MODEL TEST PAPER -1
(Marks: 80)
Question 1. 1x 10= 10
i) What are the rate of GST on an article that was sold at a price three times its marked price ?
A) 10% B) 20% C) 100% D) 200%
ii) Ram deposited ₹150 per month in a bank for 8 months under the Recurring deposit scheme. What will be the intrest of his deposits. If the rate of interest is 8% p.a.
A) 36 B) 360 C) 1236 D) 1536
iii) Solve the following inequation, 2x -5 ≤ 5x+4 < 11, x belongs to R.
A) -3, -2,-1,0,1 B) 0, 1
C) {x: x belongs to R, -3≤ x ≤ 7/5
D) none
iv) Frame the quadratic equation whose roots are 2/5, -1/2
A) x²+ x-2=0 B) x²+ x +2=0 C) 10x²+ x-2=0 D) 19x²+ x + 2=0
v) The remainder on dividing f(x) by x-2 where f(x)= 5x² -7x +4
A) 10 B) 9 C) -9 D) -11
vi) If (2x -5):(3x+1) is the duplicate ratio of 2:3, find the value of x
A) 6 B) 49 C) 49/6 D) 6/49
vii) Find the value of x if cos 63 sec(90- x)= 1
A) 27 B) 72 C) 18 D) 81
viii) Find the median of 31, 35, 27, 29, 32, 43,37,41, 34,28, 36, 44, 45, 42.
A) 34 B) 35.5 C) 44 D) 37
ix) Find the even number between 100 to 300 divisibile by 5.
A) 20 B) 3p C) 4p D) none
x) if the equation y= my+ c passes through the points (1,4( and (-2,-5) find the value of slope.
A) 1 B) 2/3 C) 5 D) none
Question 2. 2x10 = 20
i) A refrigerator is marked for sale at ₹17600 inclusive of GST. If the rate of GST is 10%, calculate
A) The list price of refrigerator.
B) The amount of GST. (2)
ii) Mrs. Mathew opened a recurring deposit account in a bank with ₹500 per month for 2 years. Find the amount she will get on maturity if the intrest is paid on monthly balance at 12.5% p.a. (2)
iii) Solve the inequation: 2x -1≥ x+ (7-x)/3 > 2. Show on the number line. (2)
iv) 3x²+ 10x + 3=0. (2)
v) If 2x+1 is a factor of 6x³ + 5x² + ax - 2, find the value of a. (2)
OR
Find the equation of a straight line parallel to y-axis and passing through the point (-3,5). (2)
vi) If X+ Y= 7 0 & X - Y= 3 0
2 5 0 3 then find the matrix X and Y. (2)
vii) a) Point A(5,0) on reflection is mapped as A'(-5,0). State the equation of the mirror line.
b) Point B(4,-3) on reflection is mapped as B'(4,3). State the equation of the mirror line. (2)
viii) Two right circular cylinder have equal volumes. If their heights are the ratio 4:9, find the ratio of their radii. (2)
ix) A man 1.8 high stands at a distance of 3.6m from a lamp post and casts shadow of 5.4m on the ground. Find the height of the lamp. (2)
x) Find the sum of the series 2, 7, 12, 17,...............20th term.
Question 3. 3 X10= 30
i) If P is the solution set of - 3x+4 < 2x -3, x belongs to N, and Q is the solution set of 4x - 5< 12, x belongs to W, Find:
A) P∩Q B) Q - P .
ii) 4x²- 4ax + (a² - b²)=0
iii) Factorise completely: x³ + x² - 4x -4.
iv) If A= 1 -2 and B= 3 2
2 -1 -2 1 find 2B - A².
OR
Find the coordinates of the point that divides the line segment joining the point P(5,2) and Q(9,6) internally in the ratio 3:1
v) Prove: (1+ cos x)/(1- cos x)= (cosec x + cot x)².
vi) The radius of a sphere in 9cm. It is melted and drawn into a wire of diameter 2mm. Find the length of the wire in metres.
vii) The following table gives the doing wages of 50 works of a factory:
Marks: 20 70 50 60 75 90 40
F: 8 12 18 6 9 5 12 calculate the median marks.
ix) A letter is chosen from the word TRIANGLE, what is the probability that it is vowel.
Or
The nth term of an AP is 4n - 1. Find the common difference and 10th term of the AP.
x) Find x :
{√(2- x)+ √(2+ x)}/{√(2- x) - √(2+ x)} = 3.
OR
If x= 6ab/(a+ b) prove (x+ 3a)/(x- 3a) + (x+ 3b)/(x- 3b)
Question 4 4x5= 20
i) 'A' manufacturer motorbike at a cost price of ₹30600. Hence he sells it to a dealer B. B sells it to the dealer C. C sells it to a cust6. If the profit at each stage of selling chain is ₹1000 and the rate of GST is 12.5%, find
A) the total amount of GST paid by customer.
B) The amount which the consumer paid for the motorbike.
OR
On depositing ₹200, every month in a cumulative time deposit account, paying 9% p.a. intrest, a person collected ₹2517 at maturity. Find the period.
ii) In a flight of 2800km, an aircraft was slowed down due to bad weather. It's average speed for the trip was reduced by 100km/hr and time increased by 30 minutes. Find the original duration of flight.
iii) If f(x)= 24x³ + px² - 5x +q has two factors 2x+1 and 3x -1, then find p and q. Also factorise completely.
iv) The vertices of a triangle are A(10,4), B(4,-9) and C(-2,-1). Find the equation of the altitude through A.
OR
Draw a histogram and find Mode:
Marks obtained. No of students
24-29 2
29-34 1
34-39 5
39-44 9
44-49. 21
49-54 10
54-59 2
v) A box contains 25 cards, numbered from 1 to 25. A card is drawn from the box at random. Find the probability that the number on the card is:
a) even b) prime c) multiple of 6.
OR
Construct a triangle ABC in which AB= 5cm, BC= 8cm, and CA= 7cm. Draw the circumcircle
MODEL TEST PAPER -1
SECTION A (Marks : 40)
Question 1)
a) Mamta has a cumulative Time Deposit Account in a Bank. She deposits ₹ 800 per month and gets ₹15198 as maturity value. If the rate of interest be 7% p.a, find the total time for which the account was held. (4)
b) The vertical and slant height of a cone are 24cm and 25cm respectively. Calculate
i) curved surface
ii) volume of the cone. (4)
c) The diameter of an iron sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform cross section. If the length of the wire is 108 m, find its diameter. (4)
d) Solve: (3)
2x/(x-4) + (2x -5)/(x-3) = 25/3.
e) The marks scored by 40 pupils of a class in a test test test in a test test test class in a test test test a test test were as:
Marks: 0 1 2 3 4 5
Frequency: 2 4 5 14 11 4
calculate the mean marks. (3)
f) Find the sum of all the numbers between 100 and 200 which are divisible by 7. (3)
g) Solve 2 ≤ 2x - 3 < 5, x belongs to R and mark it on the number line. (3
h) Find the value of m if (x - m) is a factor of 3x³ + 2x² - 19x +3m. (3
I) find x and y if
- 3 2 x = - 5
0 - 5 . 2 y (3)
j) What must be added to each of the numbers 7, 15, 19 and 35 so that the resulting numbers numbers the resulting numbers are in the proportion? (2)
k) Find the value of k so that 8k+4, 6k-2, and 2k+7 will form an A. P. (2)
l) without using trigonometric tables, calculate:
2 tan 40°/cot 50° - cosec 61°/sec29°. (1)
m) Using the remainder theorem, find the remainder when 7x³ + 5x² - 4x - 1 is divided by (x+1). (2)
n) Find the equation of m so that the roots of the Equation (4-m)x² + (2m+4)x + (8m+1)= 0 may be equal. (3)
SECTION B(40 Marks)
(Answer any four questions)
Question 2)
A) A shopkeeper bought a washing machine at a discount of 30% from a wholesaler, the printed price of the machine being 30000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the sales are intea-state and the rate of GST is 15%, find
a) the price inclusive of tax(under GST) at which the shopkeeper bought the machine.
b) the price which consumer pays for the machine.
c) the tax(under GST) Paid by the wholesaler to the State Government
d) the tax(under GST) Paid by the shopkeeper to the State Government.
e) the tax(under GST) received by the Central Government. (4)
B) On depositing ₹200, every month in a cumulative Time Deposit Account, paying 9% p.a., interest, a person collected ₹2517 at maturity. Find the period. (4)
C) Prove: (tanA + cot A) sinA . cos A = 1. (2)
Question 3)
A) The point A(-3,0) on reflection in a line is a line is mapped as A'(3,0) and the point (2, -3) on reflection in the same line mapped as B'(-2,-3)
a) Name the mirror line. (3)
b) Write the co-ordinates of the image of (-3, -4) in the mirror line.
B) Using quadratic formula, solve
4x² - 4ax + (a² - b²) = 0. (5)
C) How many terms of the A. P 1, 4, 7,, ....are needed to give the sum 715 ? (2)
Question 4)
A) The last term of an A. P 2, 5, 8, 11,....is x. The sum of the terms of the A. P is 155. Find the value of x. (3)
B) ABCD is a cyclic quadrilateral in which AB and DC on being produced, meet at P such that PA= PD Prove that AD is parallel to BC. (3)
C) Show that X= 2 3
3 2 is the solution of the matrix Equation X² - 4X - 5I= O. (3)
Question 5)
A) The horizontal distance between two Towers is 140m. The angle of elevation of the top of the first Tower when seen from the top of the second Tower is 30°. If the height of the second Tower is 60 m, find the height of the first tower. (5)
B) The sum of the first fifteen terms of an arithmatic progression is 105 and the sum of the next fifteen terms is 780. Find the first three terms of the arithmatic progression. (5)
Question 6)
A) The ratio of a sphere is doubled. Find the increase % in its surface area. (3)
B) Find the equation of a straight line parallel to y-axis and passing through the point (-3,5). (3)
C) Prove: (cotx +cosecx-1)/(cot x - cosec x +1)= (1+cosx)/sinx. (4)
Question 7)
A) Find the equation of a straight line passing through (-1,2) and whose slope is 2/5. (3)
B) Using step deviation method, calculate the mean of the following frequency distribution:
Class Frequency
50-60 9
60-70 11
70-80 10
80-90 14
90-100 8
100- 110 12
110- 120 11. (7)
Question 8)
A) On a map drawn to a scale of 1: 250000, a triangle plot of kand has the following measurements. AB= 3 cm, BC= 4 cm and Angle ABC= 90°.
Calculate (3)
a) the actual length of AB in km.
b) the area of the plot in sq.km
B) Prove: (1+cosA)/(1- cosA) = (cosec A + cotA)². (3)
C) Draw a histogram and hence estimate the mode for the following frequency distribution:
Class-interval frequency
0-10 2
10-20. 8
20--30 10
30-40 5
40-50 4
50-60. 3 (4)
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