CBSE Class 10 Compt Maths Standard 2021, Paper Code-30B, Set 4
Read the following instructions very carefully and strictly follow them :
(i) This question paper contains two parts A and B.
(ii) Both Part A and Part B have internal choices.
Part A
(i) It consists of two Sections, I and II.
(ii) Section I has 16 questions of 1 mark each. Internal choices are provided in 5 questions.
(iii) Section II has 4 questions (Q.No. 17 to 20). Each question has 5 sub-parts. An examinee is to attempt any 4 out of 5 sub-parts. Each sub-part is of 1 mark.
Part B
(i) It consists of three sections, III, IV and V.
(ii) Section III has 6 questions No. 21 to 26 of Very-short Answer Type of 2 marks each.
(iii) Section IV has 7 questions No. 27 to 33 of Short Answer Type of 3 marks each.
(iv) Section V has 3 questions No. 34 to 36 of Long Answer Type of 5 marks each.
(v) Internal choice is provided in 2 questions in Section III, 2 questions in Section IV and 1 question in Section V.
PART A
SECTION I
1. If 2 tables and 2 chairs cost ₹ 700 and 4 tables and 3 chairs cost ₹ 1,250, then find the cost of one table. (1Mark)
2. If the graph of a pair of lines x 2y + 3 = 0 and 2x 4y = 5 be drawn, then what type of lines are drawn ? (1Mark)
3. If one zero of the polynomial p(x) = (a²
+ 4) x² + 20x + 4a is reciprocal of the other, find the value of a. (1Mark)
4. (a) After how many decimal places will the decimal expansion of the rational number 14587/1250 terminate ? (1Mark)
OR
(b) State giving reason whether 5 × 7× 11 + 11 is a composite number or a prime number. (1Mark)
5. (a) If the 6th and 14th terms of an A.P. are 29 and 69 respectively, then find the 10th term of the A.P. (1Mark)
OR
(b) If the first three consecutive terms of an A.P. are 3y 1, 3y + 5 and 5y + 1, find the value of y. (1Mark)
6. Find the roots of the quadratic equation x²
+ x (a + 1) (a + 2) = 0. (1Mark)
7. (a) In a right triangle ABC, right-angled at B, BC = 6 cm and AB = 8 cm. A circle is inscribed in the ABC. Find the radius of the incircle. (1Mark)
OR
(b) Two circles touch externally at P and AB is a common tangent, touching one circle at A and the other at B. Find the measure of APB.
8. Solve for x : 1
10x + 1/x = 3, x ≠ 0
9. (a) In a triangle ABC, a line is drawn parallel to base BC meeting AB in D and AC at E. If BD
AB = 4 and CE = 2 cm, then find the value of AE. 1
OR
(b) Two poles, 6 m and 11 m high, stand vertically on the ground. If the distance between their feet is 12 m, find the distance between their tops. 1
10. From an external point P, tangents PQ and PR are drawn to a circle with centre O, touching the circle at Q and R. If QOR = 140 , find the measure of QPR. 1
11. Draw AB, a line segment of length 4·8 cm and find a point P on AB such that AP = 1/4 AB. 1
12. In ABC, B = 90 and tan A = 1/3. Then find the value of sin A cos C + cos A sin C. 1
13. A solid sphere of radius r is melted and cast into the shape of a solid cone of height r. What is the radius of the base of the cone
in terms of r ? 1
14. (a) In a single throw of a pair of dice, find the probability that both dice have the same number. 1
OR
(b) A card is drawn from a well-shuffled pack of 52 cards. Find the probability that it is not an ace.
15. The coordinates of the three consecutive vertices of a parallelogram ABCD are A (1, 3), B ( 1, 2) and C (2, 5). Find the coordinates of the fourth vertex D. 1
16. If x = a sin + b cos and y = a cos b sin , then find the value of (x2 + y2). 1
SECTION II
17. Answer any four of the following questions :
(i) If the sum of the areas of two circles with radii r1 and r2 is equal to the area of a circle of radius r, then
(A) r1 + r2 = r
(B) r12 + r22 = r²
(C) r1 + r2 < r
(D) r12 + r22 < r2
(ii) The area of a circle that can be inscribed in a square of side 8 cm is
(A) 64 cm²
(B) 24 cm²
(C) 16 cm²
(D) 8 cm²
(iii) The area of a square that can be inscribed in a circle of radius 6 cm is
(A) 36 cm²
(B) 72 cm²
(C) 18 cm²
(D) 36 2 cm²
(iv) The radius of a circle whose circumference is equal to the sum of the circumferences of two circles of diameters 36 cm and 20 cm is
(A) 56 cm
(B) 42 cm
(C) 28 cm
(D) 16 cm
(v) If the circumference of a circle is equal to the perimeter of a square, then the ratio of their areas is
(A) 22 : 7
(B) 14 : 11
(C) 7 : 22
(D) 11 : 24
18. Answer any four of the following questions :
(i) ABC and BDE are two equilateral triangles such that D is the mid-point of BC. The ratio of the areas of the triangles ABC and BDE is
(A) 2 : 1
(B) 1 : 2
(C) 4 : 1
(D) 1 : 4
(ii) In ABC, AB = 4 3 cm, AC = 8 cm and BC = 4 cm. The angle B is
(A) 120°
(B) 90°
(C) 60°
(D) 45°
(iii) The perimeters of two similar triangles are 35 cm and 21 cm respectively. If one side of the first triangle is 9 cm, then the corresponding side of the second triangle is
(A) 5·4 cm
(B) 4·5 cm
(C) 5·6 cm
(D) 15 cm
(iv) In a ABC, D and E are points on the sides AB and AC respectively such that DE BC and AD : DB = 3 : 1. If AE = 3·3 cm, then AC is equal to
(A) 4 cm
(B) 1·1 cm
(C) 4·4 cm
(D) 5·5 cm
(v) In an isosceles triangle ABC, if AC = BC and AB² = 2AC², then C is equal to
(A) 30
(B) 45
(C) 60
(D) 90
19. Answer any four of the following questions :
(i) The sum and the product of the zeroes of a quadratic polynomial are 1 and 12 respectively. The polynomial is
(A) x² – x – 12
(B) x² + x – 12
(C) x² – x + 12
(D) x² + x + 12
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