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Type of Announcement : Model Question Paper for X - Solution Maths
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Question Paper X - Solution Maths
Subject Name : Solution Maths Time : 2.30 Hrs Marks : 100

General instructions:
(i) This question paper consists of four sections. Read the note carefully under each section before answering them.
(ii) The rough work should be shown at the bottom of the pages of the answer book.
(iii) Calculator and other electronic devices are not permitted

Section – A
Note:
(i) Answer all the 15 questions.
(ii) Each question contains four options. Choose the most suitable answer from the four alternatives.
(iii) Each question carries 1 mark

1. Given f (x) = (-1)x is a function from N to Z. Then the range of f is
(A) { 1} (B) N (C) { 1, – 1 } (D) Z
2. The sequence –3, –3, –3,......is
(A) an A.P. only (B) a G.P. only (C) neither A.P. nor G.P (D) both A.P. and G.P.
3. The 108th term of the sequence 1, –1,0, 1, –1, 0 ... is
(A) 1 (B) –1 (C) 0 (D) 108
4. The remainder when 7x² - 2x -1 + is divided by x-3 is
(A) 58 (B) 70 (C) 0 (D) 3
5. A is of order m×n and B is of order p×q, addition of A and B is possible only if
(A) m = p (B) n = q (C) n = p (D) m = p, n = q
6. The value of k if the straight lines 3x + 6y + 7 = 0 and 2x + ky = 5 are perpendicular is
(A) 1 (B) –1 (C) 2 (D)2
7. The length of a diagonal of the quadrilateral whose vertices are (1,0), (0,1), (–1,0) and(0,–1) is ______ units.
(A) 1 (B) –1 (C) 2 (D) 1/2
8. The areas of two similar triangles are 16 cm2 and 36cm2 respectively. If the altitudes are in the ratio 2 : x , then x is
(A) 2 (B) 3 (C) 4 (D) 6
9. If the surface area of a sphere is 36π cm², then the volume of the sphere is equal to
(A) 12π cm³ (B) 36π cm³ (C) 72π cm³ (D) 108πcm³
10. If P(A) = 0.25, P(B) = 0.50, P(AυB) = 0.14 then P(neither A nor B) =
(A) 0.39 (B) 0.25 (C) 0.11 (D) 0.24

Section – B
Note :
(i) Answer 10 questions.
(ii) Answer any 9 questions from the first 14 questions. Question no. 30 is compulsory.
(iii) Each question carries 2 marks.

1. Let P = {a,b,c}, Q = {g,h, x, y} and R = {a,e, f, s}. Find R \(P∩Q)
2. Find the sum of the first 25 terms of the geometric series 16 - 48 + 144 - 432 +.....
3. If (7,3),(6,1),(8,2) and (p, 4) are the vertices of a parallelogram taken in order, then find the value of p.
4. A girl of height 150√3 cm stands in front of a lamp-post and casts a shadow of length 150 cm on the ground. Find the angle of elevation of the top of the lamp-post .
5. The radii of two right circular cylinders are in the ratio 2 : 3. Find the ratio of their volumes if their heights are in the ratio 5 : 3.
6. The smallest value of a collection of data is 12 and the range is 59. Find the largest value of the collection of data
7. A ticket is drawn from a bag containing 100 tickets. The tickets are numbered from one to hundred. What is the probability of getting a ticket with a number divisible by 10?

Section – C
Note :
(i) Answer 9 questions.
(ii) Answer any 8 questions from the first 14 questions. Question no. 45 is compulsory.
(iii) Each question carries 5 marks

1. Find the sum of first n terms of the series. 7 + 77 + 777 +....
2. If all sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.
3. Find the area of the quadrilateral whose vertices are (6,9), (7,4), (4,2) and (3,7)
4. The vertices of a ∆ABC are A(1 , 2), B(-4 , 5) and C(0 , 1). Find the slopes of the altitudes of the triangle
5. A vertical tree is broken by the wind. The top of the tree touches the ground and makes an angle 30° with it. If the top of the tree touches the ground 30 m away from its foot, then find the actual height of the tree.

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