SQP-10
TEST PAPER - 2
Section - A (40 Marks)
(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 cm³ 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:
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 median 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 persons . 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 & their product is 1000. Find the numbers. (4)
Question 3:
i) Pawan deposited Rs 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(40 Marks)
(Attempt any four questions from this section)
Question 4:
i) A dealer in Patna (Bihar) supplies goods worth Rs 15000 to a dealer in Sonepat (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 & give answer to correct to 2-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 remainder. Find the value of p. (4)
Question 6:
i) Find the coordinates of the points 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 are given below:
Wages in(Rs) 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 y-axis). Use your ogive to estimate :
a) the median wage of the workers .
b) the lower quartile wage of workers.
c) the number of workers who earn 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. Assuming 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 & 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 AB 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)
TEST PAPER -1
Max. Marks: 80
SECTION - A(40 Marks)
(Attempt all questions from this Section)
Question 1: Choose a correct answer to the questions from the given options:
(Do not copy the questions , write the correct answers only ). (15)
i) If Matrix
A= [-1 2] & B= [1 -2
0 3]
Which of the following operation is possible ?
a) A- B b) A+ B c) AB d) BA
ii) If x²+ kx + 6=(x -2)(x -3) for all values of x, then the value of k is:
a) -5 b) -3 c) -2 d) 5
iii) A retailer purchased an item for Rs 1500 from a wholesale and sells it to a customer at 10% profit. The sales are intra-state and the rate of GST is 10%. The amount of GST paid by the customer is:
a) Rs 15 b) Rs 30 c) Rs 150 d) Rs 165
iv) If the roots of equation x²- 6x + k=0 are real and distinct, then value of k is
a) > -9 b) > - 6 c) < 6 d) < 9
v) Which of the following is/are an arithmetic progression (AP) ?
1)1, 4, 9, 16, ... 2) √3,2√3, 3√3, 4√3,... 3) 8, 6, 4, 2, ....
a) only 1 b) only 2 c) only 2 and 3 d) all 1, 2, and 3
vi) The table shows the value of x and y, where x is proportional to y.
x : 6 12 N
y: M 18 6
What are the values of M and N?
a) M=4, N= 9 b) M=9, N= 3 c) M=9, N= 4 d) M=12, N= 0
vii) In the given diagram, ∆ ABC ~ ∆ PQR and AD/PS= 3/8.
The value of AB: PQ is:
a) 8:3 b) 3:5 c) 3:8 d) 5:8
viii) A right angle triangle shaped piece of hard board is rotate completely about its hypotenuse, as shown in the diagram.
The solid is so formed is always:
1) a single cone 2) a double cone
Which of the statement is valid ?
a) only 1 b) only 2 c) both 1 and 2 d) neither 1 nor to 2.
ix) Event A: The Sun will rise from east tomorrow.
Event B: It will rain on Monday.
Event C: February month has 29 days in a leap year.
Which of the above event/s has probability equal to 1 ?
a) all events A, B and C
b) both events A and B.
c) both events B and C
d) both events A and C.
x) The three vertices of a scalene triangle are always equidist from a fixed point. The point is:
a) Orthocentre of the triangle.
b) Incentre of the triangle.
c) Circumcenter of the triangle.
d) Centroid of the triangle.
xi) In a circle with radius R, the shortest distance between two parallel tangents is equal to:
a) R b) 2R c) 2πR d) πR
xii) An observer at point E, which is at a certain distance from the lamp post AB, finds the angle of elevation of top of lamp post from the positions C, D and E as α, β and γ. it is given that B, C and D and E are along a straight line.
Which of the following condition is satisfied ?
a) tanα > tanβ b) tanβ < tanγ c) tanγ> tanα d) tanα< tanβ
xiii) 1) Shares of company A, paying 12%, Rs100 shares at Rs 80.
2) Shares of company B, paying 12%, Rs 100 shares are at Rs 100.
3) Shares of company C, paying 12%, Rs 100 shares are at Rs 120.
Shares of which company are at premium?
a) company A
b) company B
c) Company C
d) Company A and C
xiv) Which of the following equation represent a line passing through origin ?
a) 3x -2y+5=0 b) 2x-3y=0 c) x= 5 d) y= -6
xv) For the given 25 variables x₁, x₂, x₃,....,x₂₅
Assertion (A): To find median of the given data, the variate needs to be arranged in ascending or descending order.
Reason (R): The median is the central most term of the arranged 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) Shown below is a horizontal water tank composed of a cylinder and two hemispheres .
The tank is filled up to a height of 7m. Find the surface area of the tank in contact with water. (π=22/7). (4)
ii) In a recurring deposit account for 2 years, the total amount deposited by a person is Rs 9600. If the intrest earned by him is one-twelfth of his total deposit, then find:
a) the interest he earns .
b) his monthly deposit.
c) the rate of interest. (4)
iii) Find :
a) (sinθ + cosecθ)²
b) (cosθ + secθ)²
Using the above results, prove the following trigonometry identity.
(sinθ + cosecθ)²+ (cosθ + secθ)²= 7+ tan²θ+ cot²θ. (4)
Question 3:
i) If a, b and c are in continued proportion, then show that:
(3a²+ 5ab+ 7b²)/(3a²+ 5bc+ 7c²)= a/c. (4)
ii) In the given diagram, O is the centre of circle circumscribing the ∆ ABC. CD is perpendicular to chord AB. Angle OAC=32°.Find each of the unknown angles x, y, z. (4)
iii) Study the graph and answer each of the following: (5)
a) Name the curve plotted
b) Total number of students.
c) The median marks.
d) Number of students scoring between 50 and 80 marks.
SECTION - B(40 Marks)
(Attempt any four questions from this section)
Question 4:
i) If matrix A= 4 -4
-4 4, find A². If A²= pA, then find the value of p. (3)
ii) Solve the given equation x²- 4x -2=0 and Express your answer correct to two places of decimal.
(you may use mathematical table for this question). (3)
iii) In the given diagram,
∆ ABC is right angle at B. BDFE is a rectangle. AD= 6CPcm, CE= 4cm and BC= 12 cm
a) Prove that ∆ ADF ~ ∆ FEC
b) Prove that ∆ ADF ~ ∆ ABC
c) Find the length of FE.
d) Find area ∆ ADF : ∆ ABC. (4)
Question 5:
i) Shown below is a table illustrating the monthly income distribution of a company with 100 employees.
Income (in Rs 10000) no of employees
00-04 55
04-08 15
08-12 06
12-16 08
16-20 12
20-24 04
Using step deviation method, find the mean monthly income of an employee. (3)
ii) The following bill shows the GST rate and the marked price of articles:
Vidyut Electronic
S. No Item Marked price Quantity GST %
a) LED TV set Rs 12000 01 28%
b) MP4 player Rs 5000 01 18%
Find the total amount to be paid (including GST) for the above bill. (3)
iii) In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If angle PQB =55°.
a) find the value of the angles x, y and z.
b) prove that RB is parallel to PQ. (4)
Question 6
i) There are three positive numbers in a Geometric Progression (GP) such that:
a) their product is 3375
b) the result of the product of first and second number added to the product of second and third number is 750.
Find the numbers. (3)
ii) the table given below shows the ages of members of a society.
Age (in yrs) no of society
25-35 05
35-45 32
45-55 69
55-65 80
65-75 61
75-85 13
Use graph sheet for this question.
Take 2 cm= 10 years along one axis and 2cm = 10 members along the other axis .
a) Draw a histogram representing the above distribution.
b) Hence find modal age of the members. (3)
iii) A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 7m each and the total height of the tent is 14cm. Find the:
a) quantity of air contained inside the tent .
b) radius of a sphere whose volume is equal to the quantity of air inside the tent . (4)
Question 7
i) The line segment joining A(2, -3) and B(-3, 2) is a intercepted by the x-axis at the point M and the y-axis at the point N. PQ is perpendicular to AB produced at R and meets the y-axis at a distance of 6 units from the origin O, as shown in the diagram, at S. Find the:
b) coordinates of S.
c) slope of AB.
d) equation of line PQ. (5)
ii) The angle of the depression of two ships A and B on opposite sides of a light house of height 100m are respectively 42° and 54°. The line joining the two ships passes through the foot of the light house.
(Use mathematical tables for this question). (5)
Question 8
i) Solve the following inequation write the solution set and represent it on the real number line. (3)
3 - 2x ≥ x + (1- x)/3 > 2x/5, x ∈ R
ii) ABCD is a cyclic quadrilateral in which BC= CD and EF is a tangent at A.
a) angle ADC b) angle ABD c) angle FAD (3)
iii) A(a,b), B(-4,3) and C(8, -6) are the vertices of a ∆ ABC. Point D is on BC such that BD : DC is 2:1 and M (6,0) is midpoint of AD. Find:
a) coordinates of point D.
b) coordinates of point A.
c) equation of a line passing through M and parallel to the line BC. (4)
Question 9:
i) Using Componendo and Dividendo, find the value of x, when:
(x³+ 3x)/(3x²+ 1)= 14/13. (3)
ii) The total expense of a trip for certain number of people is Rs 18000. If three more people join them, then the share of each reduces by Rs 3000. Taking x to be the original number of people, form a quadratic equation in x and solve it to find the value of x. (3)
iii) Using ruler and compass only construct angle ABC= 60°, AB= 6cm and BC= 5cm.
a) Construct the locus of points equidistant from AB and BC.
b) construct the locus of points equidistant from A and B.
c) Mark the point which satisfies both the condition (a) and (b) as P.
Hence, Construct a circle with centre P and passing through A and B. (4)
Question 10
i) using reminder and factor theorem, factorise completely, the given polynomial:
2x³- 9x²+ 7x + 6. (3)
ii) Each of the letters of the word " HOUSEWARMING" is written on cards and put in a bag. if a card is drawn at a random from the bag after shuffling , what is the probability that the letter on the card is: (3)
a) a vowel
b) one of the letters of the word SEWING .
c) not a letter from the word WEAR.
iii) Use graph sheet for this question. Take 2cm = 1 unit along the axes. (3)
a) plot A(1,2), B(1,1) and C(2,1)
b) Reflect A, B and C about y-axis and name them as A's, B' and C'.
c) Reflect A, B, C, A'c , B' and C' about x-axis and name them as A", B", C", A"', B"' and C"' respectively .
d) join A, B, C, C", B", A", B"', C"', C', B', A' and A to form a close figure. (4)
ic iia iiid ivd vc vic viic viiib ixd xc xib xiia xiiic xivb xvc
2i) 748m² ii) Rs800, Rs 400, 8% iii) sin²x + cosec²x +2, cos²x + sec²x +2
3iii) b) 40 c) 56 d) 25 4i) 8 ii) ±0.45 iii) c) 3 d) 4/9 5i) Rs 67600 ii) Rs 21260 iii) 35°
6i) 5,15,45 or 45,15,5 ii) b) 58yrs iiia) 1437(1/3)m³ b) 7m.
7i)b) (0,6) c) -1 d) x- y+6=0 ii) a)183.57m, b) 184m
8) {x: 1≥ x > -5/4, x ∈R} ii) 105°, 32°, 31° iii) (4,-3), (8,3) , 18
9)i) 2 ii) 3 10)i) (x-2)(x-3)(2x+1) ii) 5/12, 1/2, 2/3
TEST PAPER - 2
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 cm³ 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:
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 median 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 persons . 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 & their product is 1000. Find the numbers. (4)
Question 3:
i) Pawan deposited Rs 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(40 Marks)
(Attempt any four questions from this section)
Question 4:
i) A dealer in Patna (Bihar) supplies goods worth Rs 15000 to a dealer in Sonepat (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 & give answer to correct to 2-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 remainder. Find the value of p. (4)
Question 6:
i) Find the coordinates of the points 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 are given below:
Wages in(Rs) 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 y-axis). Use your ogive to estimate :
a) the median wage of the workers .
b) the lower quartile wage of workers.
c) the number of workers who earn 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. Assuming 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 & 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 AB 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)
1) i a, ii b iii a iv c v c vi c vii c viii b ix a x a xi d xii a xiii a xiv a xv c
2) i) 24m, 550m² ii)a) 300 b) Rs4500 c) 12.5% iii) 20,10,5 or 5,10,20
3) i) Rs1236 ii) x + 2y -4=0 iii) b) (-3,-2) c) kite
4) i) a) Rs21240 b) Rs540 ii) 1.69 or -0.44 iii) a) 7.5km b) 37.5 km²
5) i) -3 -2
19 16 iii) 1 6) i) (4,-5),(3,-7) iii) 25
7) i) Rs600 b) Rs550 c) 29 ii) x²- 10x -1200=0, x= 40. 8) i) 1/5
9) i) {x: -4≤ x < 2, x ∈R} ii) 31.3 iii) a) 40 m² b) 120 m² 10) i) 5/8 iii) 1095 m
TEST PAPER - 3
SECTION - A(40 Marks)
(Attempt all questions from this section)
Question 1: Choose the correct option : (15)
i) Dividend Is always paid on.
a) the face value of share
b) the market value of share
c) the amount invested d) none of these
ii) The roots of the quadratic equation x²-5x +5=0 are:
a) real and equal b) real and unequal c) rational d) imaginary
iii) The remainder when x³- 2x²- 5x +6 is divided by (x + 2) is
a) -1 b) 1 c) 2 d) 0
iv) For a GP with first term a, common ratio r and last term l, The n-th term from the end is :
a) lrⁿ⁻¹ b) rⁿ⁻¹/l c) rⁿ⁻¹/l d) l/rⁿ⁻¹
v) 30th term of the AP 10, 7, 4,.....is
a) 97 b) 77 c) - 77 d) -87
vi) The reflection of the point A(4,-1) in the line x=2 is
a) ( 0,-1) b) (8,-1) c) (0,1) d) (-1,0)
vii) in the figure, if AB || CD, then
a) ∆ AOB ~ ∆ COD b) ∆ AOB ~ ∆ DOC c) ∆ AOB ~ ∆ ODC d) none
viii) A shed of a workshop is of the given shape.
The volume of the air that the shed can hold is:
a) 200m³ b) 288.75cm³ c) 300m³ d) 307.25m³
ix) If 8- x ≥ 6 - 2x, x ∈N, then the solution set is:
a) {-2,-1,0,1,....} b) {1,2,3,....} c) {0,1,2,3....} d) {--1,0,1,2....}
x) A book has pages numbered from 1 to 85. What is the probability that the sum of the digits of the page number is 8, if a page is chosen at random.
a) 6/85 b) 7/85 c) 9/85 d) 8/85
xi) The order of a column matrix is of the form :
a) m x1 b) 1 x m c) m x2 d) 2 x 2
xii) Two vertices of ∆ ABC are (-1,4) and B(5,2) and its centroid G(0,3). The co-ordinates of C are:
a) (4,3) b) (4,15) c) (-4,-15) d) (-15,-4)
xiii) In the given figure, O is the centre of a circle. If the length of chord PQ is equal to the radius of the circle, then angle PRQ is:
a) 15° b) 30° c) 45° d) 60°
xiv) In a size transformation, if the scale factor k is equal to 1, then it is:
a) an enlargement b) a reduction c) an identity transformation d) none of these
xv) Assertion (A): Daily wages of the workers of a factory are as below :
Daily wages (in Rs) No of workers
131-136 5
137-142 27
143-148 20
149-154 18
155-160 12
The lower limit of the modal class of the above data is 137.
Reason (R): The observation which occurs maximum number of times is called the mode 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) Anupama has a recurring deposit account in a bank for 7/2 years. if the bank pays the interest at the rate of 12% p.a. and Anupama gets Rs 3961.80 on maturity. Find the value of monthly installment. (4)
ii) Rs8000 and Rs10000 were invested in Rs100 shares giving dividend 12% and 8% respectively. The dividend are collected and all the shares are sold at a loss of 2% and 3% respectively on the investment, find:
a) the dividend collected
b) the total sale proceeds
c) gain% on the whole transaction. (4)
iii) Show: cosx/(cosecx +1) + cosx/(cosecx -1) = 2 tanx. (4)
Question -3:
i) Find three numbers in GP whose sum is 52 and the sum of whose product in pairs is 624. (4)
ii) A(2,-4), B(3,3) and C(-1,5) are the vertices of ∆ ABC. Find the equation of the altitude of the triangle through C. (4)
iii) Use graph paper for this question. (Take 2cm=1 unit along both x and y axis). ABCD is a quadrilateral whose vertices are A(2,2), B(2,-2), C(0,-1) and D(0,1).
a) Reflect quadrilateral ABCD on the y-axis and name it as A'B'CD.
b) Write down the coordinates of A's and B '.
c) Name two points which are invariant under the above reflection.
d) Name the polygon A'B'CD. (5)
Section - B (40 marks)
(attempt any four questions from this section)
Question 4:
i) A dealer marks a juicer-mixer for Rs2150. A customer requests the dealer to reduce the price so that he has to pay Rs2124 including GST. if the rate of GST is 18%, how much reduction is needed in the price of the juicer mixture ? (3)
ii) Solve the following equation using quadratic formula: 6x²+ (12- 8a)x - 16a =0. (3)
iii) The daily profits in rupee of 100 shops in a department store are distributed us follows:
Profit (in Rs) No.of shops
000-100 12
100-200 18
200-300 27
300-400 20
400-500 17
500-600 6
Draw a histogram of the data given above on a graph paper and estimate the mode. (4)
Question 5:
i) If A= 3 2 & B= 14 3
-1 1 2 4, find a matrix C such that AC= B. (3)
ii) In ∆ PQR,
Angle PQR= 90°, PQ= 24cm and QR=7 cm. Find the radius of the inscribed circle. (3)
iii) Find the value of k such that (x- 2) is a factor of the polynomial x³+ kx²- 5x -6. (4)
Question 6:
i) Find the equation the line parallel to 2x + 5y -9=0 and passing through the midpoint of the line segment joining A(2,7) and B(-4,1). (3)
ii) The side of a triangle plot of land in a map were 6cm, 8cm and 10cm. If the scale of the map was 1: 1000. Find the actual area of the plot in m². (3)
iii) The 10th term of an AP is 52 and 16th term is 82. Find its general term. (4)
Question 7:
i) Construct angle ABC=120°, where AB = BC=5cm. Mark two points D, E which satisfy both the following conditions .
a) equidistant from BA and BC.
b) at a distance of 5cm from B, point E is on the side of reflex angle ABC. join AE and EC. Describe the figures AECD, ABD and ABE. (5)
ii) Use graph paper for the question. (5)
The following table shows the weight in gram of a sample of 100 potatoes taken from a large consignment.
Weight (in gm). Frequency
50-60 8
60-70 10
70-80 12
80-90 16
90-100 18
100-110 14
110-120 12
120-130 10
a) Calculate the cumulative frequencies .
b) Draw the cumulative frequency curve and from it determine the median weight of the potatoes.
Question 8:
i) What is the probability that an ordinary year has 53 Sundays ? (3)
ii) A spherical metallic ball of radius 3cm is melted and recast into three spherical balls. The radii of two of these balls are 2.5cm and 2cm respectively. Find the radius of the third ball. (3)
iii) In the figure,
O is the centre of the circle and angle AOC= 100°.
Calculate angles ADC and ABC. (4)
Question 9:
i) Solve the following inequation and represent the solution set on the number line:
-2/3 < 1 + x/3 ≤ 2/3, x ∈ R. (3)
ii) Find the mean of the following distribution .
X: 5 6 7 8 9
f: 3 7 5 9 1 (3)
iii) In ∆ ABC,
D is a point on BC such that angle ABC= angle CAD, AB= 20cm, AD= 10cm and AC = 14cm. Find
a) DC b) BD c) ar(∆ ADC): ar(∆ ABC). (4)
Question 10:
i) Using properties of proportion find x : y, given:
(x²+ 2x)/(2x +4) = (y²+ 3y)/(3y +9). (3)
ii) Construct a regular hexagon of side 2.8 cm. Inscribe a circle in it. (3)
iii) The angle of elevation of an aeroplane from a point P on the ground is 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. if the aeroplane is flying at a constant height of 1500√3 m, find the speed of the aeroplane. (4)
1) ia iib iiid ivd vc via viib viiib ixb xc xia xiic xiiib xivc xvb
2) i) 60 ii) Rs1760 b) Rs17540 c) 65/9%
3) i) 4,12,36 or 36,12,4 ii) x + 7y -34=0 iii) b) (-2,2),(-2,-2) c) C and D d) isosceles trapezium 4) i) Rs350 ii) 4a/3, -2 iii) Rs255
5) i) 2 -1
4 3 ii) 3cm iii) 2 6) i) 2x + 5y =18 ii) 2400 m² iii) 2+ 5n
7) i) kite, equilateral triangle, isosceles triangle ii) b) 93 g 8) i) 1/7 ii) 1.5 cm iii) 50,130
9) i) {x: -5< x ≤ -1, x belongs to R} ii) 6.92 iii) a) 7cm b) 14cm c) 1/4
10) i) 2:3 iii) 720 km/h.
TEST PAPER -4
SECTION - A(40 MARKS)
(Attempt all questions from this section)
Question -1 : Choose the correct answers to the questions from the given options. (15)
i) A dealer in Rohtak(Haryana) sold a table for Rs16000 to a consumer in Sonpat (Haryana). If the GST rate is 18%, then IGST is:
a) Rs1440 b) Rs2880 c) Rs3000 d) nil
ii) The roots of x²- 5x +1=0 are:
a) real and unequal
b) real and equal
c) imaginary d) none
iii) On dividing x²- 4x + m by (x -2), the remainder is -1. The value of m is
a) 1 b) 2 c) -2 d) 3
iv) An identity matrix is always:
a) a square Matrix
b) rectangular Matrix
c) a row matrix
d) a null matrix
v) The sum of 1+ 3+ 7+....199 is:
a) 10000 b) 9000 c) 8000 d) 8500
vi) Which of the following points is invariant with respect to the line y=-2 ?
a) (3,2) b) (3,-2) c) (2,3) d) (-2,3)
vii) In the figure,
the product ab is equal to :
a) c + x b) cx c) bc d) b + c
viii) A right circular cylinder of radius r and height h (h > 2r) just encloses a sphere of diameter:
a) r b) 2r c) h d) 2h
ix) if Disha invests Rs15500 on Rs100 shares at a premium of Rs25, then the number of shares she buys is:
a) 124 b) 155 c) 160 d) 180
x) What is the probability of not picking a face card when you draw a card at random from a deck of playing cards ?
a) 3/13 b) 10/13 c) 1 d) 2/13
xi) 12th term of the GP 4, 8, 16, 32,..... is
a) 8000 b) 8050 c) 8120 d) 8192
xii) The y-axis divides the line segment joining the points (-4,5) and (3,-7) in the ratio:
a) 2: 7 b) 3 : 7 c) 4: 3 d) 3:4
xiii) In the figure,
if Angle ACB=50°, then angle AOB is
a) 40° b) 50° c) 60° d) 70°
xiv) A replica of a cone is made. if their surface areas are in the ratio 4 : 25, then the ratio of the radius is:
a) 4 :25 b) 8 : 125 c) 2 : 5 d) 1 : 5
xv) Assertion (A) : For a data, if mean=20 and mode= 22, then the value of median will 20.7.
Reason (R): The emperical relationship between mean, mode and median is given by: mean = 3 median - 2 mode
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) Shalini has a cumulative time deposit account of Rs340 per month at 6% . if she gets Rs7157 at the time of maturity, find the total time for which the account was held. (4)
ii) A man bought 1000 shares, each of face value Rs5 at Rs 7 per share . At the end of the year, the company from which he bought the shares declared a dividend of 8%. Calculate
a) the amount of money invested by the man.
b) the percentage return on his outlay. (4)
iii) Prove (1+ cosA)/(1- cosA)= (cosecA + cotA)². (4)
Question 3:
i) The n-th term of a sequence is (4ⁿ + 7n). Find the sum of first n terms of this sequence. (4)
ii) A(2,7) and (-3,5) are two given points . Find
a) the gradient of AB
b) the equation of AB. (4)
iii) Use graph paper for this question.
( take 2cm = 1 unit along with x and y axis)
Plot the points O(0,0), A(-4,4), B(-3,0) and C(0,-3)
a) Reflect points A and B on the y-axis and name them A' and B' respectively. Write down their coordinates.
b) Name the figure OABCB'A'.
c) State the line of symmetry of this figure. (5)
SECTION - B(40 MARKS)
(Attempt any four questions from this section)
Question 4:
i) Three friends X, Y and Z live in Ghaziabad (U.P) X sells medicine worth Rs50000 to Y. Y sells the same medicine to Z at a profit of Rs6000. if the rate of GST is 12%, find:
a) SGST paid by Y b) total CGST c) the amount paid by Z for the medicines. (3)
ii) The scale of a model ship was 1: 300
a) If the length of the model is 250 cm, find the actual length in m.
b) if the deck area of the model is 1 m², find the deck area of the ship.
c) If the volume of the ship is 108000000 m³, find the volume of the model. (3)
iii) A mathematics aptitude test of 50 students were recorded as follows :
Marks No.of students
50-60 4
60-70 8
70-80 14
80-90 19
90-100 5
Draw a histogram for the above data and locate the mode. (4)
Question 5:
i) Given matrices
A= 1 -3 & B= 2 -1 & C= 2 0
0 4 2 1 0 3
Find the 2x2 matrix X such that A+ X = 2B - C. (3)
ii) In the figure,
AP , AQ and BC are tangent to the circle. If AB = 5cm, AC= 6cm and BC= 4cm, then find the length of AP . (3)
iii) If (2x +1) is a factor of (3k +2)x³ + (k -1), find the value of k. (4)
Question 6:
i) Find slope of the line passing through the point (2,4) and (-2,-3). (3)
ii) Draw two intersecting lines to include an angle of 30°. Use ruler and compasses to locate points which are equidistant from these lines and also 2cm away from their point of intersection. How many such points exist ? (3)
iii) Which term of the AP 5, 12, 19, 26, 33.... will be 35 more than its 12th term? (4)
Question 7:
i) The distance by road between two towns A and B is 216km and by rail it is 200km. A car travels at a speed of x km/h and the train travels at a speed which is 16 km/h faster than the car. Calculate :
a) The time taken by the car to reach town B from A, in terms of x.
b) The time taken by the train to reach town B from A in terms of x.
c) if the train takes 2 hours less than the car to reach town B, obtain an equation in x and solve it. Hence, find the speed of the train. (5)
ii) The marks obtained by 200 students in an examination are given below:
Marks No.of students
0-10 5
10-20 10
20-30 11
30-40 20
40-50 27
50- 60 38
60-70 40
70-80 29
80-90 14
90-100 6
Draw an ogive for the above distribution. From the ogive, determine
a) the median b) the lower quartile. (5)
Question 8:
i) A card is drawn at random from a well shuffled pack of playing cards. Find the probability that the card drawn is
a) a king or a Jack. b) a non ace c) a red card. (3)
ii) From a solid cone of height 12cm and base radius 6cm, a cone of height 4cm has been removed. Find the total surface area of the remaining solid. (3)
iii) In the given figure,
O is the centre of the circle.
If Angle EBC = 108° and angle AOB=92°, calculate the value of angle BDC. (4)
Question 9:
i) Solve the following inequation and graph the solution set on the number line.
3 ≥ (x -4)/2 + x/3 ≥ 2; x ∈ R. (3)
ii) Find the mean of the following frequency distribution:
Class frequency
000-100 6
100-200 9
200-300 15
300-400 12
400-500 8 (3)
iii) in the figure,
XY|| BC . If AX =3 cm, XB=1.5cm and BC= 6cm, find XY. (4)
Question 10:
i) Using the properties of proportion, solve for x:
{√(3x) + √(2x -1)}/{√(3x) - √(2x -1)}= 5. (3)
ii) Draw a circle of radius 3.2cm. Draw two tangents to it inclined at an angle of 45° to each other. (3)
iii) At the foot of a mountain, the elevation of its summit is 45°. After ascending 500m, toward the mountain up an incline of 30°, the elevation change to 60°. Find the height of the mountain. (4)
1) id iia iiid iva va vib viib viiib ixa xb xid xii c xiiia xivc xva
2) i) 20 months ii) a) Rs7000 b) 5.7%
3i) [8(4ⁿ-1) + 21n(n +1)] ii) a) 2/5 b) 2x - 5y= - 31 iii) (-2,7),(3,5)
4) i)a) Rs360 b) Rs 3360 c) Rs 6720 ii) a) 750m b) 96000m² c) 4m³ iii) 82.5
5) i) 1 1
4 -5 ii) 7.5cm iii) 2 6) i) 7/4 ii) 4 iii) 17th
7) i) a) 216/x km b) 200/(x +16) c) 53.76 kmph
8a) 2/13 b) 12/13 c) 1/2 ii) 350.09 cm² iii) 62°
9) i) {x: 4.8≤ x ≤ 6, x belongs to R} ii) 264 iii) 4cm. 10) i) 2/3 iii) 683m
TEST- PAPER 5
SECTION - A (40 Marks)
(Attempt all questions)
Question 1: Choose the correct option:
i) For a transaction of Rs 80000 in Delhi, if GST rate is 18% then SGST is
a) Rs 7200 b) Rs 14400 c) Rs 6400 d) nil
ii) The discriminant of the quadratic equation x²- 2x + 1 = 0:
a) = 0 b) > 0 c) < 0 d) none of these
iii) The value of m so that (x + 6) is a factor of x³+ 5x² - 4x + m, is
a) 7 b) - 3 c) 6 d) 12
iv) If a share of Rs100 is selling at Rs 120, then it is said to be at :
a) a discount of Rs 20 b) a premium of Rs 20 c) par d) none of these
v) Which term of the AP 72, 68, 64, ....is 0 ?
a) 15 b) 18 c) 19 d) 20
vi) The progression a₁, a₂, a₃, ....aₙ forms an GP only if:
a) aₙ/aₙ₋₁ = constant b) aₙ - aₙ₋₁ = constant c) aₙ x aₙ₋₁= constant d) aₙ₋₁/aₙ = consr
vii) If in a triangle ABC and DEF, AB/DE = BC/FD, then they will be similar when :
a) Ang B= Ang E b) Ang A= Ang E c) Ang B= Ang D d) Ang A= Ang F
viii) if the curved surface area of a cylinder of height 14cm is 88 sq.cm, then the diameter of the cylinder is:
a) 2cm b) 4cm c) 1cm d) 3cm
ix) If 4x -2 ≥ 8 - x, x ∈ N, then the solution set is
a) {2,3,4,5...} b) {1,2,3,4,...} c) {0,1,2,3,...} d) {2,3,4,5,6}
x) quality the probability of getting sum of 13 on a pair of dices rolled is 012311 order of the matrix 21 and that is also 21 the order of the matrix is 2241 2132 the coordinates of a point the line segment joining 34 76 in the ratio 12 13 13 23 13 23 in the given figure recycling trapezium such that 75 15 55 65 705 transformation the resulting figure is called object image free image reduction assertion the median of the data 114980511 reason for calculating the median of a data we only consider positive observation money deposit 2000 per monthly regarding deposit account for 32 years 8% find the Mount Abu received the time a maturity what a least number must be added to each of the number 51937 so that the resulting numbers are the person the total surface area where in the upper radius 5 65 harikishan invested 87% 100 CR 80l after a year issold this year 75 each and invested the proceeds including is dividend in 18% 25 years at 41 each find is dividend for the first year is annual income in the 2nd year the percentage increase in his return on his original investment using graph paper for this question
A dealer in Mumbai Sholay refrigerator to a consumer in Mumbai 21500 is the rate of GST 18% 5 igstc GST sgst if the roots of the equation the real and disting prove that the roots of will be imaginary the second and fifth term of a GP is 126 respectively find the sum of the first aid answer to GP find X and Y if the matrix in the given figure is a tangent to the circle with a cyclic quadrilateral 93 35 who is infected theorem show that is a factor of right down the equation of the line is gradient is 32 and which passes through where device the line segment joining twice 634 in the ratio the surface area of a solid is 5 while the surface area of its model is 20 find still factor the volume of the solid if the volume of the model is 100 how many terms of the AP 7 11:15 1923 must be taken to get some cookie draw an for the following frequency distribution class frequency 6518 7500 8000 228500 2500 from those are find the medians dry line segmentane the midpoint draw and describe the locus of the point which is 2 cm 4 mark the point which satisfy both the above condition describe the figure what kind of triangle is large farm employees 4250 employees one person is chosen at random what is the probability that the persons birthday is on Monday is in the year 2016 accelerator based is horizontal and upper radius 3.5 content water so that when a spear is placed in the pen the water just forward this year given that this period speeds in into the can calculate the total surface area of the can contact in the sphere is in it the death of the water in the can before this year was putting to the can in the given figure solve the following any two ways and represent your solution on the real number line calculate the main daily wage at work from the following table number of workers 4045 to 25 50 355 755 60 12 60 65 6 in the figure is a right angle triangle A boy standing on the bank of a river observe the dangel accepting by a tree on the opposite Bank at 60 when he moves 20 back from the bank angle to be 30 find the height of the area and the breath of the river
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