i-Tutor Mock Test-1 (Basic)

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i-Tutor Mock Test-1A (Basic) Mathematics-CBSE (Class X)

Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005

Ph.: 011-47623456

M.M. : 80 i-Tutor Mock Test-1 (Basic) Time : 3 Hrs. Mathematics-CBSE (Class X)

(i) All questions are compulsory. (ii) The question paper consists of 36 questions divided into Part A and Part B. (iii) Both Part A and Part B have internal choices. (iv) Part A consists of Section I and Section II. (v) Section I has 16 questions. (vi) Section II has 4 questions. One case study has 4 case-based sub-parts. (vii) Question number 21 to 26 are Very Short Answer Type Questions of 2 marks each, Question number 27 to

33 are Short Answer Type questions of 3 marks each, Question number 34 to 36 are Long Answer Type questions of 5 marks each.

(viii) Internal choice is provided in 5 questions of 1 mark, 2 questions of 2 marks, 2 questions of 3 marks and 1 question of 5 marks.

(ix) Use of calculator is not permitted. (x) It is mandatory to use Blue/Black Ballpoint Pen to write the answer.

PART-A (Section-I) Very Short Answer Type Questions : [16×1=16]

1. Find the value of tan2 30° – sec2 30°. [1] 2. If the area of a circle is 616 cm2, then find its perimeter. [1] 3. Write a quadratic polynomial, whose zeroes are –2 and 3. [1] 4. Find the number of solutions the pair of equations x + 3y +3 = 0 and –2x – 6y +2 = 0 has. [1] 5. Find the distance of the point P(–5, 12) from the origin. [1] 6. A pole 12 m high casts a shadow 4 3 m long on the ground, then find the Sun’s elevation. [1] 7. If angle of a sector of a circle of radius 7 cm is 30°, then find area of the sector. [1]

OR If angle of sector of a circle of radius 14 cm is 60°, then find its perimeter. [1]

Topics Covered : Mathematics : Complete Syllabus on Board Exam Pattern* *(Excluding Chapters/Topics Deleted by CBSE for this Academic Year)

Code A Date : 24-01-2021

GENERAL INSTRUCTIONS :

Phase-I

Mathematics-CBSE (Class X) i-Tutor Mock Test-1A (Basic)

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8. Number of tangents in a circle can have _______. [1] 9. Find the 11th term of the AP 3, 7, 11, 15, …... [1] 10. Find the value of discriminant for equation 3x2 + 4x + 2 = 0. [1] 11. If P = maximum value of sin α and Q = maximum value of cos β, then find the value of 6P – 3Q. [1]

12. The probability of occurring an event is 310

. Find the probability of not occurring the same event. [1]

13. In an A.P., d = –4 and a = 3. Find the 6th term. [1] OR

If in an AP, d = –3, n = 5, an = 15, then find the value of a. [1]

14. In right ∆ABC, right-angled at B, find the value of cosA. [1] OR

Prove that sin2θ + 5cos2θ + 2 = 4cos2θ + 3. [1] 15. Find the LCM of 84 and 7. [1]

OR HCF of 306 and 657. [1] 16. Two triangles ∆ABC and ∆DEF are similar. If AB = DE and perimeter of ∆ABC is 30 cm, then find the perimeter

of ∆DEF [1] OR

In two triangles ABC and PQR, AB BC ACRQ QP RP

= = , then ∆ABC is similar to which triangle? [1]

PART-A (Section-II) Case Study-Based Questions : (Any four out of five) [4×4=16] 17. Mathematics teacher of a school took her 10th standard students to show Taj Mahal. It was a part of their

educational trip. The teacher said, in this monument we can find combination of solid figures. There are 4 pillars which are cylindrical in shape surmounted by hemispherical domes. Also a large hemispherical dome surmounted on the central building.

(i) How much cloth material will be required to cover 1 big dome of radius 3.5 metres? 22Take 7

π =

[1]

(1) 231 m2 (2) 38.5 m2 (3) 77 m2 (4) 154 m2 (ii) The formula to find the curved surface area of only cylindrical portion of pillar is [where r is radius and h

is height] [1] (1) 2πrh (2) 2πr(r + h) (3) πr2h (4) 2πr (r + 2h) (iii) The volume of four pillars (only cylindrical portion) if height of the cylindrical portion of the pillar is 14 m

and radius of the base is 0.7 m is [1] (1) 28.75 m3 (2) 21.56 m3 (3) 43.12 m3 (4) 86.24 m3 (iv) The volume of four hemispherical domes surmounted on the four pillars of radius of base 0.7 m

approximately is [1] (1) 2.156 m3 (2) 2.875 m3 (3) 8.624 m3 (4) 1.437 m3


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(v) The ratio of volume of cylindrical portion of four pillars having height 14 m and base radius 0.7 m to the volume of a sphere of radius 21 m is [1]

(1) 1 : 450 (2) 7 : 25 (3) 49 : 5 (4) 7 : 100 18. Class X students of a secondary school in Delhi have been allotted a rectangular plot of a land for gardening

activity. Saplings of Mango tree are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the fig. The students are to row seeds of plants on the remaining area of the plot.

Considering A as origin, (i) The coordinates of A are [1] (1) (1, 0) (2) (–1, –1) (3) (0, 0) (4) (1, 1) (ii) Coordinates of P are [1] (1) (5, 4) (2) (4, 3) (3) (4, 5) (4) (3, 4) (iii) Coordinates of R are [1] (1) (6, 3) (2) (7, 4) (3) (5, 2) (4) (8, 6) (iv) Coordinates of D are [1] (1) (7, 1) (2) (0, 7) (3) (7, 0) (4) (1, 7) (v) Coordinates of P if D is taken as the origin [1] (1) (3, 3) (2) (–3, –3) (3) (3, –3) (4) (–3, 3) 19. Rohan is studying in X standard. He is making a kite to fly it on a Sunday. Few questions came to his mind

while making the kite. Give answers to his questions by looking at the figure.


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(i) Which of the following options is correct? [1] (1) ∆AED ~ ∆CBA (2) ∆AED ~ ∆ABC (3) ∆AED ~ ∆ACB (4) ∆AED ~ ∆BAC (ii) Sides of two similar triangles are in the ratio 9 : 16. Corresponding medians of these triangles are in the

ratio [1] (1) 4 : 3 (2) 81 : 256 (3) 3 : 4 (4) 9 : 16 (iii) In a right angled triangle, sum of squares of perpendicular sides is equal to squares of its hypotenuse.

This theorem is called [1] (1) Pythagoras Theorem (2) Converse of Pythagoras Theorem (3) Basic Proportionality Theorem (4) Converses of BPT (iv) Which of the following options is correct? [1] (1) AE × AC = AD × AB (2) AE × AB = BC × DE (3) AE × AB = BD × AD (4) AE × AB = AD × DE (v) Which of the following options is correct? [1] (1) AC2 = AD2 + DE2 (2) AC2 = AB2 – BC2 (3) AE2 = AD2 – DE2 (4) AD2 = AE2 – DE2 20. Due to heavy storm an electric wire got bent as shown in the figure. It followed a mathematical shape. Answer

the following questions below.

(i) How many zeroes are there for the polynomial (shape of the wire) [1] (1) 3 (2) 2 (3) 4 (4) 1 (ii) The zeroes of the polynomial are [1] (1) 1, 4 (2) 0, 0 (3) 4, 4 (4) 0, 4 (iii) The expression for the polynomial is [1] (1) x2 – 4x (2) x2 + 4x (3) x2 – 4x + 1 (4) x2 + 4x + 1 (iv) The value of polynomial for x = 2 is [1] (1) –6 (2) 6 (3) –4 (4) 4 (v) Minimum value of polynomial is [1] (1) –1 (2) –4 (3) 0 (4) 1


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PART-B Very Short Answer Type Questions : [6×2=12] 21. Find the area of the segment of a circle which makes an angle of 60o at the centre having diameter as 14 cm.

[2] 22. If the ratio of median and mean of a data is 5 : 4, then find the ratio of mode and median. [2]

OR Find the mean of the given data [2]

Class 0 - 10 10 - 20 20 - 30 30 - 40

Frequency 5 10 6 5

23. Check whether the given statements are true or not?

(i) cos2θ + sin2θ = cos2θ [1] (ii) tan2θ – sec2θ = –1 [1] 24. A card is drawn at random from a well shuffled deck of 52 playing cards. If face cards are removed, then find

the probability of (i) Not getting an ace. [1] (ii) Getting a red numbered card greater than 7. [1] 25. Find HCF and LCM of 6, 36 and 120 using prime factorisation method. [2]

OR By using Euclid’s division algorithm, prove that the numbers 703 and 2419 are co-prime. 26. Find the remainder and the quotient, when the polynomial p(x) = 3x3 + 6x2 + 2x + 3 is divided by

3x2 + 6x + 3. [2] Short Answer Type Questions : [7×3=21]

27. If vertices of a ∆ABC have the coordinates A(1, 0), B(3, 4) and C(4, 5). If G is the centroid of the ∆ABC, then find the length of AG. [3]

28. In the given figure, prove that AB + CD = AD + BC. [3]

29. Solve the following system of equations by using elimination method. [3] 2x + 5y = 2xy

4x + 6y = 5xy

OR The sum of the digits of a two-digit number is 10. The number obtained by interchanging the digits exceeds

the original number by 36. Find the original number. [3] 30. A conical container whose internal radius is 8.4 cm and height 27 cm is full of fluid. The fluid is poured

completely into a cylindrical container with internal radius 10.5 cm. Find the height to which the fluid level rises. [3]


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31. Draw a circle of radius 3 cm. Take a point P at a distance of 7 cm from the centre of that circle. Draw two tangents from P to the given circle. [3]

32. Find the number of terms of the A.P. 30, 28, 26, ....... so that their sum is zero. [3] OR

The sum of three consecutive terms of an A.P. is 27 and the product is 693. Find the possible common difference of A.P. [3]

33. The top of a 25 m high tower makes an angle of depression of 60° with the bottom of a pole and angle of depression of 30° with the top of the pole. Find the height of the pole. [3]

Long Answer Type Questions : [3×5=15] 34. Find a quadratic equation whose roots are

(i) 3 195

+ and 3 195

− [3]

(ii) 3 and 1 [2] 35. If AB is the chord of a circle with centre O, PA and PB are two tangents, then prove that : [5] (i) ∠PAB = ∠PBA

(ii) ∠OAB = ∠OBA

OR Prove that the parallelogram circumscribing a circle is a rhombus. [5] 36. Find the circumcentre of the triangle with vertices at (6, –6), (3, –7) and (3, 3). [5]

Edition: 2020-21

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i-Tutor Mock Test-1 (Basic)