TEST PAPER - 2
SECTION A(40 Marks)
Answer All questions from this Section
Question 1.
a) Solve the following Quadratic Equation: x²- 7x +3=0
Give your answer correct to two decimal places. (3)
b) Given A= x 3
y 3
If A²= 3I , where I is the identity matrix of order 2. Find x and y. (3)
c) Using ruler and compass construct a triangle ABC where AB= 3cm. BC= 4cm and angle ABC= 90°. Hence constructed a circle circumscribing the triangle ABC . Measure and write down the radius of the circle. (4)
Question 2
a) Use factor theorem to factorise 6x³+ 17x²+ 4x - 12 completely. (3)
b) Solve the following inequation and represent the solution set on the number line.
3x/5 + 2< x + 4 ≤ x/2 + 5, x ∈R. (3)
c) Draw a Histogram for given data, using a graph paper:
Weekly wages(Rs) no of people
3000-4000 4
4000-5000 9
5000-6000 17
6000-7000 6
7000-8000 7
8000-9000 2
9000-10000 4
Estimate the mode from the graph. (4)
Question 3
a) In the figure given below,
O is the centre of the circle and AB is a diameter.
If AC= BD and angle AOC= 72, find: angle ABC, BAD, ABD. (3)
b) Prove that: sinA/(1+ cotA) - cosA/(1+ tanA)= sinA - cosA. (3)
c) In what ratio is the line joining P(5,3) and Q(-5,3) divided by the y-axis? Also find the coordinates of the point of intersection. (4)
Question 4
a) A solid spherical ball of radius 6cm is melted and recast into 64 identical spherical marbles.
Find the radius of each marble. (3)
b) Each of the letters of the word AUTHORISE is written on identical circular disc and put in a bag. They are will suffered. If a disc is drawn at random from the bag, what is the probability that the letter is:
(i) a vowel
ii) one of the first 9 letters of the English alphabet which appears in the given word.
iii) one of the last 9 letter of the English alphabet which appears in the given word ? (3)
c) Mr. Bedi visit the market and buys the following articles:
Medicine costing Rs 950, GST @ 5%
A pair of shoes costing Rs 3000, GST @ 18%
A laptop bag costing Rs 1000 with a discount of 30%, GST @ 18%.
i) Calculate the total amount of GST paid
ii) The total bill amount including GST paid by Mr. Bedi. (4)
SECTION B(40 Marks)
Attempt any four questions from this Section.
Question 5
a) A company with 5000 shares of nominal value Rs 120 declares an annual dividend of 15%, calculate
i) the total amount of dividend paid by the company.
ii) annual income of Mr. Sharma who holds 80 shares of the company.
If the return percentage of Mr. Sharma from his shares is 10%, find the market value of each share . (3)
b) The mean of the following data is 16, Calculate the value of f.
Marks : 5 10 15 20 25
No of boys: 3 7 f 9 6. (3)
c) The 4th, 6th and the last term of a geometric progression are 10, 40 and 640 respectively. If the common ratio is positive, find the first terms , common ratio and the number of terms of the series. (4)
Question 6
a) if A= 3 0 & B= -4 2
5 1. 1 0
Find A²- 2AB + B². (3)
b) In the given figure AB= 9cm, PA= 7.5cm and PC= 5cm
Chords AD and BC intersect at P
i) prove that ∆ PAB ~ ∆ PCD
ii) Find the length of CD
iii) Find area of ∆ PAB: area of ∆ PCD. (4)
c) From the top of a cliff, the angle of depression of the top and bottom of a tower are observed to be 45° and 60° respectively. If the height of the tower is 20m. Find
i) the height of the cliff .
ii) the distance between the Cliff and the tower. (4)
Question 7
a) Find the value of p if the lines, 5x - 3y +2=0 and 6x - py+7=0 are perpendicular to each other. Hence find the equation of a line passing through (-2, -1) and parallel to 6x - py+7= 0. (3)
b) Using properties of proportion find x: y. Given (x²+ 2x)/(2x +4)= (y²+ 3y)/(3y +9). (3(
c) In the given figure TP and TQ are two tangents to the circle with centre O,
touching at A and C respectively. If angle BCQ= 55° and angle BAP= 60°, find:
Angle OBA, OBC, AOC, ATC. (3)
Question 8
a) What must be added to the polynomials 2x³- 3x²- 8x, so that it leaves a remainder 10 when divided by 2x +1. (3)
b) Mr. Sonu has a recurring deposit account and deposits Rs 750 per month for 2 years. If he gets Rs19125 at the time of maturity, find the rate of interest. (3)
c) Use graph paper for this question.
Take 1cm= 1 unit on both x and y axes.
i) Plot the following points on your graph sheets:
A(-4,0), B(-3,2), C(0,4), D(4,1) and E(7,3).
ii) Reflect the points B, C, D and E on the x-axis and name them as B',C', D', E' respectively.
iii) join the points A,B, C, D, E, E', D', C', B' and A in order.
iv) Name the closed figure formed. (4)
Question 9
a) 40 students enter for a game of shot-put competition. The distance thrown (in metres) is recorded below:
Distance (in m) no of students
12-13 3
13-14 9
14-15 12
15-16 9
16-17 4
17-18 2
18-19 1
Use graph paper to draw on Ogive for the above distribution.
Use a scale of 2cm = 1m on one axis and 2cm= 5 students on the other axis.
Hence using your graph find:
i) the median
ii) Upper quartile
iii) Number of students who cover a distance which is above 33/2 m. (6)
b) If x= {√(2a +1) + √(2a -1)}/{√(2a +1) - √(2a -1)} , prove that x²- 4ax +1=0. (4)
Question 10
a) if the 6th term of an AP is equals 4 times its first term and the sum of first six terms is 75, find the first term and the common difference. (3)
b) The difference of two natural numbers is 7 and their product is 450. Find the numbers. (3)
c) Use ruler and compass for this question. Construct a circle of radius 4.5cm. (4)
Question 11.
a) A model of a high rise building is made to a scale of 1:50.
i) If the height of the model is 0.8m, find the height of the actual building.
ii) if the floor area of a flat in the building is 20m², find the floor area of that in the model. (3)
b) From a solid wooden cylinder of height 28cm and diameter 6cm, two conical cavities are hollowed out.
The diameter of the cones are also 6cm and height 10.5cm. (3) find the volume of the remaining solid prove The Identity
Section - A (Attempt all questions)
Question 1: Choose the correct answers to the question from the given options: (15)
i) A Dealer in Mumbai sold a washing machine to a consumer in Mumbai for Rs18000. If the rate of GST is 18%, then SGST is
a) Rs1620 b) Rs3240 c) nil d) none
ii) Roots of the equation 3x²- 2√6x + 2=0 are:
a) ±√(2/3) b) √(2/3), √(2/3) c) - √(2/3) , -√(2/3) d) -√(2/3) , -√(3/2)
iii) if x - 2 is a factor of x²- 7x + 2m, then the value of m is
a) 5 b) 6 c) 4 d) 3
iv) The transpose of the matrix
1 5 4
-2 1 6 is
a) 1 -2 b) -2 1 6 c) 1 -2 d) 4 5 1
5 1 1 5 4 5 1 -6 1 -2
-2 6 4 6
v) 21% Rs 100 shares at Rs 140 gives rate of return as:
a) 10% b) 120% c) 15% d) 25%
vi) The Reflection of the point P(0,3) in the y-axis is:
a) (0,-3) b) (3,0) c) (0, 3) d) (0,0)
vii) In the figure,
all dimensions are in cm.
The length of AD is:
a) 12cm b) 14cm c) 16 cm d) 18 cm
viii) Richa attaches a conical attachment to one side of the coin. The radius of coin and conical attachment is same. Which of the following is the surface area of the combined solid ?
a) coin base area + coin CSA
b) coin base area + coin CSA + cone CSA
c) total surface area of coin + total surface area cone.
d) total surface area of cone.
ix) Which term of the GP 18, 12, 8, ...., is 512/729 ?
a) 9th b) 10th c) 11th d) 12th
x) if a coin is tossed 3 times, what is the probability of getting a tail each time ?
a) 1/8 b) 1/4 c) 1/16 d) 1/6
xi) Two similar jugs have heights of 4cm and 6cm respectively. If the capacity of the smaller jug is 48 cm³, then the capacity of the larger jug is:
a) 100 cm⅔ b) 130cm³ c) 152cm³ d) 162cm²
xii) x-axis divides the line segment joining the points (2,-3) and (5,6) in the ratio.
a) 1:2 b) 2:1 c) 3:5 d) 2:3
xiii) In the given figure,
O is the centre of the circle. If Angle OAB=40°, then angle ACB is equal to
a) 50° b) 40° c) 60° d) 70°
xiv) The sum of the first 16 terms of the AP is 10, 6, 2,.... is
a) -320 b) 320 c) -350 d) -300
xv) Assertion (A): The median of the following: 12.5, 12, 13, 15, 11, 12, 14, 16, 10, 12, 13
Reason (R): The value of the middle most observation obtained after arranging the data in an ascending and descending order is called the medium of the data
a) A is true, R is false
b) A is false, R is true
c) both A and R are true
d) both A and R are false
Question 2:
i) A conical tent is to accommodate 77 perso. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7m, find the height of the tent and also its curved surface area. (4)
ii) Amit Kumar invests Rs 36000 in buying Rs100 shares at Rs20 premium. The dividend is 15% per annum. Find :
a) the number of shares he buys.
b) his yearly dividend.
c) the percentage return on his investment. (4)
iii) The sum of three numbers in GP is 35 and their product is 1000. Find the numbers . (4)
Question 3:
i) Pawan deposituRs 150 every month in a bank for 8 months under the recurring deposit scheme. Find the maturity value of his deposit, if the interest is calculated every month and the rate of the interest is 8% per annum. (4)
ii) Find the equation of a line passing through the point (-2,3) and having the x-intercept of 4 units. (4)
iii) Use graph paper to solve this question.
a) Plot the points P(0,3), Q(3,-2) and O(0,0) .
b) Plot R, the image of Q, when reflected in the y-axis and write its coordinates.
c) What is the geometrical name of the figure PQOR ? (5)
SECTION - B
(Attempt any four questions from this section)
Question 4:
i) A dealer is Patna (Bihar) supplies goods worth Rs 15000 to a dealer in Sonipat (Haryana). The dealer in Sonepat supplies the same goods to a dealer in Rohtak (Haryana) at a profit of Rs3000. If the rate GST is 18%. calculate:
a) The cost of goods to the dealer in Rohtak.
b) Net GST paid by the dealer in Sonepat . (3)
ii) Solve the equation 4x²- 5x -3=0 and give your answer to correct to two decimal places. (3)
iii) On a map drawn to a scale if 1: 250000, a triangular plot of land has the following measurements. AB= 3cm, BC =4 cm and angle ABC=90°. Calculate
a) the actual length of AB in km.
b) the area of the plot in km². (4)
Question 5:
i) If A= 0 -1 B= 1 3 C= 1 0
2 5 6 4 -3 -2
find A(B + C). (3)
ii) Two circles touch externally at P. a tangent touches the circles at A and B. Prove that the tangent at P bisects AB. (3)
iii) The polynomial (px³+ 3x²-3) and (2x³- 5x +p) when divided by (x -4) leave the same reminder. Find the value of p. (4)
Question 6:
i) Find the coordinates of the point of trisection of the line segment joining the points A(5,-3), and B( 2,-9). (3)
ii) Prove that: cotA - tanA = (2cos²A -1)/(sinA cosA). (3)
iii) How many terms of the AP 72, 66, 60,..... must be taken to give the sum 0 ? (4)
Question 7:
i) The daily wages of 80 workers in a project ate given below:
Wages No. Of workers
400-450 2
400-500 6
500-550 12
550-600 18
600-650 24
650-700 13
700-750 5
Use a graph paper to draw an ogive for the above distribution, (use a scale of 2cm = Rs50 on x-axis and 2cm= 10 workers on yaxr). Use your ogive to estimate :
a) the median wagy of the workers .
b) the lower quartile wage of workers.
c) the number of workers who earns more than Rs625 daily. (5)
ii) A bus covers distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/hr and as such it takes two hours longer to cover the total distance. Assume the uniform speed to be x km/hr, form an equation and solve it to evaluate x. (5)
Question 8:
i) In a lottery there are 5 prizes and 20 blanks. What is the probability getting a prize ? (3)
ii) Construct a quadrilateral ABCD which AB= 5cm, BC= 4cm, angle B= 60°, AD= 5.5cm and D is equidistant from AB and BC. (3)
iii) In the given figure,
PQ is a tangent to the circle at A. AB and AD are bisectors of angle CAQ and angle PAC. If Angle BAQ= 30°, show that
a) BD is a diameter of the circle.
b) ABC is an isosceles triangle. (4)
Question 9:
i) Solve the following inequation and graph the solution set on the number line:
-1/5 ≤ 3x/10 +1 < 2/5, x ∈ R. (3)
ii) Calculate the mean of the following distribution using step deviation method.
Marks no.of students
00-10 10
10-20 9
20-30 25
30-40 30
40-50 16
50-60 10 (3)
iii) In the figure,
ABCD is a parallelogram. P is a point on BC such that BP: PC= 1:2. DP produced meets produced at Q. Given ar(∆CPQ) is 20 m², find
a) ar(∆ DCP)
b) ar(|| gm ABCD). (4)
Question 10:
i) using properties of proportion, solve for x. Given that x is positive:
{2x + √(4x²-1)}/{2x - √(4x²-1)}= 4. (3)
ii) Draw a circle with centre O and radius 3.1cm. Take a point P outside the circle at a distance of 6.2cm from its Centre. Draw two tangents to the circle from the point P. (3)
iii) An aeroplane at an altitude of 1500 metres finds that two ships are selling towards it in the same direction. The angles of depression as observed from the aeroplane are 45° and 30° respectively. Find the distance between the two ships. (4)
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