Time: 3 hrs). M. M.: 50
Note: Question paper is divided in 3 Sections A. B. C. D. E. Section A consists of 12 multiple choice questions and each carries 1 mark each. Section B consists of 8 multiple choice questions based on two case studies and each carry 1 mark each. Section C consists of 4 questions and each carries two marks. It has Questions from 21 to 24. Question No. 23 and 24 have been provided with internal choice. Section D consists of 4 questions from Q. No. 25 to 28 Question No. 26, 27 and 28 have been provided with internal choice and carries 3 marks cach. Section E consists of two questions Q. No. 29 and 30. Both have been provided with internal choice. Each question carries 5 marks.
SECTION-A
1 x 12=12
All questions carry one mark each.
1. LCM of two integers 26 and 91 is:
(a) 13
(b) 182
(c) 26.
2. The polynomial of power one is called :
(a) Linear
(b) Quadratic polynomial.
(c) Cubic.
3. The discriminant of quadratic equation 2x²-6x+5=0 is:
(a) 12
(b) 15
© -4
4. According to Pythagoras Theorem
(8)2 + (6)2 =
(a) (9)2
(b) (7)2
(c) (10)2
5. The coordinates of the mid point of the line se10gment joining the points
A (x1, y1) and B (x2 y2) are:
6. For any two positive integers a and b HCF (a, b)=
(a) a × b/LCM (a, b)
(b) a + b/LCM(a, b))
© a - b)/LCM(a, b))
7. Number of zeroes in cubic polynomial is:
(a) 1
(b) 2
(c) 3.
8. Which of the following statement is not true?
(a) The roots are real, if b^2-4ac < 0
(b) The roots are equal, b^2 - 4ac = 0
(c) The roots are real, if b^2-4ac > 0
9. In an isosceles triangle…………… sides are equal.
(a) Two
(b) Three
©. One
10. In a right triangle, the square of the…………….is equal to the sum of the squares of the other two sides
(a) Perpendicular.
(b) Hypotenuse
©. Base
11. Quadratic equation x ^2 + 7x +1 has sum of zeroes:
(a) 1
(b) 7
(c) -7.
SECTION-B
Section B consists of 8 questions based on two case study. Each question is of 1 mark.
Case-1 (4 Part)
The resident welfare association of a Gokuldham society decided to build two straight paths in their neighbourhood park such that they do not cross each ober, and also plant trees along the boundary lines of each path one of the member of association popat lal suggested that the paths should be constructed represented by the two linear equations. x - 3y = 2 and 2x + 6y = 5
13. 
14. If the pair of lines are parallel, then pair of linear equation
(a) consistent
(b) inconsistent
(c) none of these.
15. How many points lie on the line x - 3y = 2
(a) one
(b) two
(c) infinite.
16. If the line 2x + 6y = 5 intersect the x-axis then find its co-ordinates.
(a) (2.5, 0)
(b) (0, -2.5)
(c) (0, 2.5).
Case-2 (4 Part)
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections-Section A and Section B of grade X. There are 32 students in Section A and 36 students in Section B. On the bases of above information answer the following Questions:
17. 36 can be expressed as a product of its primes as:
(a) 2^3 × 2^1
(b) 2^2 × 3^2
(c) 2^3 × 3^3
18. The minimum number of books required for the school library, so that they can be distributed equally among students of Section A or B will be:
(a) 288
(b) 272
(c) 144.
19. If the product of two positive integers is equal to the product of their HCF and LCM is true then find HCF (32, 36).
(a) 8
(b) 4
(c) 6.
20. The relation between H.C.F. and LCM of a and b is:
(a) LCM > HCF
(b) HCF > LCM
(c) LCM = HCF.
SECTION C
All questions carry two marks.
21. Use Euclids division algorithm to find the HCF of 867 and 255.
22. Find a quadratic equation with -3 and 2 as the sum and product of its zeroes respectively.
23. The difference between two numbers is 26 and one number is three times the other. Find them.
Or
Find the value of k for the quadratic equation 2x^2 + kx + 3 = 0 so that it has two equal roots.
24. Determine if the points (1, 5), (2, 3) and (-2,-11) are collinear.
Or
In Fig., AODC - AOBA, angle BOC = 125 deg and angle CDO = 70 deg . Find angle DOC angle DCO and
ZOAB.
(b) consistent
(c) none of these.
(a) inconsistent
15. How many points lie on the line x - 3y = 2
(a) one
(b) two
(c) infinite.
16. If the line 2x + 6y = 5 intersect the x-axis then find its co-ordinates.
(a) (2.5, 0)
(b) (0, -2.5)
(c) (0, 2.5).
Case-2 (4 Part)
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections-Section A and Section B of grade X. There are 32 students in Section A and 36 students in Section B. On the bases of above information answer the following Questions:
17. 36 can be expressed as a product of its primes as:
(a) 2^3 × 2^1
(b) 2^2 × 3^2
(c) 2^3 × 3^3
18. The minimum number of books required for the school library, so that they can be distributed equally among students of Section A or B will be:
(a) 288. (b) 272. (c) 144.
19. If the product of two positive integers is equal to the product of their HCF and LCM is true then find HCF (32, 36).
(a) 8. (b) 4. (c) 6.
20. The relation between H.C.F. and LCM of a and b is:
(a) LCM > HCF
(b) HCF > LCM
(c) LCM = HCF.
SECTION C
All questions carry two marks.
21. Use Euclids division algorithm to find the HCF of 867 and 255. 22. Find a quadratic equation with -3 and 2 as the sum and product of its zeroes it has two equal respectively.
23. The difference between two numbers is 26 and one number is three times the other. Find them.
Or
Find the value of k for the quadratic equation 2x^2 + kx + 3 = 0 so that
roots.
24. Determine if the points (1, 5), (2, 3) and (-2,-11) are collinear.
Or
In Fig., ∆ODC ~ ∆OBA, < BOC = 125 deg and < CDO = 70 deg . Find < DOC and <DCO
SECTION-D
All questions carry 3 marks
25. Prove that 5- √3 is irrational.
26. Divider³-3x²+5x-3 by x²-2.
Or
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes if ½ if we only add 1 to the denominator. What is the fraction?
27. How many terms of the A.P: 9, 17, 25... must be taken to give a sum of 636? Or
Find two numbers whose sum is 27 and product is 182.
28. Find the area of the quadrilateral whose vertices taken in order, are (-4,-2); (-3,-5); (3,-2); (2, 3).
Or
ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that ÁO/BO = CO || DO
SECTION-E
All questions carry 5 marks each.
29. The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
Or
Find the sum of the first 40 positive integers divisible by 6.
30. Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Or
Ritu can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.
Model Test Paper 2
Term 1
Time 3hrs. MM 50
Note: Question paper is divided in 5 Sections A, B, C, D, E. Section A consists of 12 multiple choice questions and each carries 1 mark each. Section B consists of 8 multiple choice questions based on two case studies and each carry 1 mark each. Section C consists of 4 questions and each carries two marks. It has Questions from 21 to 24. Question No. 23 and 24 have been provided with internal choice. Section D consists of 4 questions from Q. No. 25 to 28 Question No. 26, 27 and 28 have been provided with internal choice and carries 3 marks each. Section consists of two questions Q. No. 29 and 30. Both have been provided with internal choice. Each question carries 5 marks.
SECTION-A
All questions carry one mark each
1×12=12
1. H.C.F. of two integers 6 and 20 is:
(a) 3. (b) 6. (c) 2.
2. The polynomial having power two is known as:
(a) Linear. (b) Quadratic. (c) Cubic.
3. In quadratic equation ax^2 + bx + = 0, D = ,...................... - 4ac.
(a) b^2. (b) c^2. (c) x^2
4. According to Pythagoras Theorem 3^2 +......= 5^2
(a) 4^2. (b) 2^2. (c) 1^2
5. The distance between points, A(x1, y1) and B (x2, y2) * is :
6. L.C.M. ( a, b ) × H.C.F (a, b) = ..
(a) a + b. (b) a / b. (c) a × b
7. The number of zeroes of a linear equation is:
(a) 1. (b) 2. (c) 3
8. The quadratic equation ax^2 + bx + c = 0 has two real and different roots, if
(a) b^2 - 4ac = 0
(b) b^2 - 4ac > 0
(c) b^2 - 4ac < 0
9. There is................ right angle in a right angled triangle.
(a) One. (b) Two. (c) Three.
10. Ratios of the Areas of two similar triangles is……………... of the ratio of corresponding angles
(a) Equal to
(b) Square of
(c) Not equal to.
11. Which of the following expressions is the linear polynomial ?
(a) x+2. (b) √x +2. (c) 1/x+ √2.
12. 10 (x+1)²=2(x-3) is a :
(a) Linear equation
(b) Cubic equation.
(c) Quadratic equation
SECTION-B
Section B consists of 8 questions based on two case. Each question is of one
Case-1
(4 Part)
India's literacy rate has increased six times since the end of British rule in 1947. Yet India has the world's largest population of illiterate people according to one report. Ram aks the labour to dig a well up to a depth of 10 m. Labour charges ? 150 for 1st metre and 50 for each subsequent metres. As labour was uneducated he claim 550 for whole work.
13. What type of series is formed from the given statement ?
(a) AP
(b) None AP
(c) None of these.
14. What should be the actual amount to be paid to the labour?
(a)655 (b) 600. (c) 645.
15. How much money did Ram will save, if he agree with Rs 500
(a) 50. (b) 40 (c) 45.
16. In AP sequence, if each term is multiplied by constant K, then the new sequence will be:
(a) AP
(b) Not AP
(c) None of above.
Case-2 (4 Part)
Four friends Champa, Suruchi, Chameli and Suman are sitting on four points A, B, C and D in the class.
Answer the following questions based on the above information.
17. The coordinates of the point on which Champa is sitting are
(a) (1, 2). (b) (2,3). (c) (3, 4).
18. The coordinates of the point on which Chameli is sitting are
(a) (9, 4). (b) (5, 2). (c) (8, 2),
19. Coordinates of the mid point of AC are:
(a) (6, 1). (b) (6, 7). (c) (6,4).
20. The distance between Champa and Chameli is:
(a) 9 Units. (b) 6 Units. (c) 4 Units
SECTION-C
All questions carry two marks.
21. Use Euclid's division algorithm to find the HCF of 135 and 225.
22. Find the quadratic polynomial with 0 and √5 as sum and product of its zeroes.
23. The larger of two supplementary angles exceeds the smaller by 18°. Find them.
Or
Find value of k in quadratic equation kx (x - 2) + 6 = 0 so that they have two equal roots.
24. Check whether (5,-2); (6, 4) and (7, -2) are the vertices of an isosceles triangle.
Or
S and T are points on sides PR and QR of ∆PQR such that <P= <RTS . Show that ∆RPQ ~ ∆RTS.
SECTION-D
All questions carry 3 marks.
25. Prove that 3 + 2√5 is an irrational number.
26. Divide 2x^2 + 3x + 1 by x + 2
Or
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu ?
27. The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
Or
Find two consecutive positive integers, sum of whose squares is 365.
28. Find the area of a rhombus if the vertices are (3, 0) ; (4, 5) ; (- 1, 4) and (-2,-1) taken in order.
Or
Let ∆ ABC ~ ∆ DEF and their areas be respectively 64cm^2 and 121cm^2 If EF = 15.4 cm, find BC.
SECTION-E
All questions carry 5 marks each.
29. The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
Or
Find the sum of first 15 multiples of 8.
30. In a triangle, a line drawn parallel to one side to intersect the other two sides in distinct point divides the two sides in the same ratio. Prove it.
Or
2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by I man alone.
MODEL TEST PAPER 3
Time: 3 hrs M.M: 50
Note: Question paper is divided in 3 Sections A. B. C. D. E. Section A consists of 12 multiple choice questions and each carries 1 mark each. Section B consists of 8 multiple choice questions based on two case studies and each carry 1 mark each. Section C consists of 4 questions and each carries two marks. It has Questions from 21 to 24. Question No. 23 and 24 have been provided with internal choice. Section D consists of 4 questions from Q. No. 25 to 28 Question No. 26, 27 and 28 have been provided with internal choice and carries 3 marks cach. Section E consists of two questions Q. No. 29 and 30. Both have been provided with internal choice. Each question carries 5 marks.
SECTION-A
All questions carry one mark each:
1×12=12
1. H.C.F. of integers 17 and 23 is:
(a) 17. (b) 23. (c) 1.
2. Polynomial having power three is known as
(a) Linear. (b) Quadratic. (c) Cubic.
3. In quadratic equation ax^2 + bx + c = 0 Discriminant D=......…………..
(a) b^2 + 4ac
(b) b^2 - 2ac
(c) b^2 - 4ac 4.
4. According to Pythagoras Theorem (5)^2 + (12)^2 .....
(a) (13)2. (b) (14)2. (c) (17)2.
5. The coordinates of the point which divides the joint of A(x1, y1) and B (x2, y2) in the ratio m1:m2 internally are:
6. Express 0.15 as a rational expression.
(a) 3/19. (b) 3/20. (c) 4/15 .
7. The number of zeroes of the polynomial p(x) = 6x^2 - 7x - 3 are:
(a) 1. (b) 2. (c) 1.
8. In quadratic equation ar² + bx + c = 0 if b2-4ac = 0 then it has
(a) Two distinct real roots
(b) Two equal real roots
(c) No real roots.
9. All circles are…………….
(a) Similar
(b) Congruent
(c) None of these.
11. In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite to the first side is a...........
(a) Acute angle
(b) Right angle
(c) Obtuse angle.
12. The product of the zeroes of the polynomial x² - 2x - 8 is:
(a) 2. (b) -8. (c) 8.
13. Fill in the blank
X = -b±√........./ 2a
(a) b2. (b) b2 - ac (c) b2-4ac.
Section B
Section B consists of 8 questions based on two case study. Each question is of one mark.
Case-1 (4 Part)
Due to storm, an electric wire bent as shown in the figure. The wire form a mathematical shape.
Answer the following questions on the bases of given figure.
13. The number of the zeroes of the polynomial are:
(a) 2. (b) 1 © 3
14. Name the shape in which the wire is bent.
(a) Circle. (b) Linear. (c) Parabola.
15. The zeroes of the polynomial are:
(a) -2, 4. (b) -2,3. (c)-1-2
