrum is a part.
Section - B
13) a man invests Rs 10080 in 6%, 100 rupees shares at Rs 112. finds his annual income. When the shares fall to Rs 96. He sales out the shares and invests the proceeds in 10%, Rs 10 shares at Rs 8. Find his change in annual income.
14) Calculate the mean for the following distribution, using shortcut method :
marks students
10-20 6
20-30 8
30-40 12
40-50 15
50- 60 10
60-70 9
15) Find the solution set of the inequation:
1≤ x - 3/2 ≤ 5/2; x belongs to R.
graph the solution set on the real number line.
16) in the adjoining figure O is the centre of the circle and ABCD is a parallelogram.
If angle B= 52,
calculate
Angles BEC, EOD, ECD
17) From a solid cylinder of height 4cm and base radius 3 cm, a conical cavity of the same height and base hollowed out. Find the surface area of the remaining solid. Leave your answer in terms of π.
18) 3 years ago Amit's agge was 6 times the square of his son's age. 6 years hence his age will be three times of his son's age. Find their percentage ages.
19) If A= 60°, B= 30°, Prove the following:
a) cos(A+ B) cos(A - B)= cos²A - sin²B.
b) sin(A+ B) sin(A - B)= sin²A - sin²B.
20) For the following frequency distribution, draw an ogive:
Marks. No of students
00-10 30
11-20 50
21-30 100
31-40 150
41-50 150
51-60 130
61-70 90
71-80 60
81-90 30
91-100 10
use your ogive to determine
a) the median mark
b) the percentage of candidate that fails, if the pass marks is 50 .
c) the lower and upper quartile .
21) if the midpoint of the portion of a line between the coordinates axes is (-3,4),find equation of the line.
22) If A= 0 -1
1 0, then show that
A²= 1 0
0 1
23) If A= -1 -1
0 0, then show that A³= A.
24) At the foot of a mountain the elevation of its summit is found in 45°. After ascending 1000m towards the mountain up a slope of 30° inclination the elevation is found to be 60°. Find the height of the mountain.
Test paper - 8
Section - A
1) Vishal sold his radio set at 10% loss. If he sold it for Rs 45 more, he would have made 5% profit. Find the selling price of the radio.
2) The sum of Rs 1500 was lent in such a way that its certain part was lent at 10% per annum and the remaining part 7% per annum. The total simple interest earned in 3 years was Rs 396. Find the sum lent at each rate.
3) Prove that for an isosceles triangle, the perpendicular bisectors of the base is a line of symmetry.
4) From the adjoining diagram, prove that DE bisects angle ADC.
Hence calculate the length CE, given that AD= 3cm, AE= 2.6cm and DC= 5cm
Write down the ratio AD: DB.
5) Draw a line AB of length 6cm. Mark the mid-point M. Construct
a) the locus of points 3cm of AB.
b) the locus of points 5cm from M.
Mark two points P and Q satisfying the above loci.
Measure the distance between P and Q.
6) Find the coordinates of the image of (-2,-3) under reflection in the line y= -1, followed by reflection in the y-axis.
7) The co-ordinates of A,B,C of a rectangle ABCD are (0,2),(-2,0),(1, 3) respectively. Find the coordinates of D.
also find the area of the rectangle.
8) Two dealer offer an article at the same list price. The first allows discount of 25% and 15%, the other allows 30% and 10%. which is better offer ?
9) From the adjoining diagram,
a) prove that ∆ ADB and ∆ BDC are similar.
n) prove that BD²= AD. DC
c) prove that BC²= DC. CA.
d) find ∆ ABC : ∆ BDC.
10) If Rs 50000 amount to Rs 73205 in 4 years, find the rate of compound interest payable yearly.
11) If point A is reflected in the y-axis, coordinates of its image are (4,-3).
a) Find the coordinates of A.
b) Find the coordinates of A under reflection in the line x= -2.
Section -B
12) A man buys 400 ten rupees shares at a premium Rs2.5 each share. If the rate of dividend is 8%. find
a) his investment.
b) dividend received
c) yield
13) Water flows through a circular pipe of internal radius 7cm at 5 m per second. if the pipe is always half full. find the number of litres discharge in 10 minutes.
14) for the following distribution, construct the cumulative frequency tube and draw the ogive.
Class frequency
00-02 17
03-045 22
06-08 29
09-11 18
12-14 9
15-17 5
From the ogive determine
a) the medium
b) the quartiles
c)
15) From the adjoining diagram
a) calculate x, if y= 2x.
b) prove that ∆ ADE is an isosceles, if y= 90.
16) A cylindrical tube with open ends of uniform thickness is made of copper. The tube has external diameter 10cm and internal diameter 7cm and is 28cm long, if the copper weight is 8.9 gm/cm³, calculate the weight of the tube in kg, correct to the nearest gm.
17) A journey of 450km would take 1 hour less, if the speed is increased by 5 kmph. Find the usual speed.
18) If tanx - 3 = 0, find
a) cosx.
b) (sin²x + cos²x)².
c) the value of x, if the angle x is acute.
d) State the value of sin90 cos90 tan45.
19) Draw a histogram for the following:
Marks no of students
00-10 6
10-20 8
20-30 12
30-40 8
40-50 6
Hence find the mode.
20) The ordinate of the point P and Q are (-1, 2) and (2,4) respectively. Find
a) the gradient of PQ.
b) the inquation of PQ.
c) the co-ordinates of the point, where the line PQ intersect the y axis.
21) using ruler compass only, draw an equilateral triangle of side 6cm and draw its incircle. Measure the radius of the circle.
22) find x and y if the relation AB= C
a) A= 3 5 & B= x & C= 2
1 2 y 8
b) A= x. 3 & B= 2 & C= 5
1 y -1 0
23) Find the height of the adjourning church .
24) find the slope of the line 11x - 10y = 13.
Teest paper - 9
Section - A
1) Ajay made a profit of 20% when selling a TV set at Rs 3000. If he has to now pay Rs 500 more for the set, what should be his new selling price in order to make the same percentage profit?
2) At what rate percent per annum will Rs2560 amount to Rs 6250 in four years at compound interest?
3) Draw a regular Pentagon. Does it have line/s of symmetry ? If yes , draw the line/s of symmetry .
4) Using ruler and compass only, construct an isosceles triangle ABC, whose base BC= 6cm and vertex angle BAC=30°(without calculating the base angles ). Hence or otherwise draw circumcircle of ∆ ABC.
5) In the adjoining figure,
if AB= AC, then show that BC= DC.
6) State the coordinates of the point (2,3) after reflection in
a) the line x= 0
b) the line y= 0.
c) the origin.
7) Show that (2,-2),(8,4),(5,7) and (-1,1) are the vertices of a rectangle.
8) Mr Joshi, a tradesman marks his goods at 25% above the cost price. if he allows his customers 10% discount, how much profit% does does he make ?
9) BM and CN are the altitude from B and C respectively to the opposite sides of a triangle BC. Prove that:
a) AB/AC = BM/CN = AM/AN.
b) BN/MC . PN/MP = BP²/CP².
10) A shopkeeper buys 180 articles at Rs 40 each from a wholesaler. He fixes the selling price per article to give him a profit of 40% of the cost price and selling 2/5 of the article at this price. He then lowers the selling price per article so that the profit is only 25% of the cost price. Find his total profit, if all the articles are sold.
11) A race track is an form of a circular ring whose inner circumference is 440m and the outer circumference is 506m. Find the width of the track and also area of the track. (π= 22/7)
Section - B
12) Mrs. Shah invests Rs 4800 in shares of a company which was paying 8% dividend at the time when Rs 100 shares were available at Rs 60 premium. Find
a) her annual income from the shares .
b) the rate of interest she gets from her investment.
13) The following data shows a record of weight of 200 students in kg. Draw an ogive for this distribution.
Wt in kg no of students
40-45. 5
45-50 17
50-55 22
55-60 45
60-65 51
65-70 31
70-75 20
75-80 9
Use the ogive to estimate
a) what fraction of the students weigh 55 kg or above ?
b) what is the weight above which we can find the heftiest 30% of the students ?
14) Solve the following inequation and represent the solution set on the number line : -20≤ 2x - 24 ≤ 16 - 3x, x belongs to W.
15) A rectangular vessel is 40 cm x 16 cm x 11cm and is full of water. This water is poured into a conical vessel of base radius 20cm. If the vessel is completed filled, find the height of the conical vessel .
16) a journey of 192 km from Bombay to Pune takes two hours less by a fast train than by a slow train. if the average speed of the slow train is 16 kmph less than that of the first train , find the average speed of each train.
17) In the adjoining figure
AB|| EC sides AD and BC are 4cm each and perpendicular to AB. Given that angle AED= 60°, angle ACD= 45° find
Ai) AB ii) AC iii) AE.
18) A(2,5) and B(4,1) are two points. Find the equation of the perpendicular bisector of AB. Find the intercepted made by the perpendicular bisector on the axis.
19) Draw two circles with radius 3cm and 5cm with their centres 8 cm apart. Draw a direct common tangent and hence find its length.
20)
If A= 0 1 -1 & B= 1 2 3 & C= 1 -1 1
-1 0 2 2 3 1 -1 1 -1
0 2 -2 1 -1 1
Verify that (BC)A= B(CA).
Test paper - 10
Section - A
1) A merchant buys 200 kg of rice at Rs 1.25 per kilogram, 400 kilogram of rice at 75 paise per kilogram. He mixes them and sells one third of the mixture at 1 rupee per kilogram. At what rate should he sell the remaining mixture so that he may earn a profit of 20% on the whole outlay.
2) the compound interest on a sum of money for 2 years is Rs 410 and the simple interest on the same sum for the same period and aat the same rate is Rs 400. Find the sum of the rate percent ?
3) in the adjoining diagram. AB is a diameter of a circle of radius 10cm, BC =12 cm, CD= 5cm.
a) calculate the lengths of BD and DA.
b) calculate the lengths of DE and AE.
c) Name a pair of similar triangles in the diagram.
d) find ∆ ADE ~ ∆ BDC.
4) State the locuss of the centre of a circle of varying radius, touching fixed lines BC and BD. if angle CBD=45°, draw the locus.
5) A is (6,-1) what are the co-ordinates of the image of a A under reflection in the x-axis followed by reflection in the y-axis ?
6) In the figure diameter of the biggest semi circle is 216cn and diameter of the smallest circle is 72cm. Calculate the area of the shaded portion.
7) If the following pairs of lines are perpendicular, find p, 2y - px =3 and 5y+ 2x =7.
8) a bicycle agent allows 25% discount on his advertisement price and then makes profit of 20% of his outlay. What is the advertised price on which he gains Rs 40.
9) The median BD, CE of a triangle ABC meet at G.
a) prove that the triangle EGD and CGB are similar, hence show that CG= 2GE.
b) prove that AE. AC = AB. AD.
10) find the compound interest on Rs4000 for 3/2 years at 8% p.a, if interest is compounded semi annually.
11) Find the coordinate of the image of (-1,-2) under reflection in the line x= -1 followed by reflection in the y axis.
Section - B
12) A man invests Rs 5400 in 6% Rs 100 shares at Rs 112. Find his annual income. When the shares fall to Rs 96, he sales out the shares and Invests the proceeds in 10% Rs 10 shares at Rs 8. Find his change in annual income.
13) in the ad 0joining diagram: PS = SQ, angle QPS= 54, angel SRQ= 26. Find angle TQR, RTQ
14) in a class test the marks of 30 peoples were:
6, 5, 3,4,5, 5, 8, 3, 1, 4,3, 6,4, 5, 8, 5, 4, 2, 3, 4, 4, 7, 4, 2, 5, 4, 7, 9, 8, 10 .find
a) the mean
b) the mode
c) the median
15) If x belongs to R, find the solution set for the following inequation.
25x²≥ 16
Represent the solution set on a number line.
16) In the adjoining diagram, if angle ABC=50°,
Calculate angle CXO
b) Angle AOC
Hence prove that AXCO is a cyclic quadrilateral.
17) The dimension of the hut closed at both ends, are shown in the adjoining figure. Calculate
a) the volume of the hut.
b) The total surface, excluding the floor.
Given AB= 12m, BC= 20m, CD= 10m, PM= 8m and PR= PS.
18) Find the area of the rectangular plot of ground whose perimeter is 68m and whose diagonal is 26m,
19) Evaluate :
(Sin²60°+ cos²45)/(Tan²60 - son90 cos90).
20) draw a histogram to illustrate the marks of 100 students in an examination.
Marks no of students
00-09 12
10-19 16
20-29 34
30-39 24
40-49 14
Hence estimate the mode.
21) Find the equation of the line joining (-2,3) and (1,-2). If the above line passes through (4, k), find k.
22) If A= sinx cosx
cosx - sinx show that A²= I.
I is unit Matrix and x =90°
23) a man 2 m tall is 50m away from a building 40m high. What is the angle of elevation of the top of the building, from his eye ?
Test paper- 11
Section - A
1) A man sold his watch at a loss of 5%. Had he sold it for Rs 56.25 more he would have gained 10%. Find the cost price of the watch.
2) Find the sum which amounts to Rs 4410 at 10% compound interest for 3/2 years, interest calculated half yearly.
3) In the adjoining ∆ ABC, PR|| CA and RQ||BC. if BP= 15cm, PC= 20cm, AQ= 16cm and BR= 18 cm, calculate
a) AR
b) QC
c) RQ/BC. AR/ABA.
4) PQ is a line of length 8 cm. State the locus of the sense of the circle if its radius is 3 cm and it touches PQ. Draw the locus completely.
5) The boundary of the shaded region in the given diagram consists of 5 semi circular areas, calculate
a) the length of the boundary.
b) the area of the shaded region correct to the nearest square metre.
6) if the point (-5, a)(-1,5) and (7,1) are collinear, find a.
7) A tradesman marks his goods at 25% above cost price. If he allows his customers 10% discount, how much percent profit does he make ?
8) in the adjoining trapezium PQRS , PQ=12cm, RS= 24 cm, RT= 18cm, PL= 8cmQR= 20cm. , Calculate
a) RM
b) PT
c) LM.
9) A man invests Rs 4000 in 10% Rs 100 shares at Rs 125.
Find
a) his annual dividend
b) the rate of interest on is investment.
10) in the adjoining diagram, AB and XY are diameters of a circle, with Centre 0.
If angle APX = 30°,
a) angle AOX, APY, BPY, OAX
Prove that arc AX= arc BY.
11) Calculate the mean of the following distribution, using short-cut method.
marks students
10-20 6
20-30 12
40-50 15
50-60 10
60-70 9
12) Find the solution set of 2≤3(x -2)+5< 2x +5; x belongs to W. represent the solution set on a number line.
13) In the adjoining diagram AB= Cd and angle ABC= 132, calculate
a) angle BAC, AEB, AED, COD
14) A metal pipe of thickness 1cm has an external diameter of 28 cm. Find the volume of metal in 3.5m of the pipe.
15) The length of a rectangle is 3cm greater than its width and the area of the rectangle is 108cm². Find the length.
16) The vertices of a ∆ ABC are A(-1,2, B(2,1) and C(0,4). Find the equation of the median AM.
17) Draw two circles of radius 3cm and 2cm touching each other externally . Draw an arc of a circle of radius 7cm to touch these two circles .
17) Draw two circles of radius 3cm and 2cm touching each other externally . Draw an arc of a circle of radius 7cm to touch these two circles .
18) If A= 3 1
-1 2
Find the value of A²- 5A + 7I, where I is the unit matrix of order two.
19) If A= 1 -1 & B= 4 5 & C= 2 7
2 -2 3 3 1 5
Verify AB= AC.
TEST PAPER 12
1) The cost of the type-setting for a book is Rs 1200. The cost of paper binding etc., Rs 150 per hundred copies. 1000 copies are printed and only 850 copies are sold at the rate of Rs 10 each , the remaining copies are given as free specimen to the institutions . Find the profit percent on the whole transaction.
2) A man borrows Rs 6000 at 50% compound interest . If he repays Rs 1500 at the end each year. Find the amount of loan outstanding at the end of the fourth year.
3) In the adjoining trapezium, if OB: OD= 1:2, write down
a) DO: BD
b) AO: AC.
c) DC: AB
d) BD: BO.
4) Find the coordinates of the image of (-2, -3) under:
a) reflection in the x-axis
b) reflection in the origin
c) reflection in the line y= -1, followed by reflection in the y-axis.
5) A circular road runs round a circular of diameter 14m. if the difference between the circumference of the outer circle and the inner circle is 88m. Find
a) the width of the road.
b) the area of the road.
6) State the reasons whether the lines : 2x + 3y= 6 and 6x = 5+ 4y are parallel or perpendicular to each other. Write down the intercepts made by each line on the axes.
7) A dealer is selling an article at a discount of 20%.
a) what is the selling price, if the market price is Rs 300 ?
b) what is the cost price, if he makes 20% profit.
8) A(-2,4) and B(-4,2) are reflected in the y-axis.
If A' and B' are images of A and B respectively, find the coordinates of A' and B'. Assign special name to AA'BB' . state whether AB'= BA'.
9) Find the principal for which the difference of compound and simple interest in 2 years at 10% per annum is Rs 40. Hence find find the compound interest at the end of 3/2 years. if the compound is payble half yearly.
Section - B
11) Which is better investment: 7% Rs 100 shares at Rs 120 or 8% Rs 10 shares at Rs 13.50 ?
12) P and Q have coordinates (3,2) and (7,6) respectively, write down:
a) the gradient of PQ.
b) the equation of the perpendicular bisector of PQ.
c) the values of a, if (1,a) lies on the perpendicular bisector of PQ .
13) For the following distribution draw an ogive:
Age no of students
25-31 15
31-37. 18
37-43 20
43-49 13
49-55 4
from the ogive
a)state the median age.
b) state the age 20% of the teachers exceed.
14) Find the value of x, which satisfy the inequation;
(x +3)(x -5)≤ (x -2)(x +4), x belongs to Z.
15) In the adjoining circle, AC is a diameter, TC is a tangent. BD = CD and angle DCT= 50. Calculate:
AnglesnDAC, DAB, DCB.
16) A journey of 600km would take 6 hours less, if the speed is increased by 5 kmph. Find the usual speed.
TEST PAPER - 13
S
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