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30/2/1 # 1 | P a g e P.T.O.
Candidates must write the Q.P. Code on the title page of the answer-book.
Series : EGFH2 SET~
Roll No. Q.P. Code
> NOTE
(I) -
(I) Please check that this question paper contains 27 printed pages.
(II) - -
- (II) Q.P. Code given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate.
(III) - 38 (III) Please check that this question paper
contains 38 questions. (IV)
(IV) (^) Please write down the Serial Number of the question in the answer-book at the given place before attempting it.
(V) - 15
(V) 15 minute time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the candidates will read the question paper only and will not write any answer on the answer-book during this period.
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MATHEMATICS (STANDARD)
Time allowed : 3 hours Maximum Marks : 80
30/2/1 # 2 | P a g e
(i) - 38
(ii) - , , ,
(iii) 1 18 (MCQ) 19 20 1
(iv) 21 25 - (VSA) 2
(v) 26 31 - (SA) 3
(vi) 32 35 - (LA) 5
(vii) 36 38 4 2
(viii) - , 2 , 2 ,
(ix) = ,
(x)
20 (MCQ) , 1 20 1=
1. 7 cos^2 + 3 sin^2 = 4 ,
(A) 30
(B) 45
(C) 60
(D) 90
30/2/1 # 4 | P a g e
(A)
(B)
(C)
(D) 0
(A) 7x^2 50x + 7 = 0 (B) 7x^2 50x + 1 = 0 (C) 7x^2 + 50x 7 = 0 (D) 7x^2 + 50x 1 = 0
(A) 1200
(B) 100
(C) 3600
(D) 2400
(A) ± 2 (B) ± 4
(C) 4 (D) 2
(A)
(B)
(C)
(D)
30/2/1 # 5 | P a g e P.T.O.
- The probability of drawing an even prime number out of numbers from 1 to 30 is : (A) (B) (C) (D) 0
- The quadratic equation whose roots are 7 and is : (A) 7x^2 50x + 7 = 0 (B) 7x^2 50x + 1 = 0 (C) 7x^2 + 50x 7 = 0 (D) 7x^2 + 50x 1 = 0
- The least number which is a perfect square and is divisible by each of 16, 20 and 50, is : (A) 1200 (B) 100 (C) 3600 (D) 2400
- The coordinates of the end points of a diameter of a circle are (5, 2) and (5, 2). The length of the radius of the circle is : (A) ± 2 (B) ± 4 (C) 4 (D) 2
- The points ( 5, 0), (5, 0) and (0, 4) are the vertices of a triangle which is a/an : (A) right-angled triangle (B) isosceles triangle (C) equilateral triangle (D) scalene triangle
30/2/1 # 7 | P a g e P.T.O.
- In the given figure, RS is the tangent to the circle at the point L and MN is the diameter. If NML = 30 , then RLM is : (A) 30 (B) 60 (C) 90 (D) 120
- In the given figure, PQ||BC. If = and AC = 20·4 cm, then the length of AQ is : (A) 2·8 cm (B) 5·8 cm (C) 3·8 cm (D) 4·8 cm
- Which of the following statements is incorrect? (A) Two congruent figures are always similar. (B) A square and a rhombus of the same area are always similar. (C) Two equilateral triangles are always similar. (D) Two similar triangles need not be congruent.
30/2/1 # 8 | P a g e
(A) 5
(B) 4
(C) 3
(D) 2
(A)
(B)
(C)
(D)
(A) 60
(B) 90
(C) 45
(D) 72
- sin 30 tan 45 = k (A) 4 (B) 3 (C) 2 (D) 1
30/2/1 # 10 | P a g e
- x y = 0
(A) x-
(B) y-
(C) -
(D) (3, 2)
(A)
(B)
(C)
(D)
16. p(x) = x^2 x (2 + 2k) 4 k :
(A) 3 (B) 9
(C) 6 (D) 9
17. x- 3 x-
(A) x = 3 (B) x = 3 (C) y = 3 (D) y = 3
18. 40, 110 360 (HCF) :
(A) 40 (B) 110
(C) 360 (D) 10
30/2/1 # 11 | P a g e P.T.O.
- The line represented by the equation x y = 0 is : (A) parallel to x-axis (B) parallel to y-axis (C) passing through the origin (D) passing through the point (3, 2)
- The 10th^ term of the AP 5, , , (A) (B) (C) (D)
- If 4 is a zero of the polynomial p(x) = x^2 x (2 + 2k), then the value of k is : (A) 3 (B) 9 (C) 6 (D) 9
- The equation of a line parallel to the x-axis and at a distance of 3 units below x-axis is : (A) x = 3 (B) x = 3 (C) y = 3 (D) y = 3
- The HCF of 40, 110 and 360 is : (A) 40 (B) 110 (C) 360 (D) 10
30/2/1 # 13 | P a g e P.T.O. Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.
- Assertion (A) : Common difference of the AP : 5, 1, 3, Reason (R): Common difference of the AP : a 1 , a 2 , a 3 an is obtained by d = an an 1.
- Assertion (A) : The pair of linear equations px + 3y + 59 = 0 and 2x + 6y + 118 = 0 will have infinitely many solutions if p = 1. Reason (R): If the pair of linear equations px + 3y + 19 = 0 and 2x + 6y + 157 = 0 has a unique solution, then p 1. SECTION B This section has 5 Very Short Answer (VSA) type questions carrying 2 marks each. 5 2=
- If p and q are zeroes of the polynomial p(y) = 21y^2 y 2, then find the value of (1 p). (1 q).
- (a) In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and AOB = 90. If AO = OB = 42 cm, then find the perimeter of the top of the table. OR
30/2/1 # 14 | P a g e
( ) , 5 cm ,
[ = ]
23. tan A = ; A
24. ( ) ABC BC D ADC = BAC
CA^2 = CD. CB.
( ) , OA. OB = OC. OD A = C
B = D
30/2/1 # 16 | P a g e
25. 10 cm AB A XAY -
A 16 cm XY CD
6 - (SA) , 3 6 3=
cosec 1
cosec 1 = 2 sec
30/2/1 # 17 | P a g e P.T.O.
- At point A on the diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. Find the length of the chord CD parallel to XY at a distance of 16 cm from A. SECTION C This section has 6 Short Answer (SA) type questions carrying 3 marks each. 6 3=
- (a) Prove that the parallelogram circumscribing a circle is a rhombus. OR (b) Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
- (a) Prove that : = OR (b) Prove that : + = 2 sec
30/2/1 # 19 | P a g e P.T.O.
- If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and x + y 10 = 0, then find the value of k.
- The length of the hour hand of a clock is 10 cm. Find the area of the minor sector swept by the hour hand of the clock between 5 a.m. to 8 a.m. Also, find the area of the major sector.
- Prove that is an irrational number.
- A sum of 2,000 is invested at 7% per annum simple interest. Calculate the interests at the end of 1st, 2nd^ and 3rd^ year. Do these interests form an AP? If so, find the interest at the end of the 27th^ year. SECTION D This section has 4 Long Answer (LA) type questions carrying 5 marks each. 4 5=
- (a) Two ships are sailing in the sea on either side of a lighthouse. The angles of depression to the two ships as observed from the top of the lighthouse are 60 and 45 , respectively. If the distance between the ships is 100 m, then find the height of the lighthouse. OR (b) The angles of depression of the top and the bottom of an 8 m tall building from the top of another multistoried building are 30 and 45 , respectively. Find the height of the multistoried building and the distance between the two buildings.
- (a) The sum of the areas of two squares is 52 cm^2 and difference of their perimeters is 8 cm. Find the lengths of the sides of the two squares. OR
30/2/1 # 20 | P a g e ( ) 150 km 2 10 km/h
, = LM ||^ CB
LN ||^ CD
