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SECTION – A
‘ Answer all questions as directed (Que. No. 1 to 24) (Each question carries 1 mark) [24] ‘ Choose the correct option for the following given statements. (Que. no. 1 to 6) (1) 9 tan^2 q – 9 sec^2 q = ____. (A) 9 (B) 0 (C) –1 (D) – (2) ______ is true for the solution of equations 43 x + 2y = 8 and 2x + 3y = 12 (A) Infinitety many solutions (B) No solution (C) Unique solution (D) Two solutions (3) If Sn = 2n^2 + 3n, then d = ______. (A) 13 (B) 4 (C) 9 (D) 0 (4) Which measure of sides given below determine right angle triangle. (A) 50, 80, 100 (B) 3, 8, 5 (C) 7, 24, 25 (D) 3, 3, 3 (5) One of the root of quadratic equation kx^2 – 7x + 3 = 0 is 3 then k = ____. (A) –2 (B) 3 (C) – 3 (D) 2 (6) In DABC, – B = 90º and AB = BC then AB : AC = _____. (A) 1 : 3 (B) 1 : 2 (C) 1 : ÷¯ 2 (D) ÷¯2 : 1 12 (E) 1 [P.T.O.]
Instructions : (1) This question paper contains 53 questions. It consists sections A, B, C and D. (2) The number written right side of each section indicates the total marks of that section. (3) Each section start writing on new page. Write answers in sequence. (4) Don't use calculator. (5) Draw figure wherever its required.
[This Question paper contains 5 printed pages, Std - 10th] Date :07/05/
[ Time : 3 Hours ] Maths (E - 12) [Maximum Marks : 80]
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12 (E) 2
’ Choose the correct option for the following given statements. (Que. no. 7 to 12) (7) H.C.F. (156, 455) = ___________. (4, 13, 26) (8) If x = 2, y = 3 is a solution of equation 5x – 3y = k, then k = _____. (1, 2, 3) (9) The distance of the point p(–6, 8) to the origin is ____. (10, 2÷¯7, 8) (10) If P(A) : P(A¯) = 3 : 5, P(A) = __________. ^58 ,^^38 ,^35
(11)
2 1 + cot A 1 + tan A 2 = ______. (tan (^2) A, cot (^2) A, 1)
(12) A line that intersect the circle at two points is called ____ of the circle. (tangent, secant, chord) ’ Answer the following in the one word, one number or one statement. (Que. no. 13 to 18) (13) Find the roots of quadratic equation ax^2 + bx + c = 0 (a π 0) if D = 0. (14) Find first four terms of AP where a = 4 and d = – 3. (15) How many tangants a circle have? (16) If x¯ = 21.44 and Z = 19.13 they find the value of M. (17) What is the value of 8 sec^2 q – 8 tan^2 q? (18) What is the probability of complemently event of impossible event? ’ State whether the following statements are true or false. (Que. no. 19 to 22) (19) The decimal expansions of 256125 is non-terminating repeating. (20) If the two of the zeroes of a cubic polynomial are zero, then it does not have the term with x and constant term. (21) The perimeter of a square circumscribing a circle of radius 'a' cm is 8a cm. (22) Two identical solid cubes of side 'a' are joined end to end. Then, the total surface area of the resulting cuboid is 12a^2. ’ Match the columns. (Que. no. 23 & 24) Part – A Part – B (23) Common difference of (a) 4 2, –2, –6, –10 (b) – 4 Part – A Part – B (24) Formula to find mean (a) x¯ = a + Σ Σ^ f d^ i^ f ii (b) x¯ = a + Σ Σ^ f u^ i^ f ii
12 (E) 4
(41) Point P lies on the line segment AB joining A (–2, –2) and B (2, –4) such that AP = 37 AB. Find the coordinates of point P. (42) Find the coordinates of the point which divides the line segment joining points A(3, 8) and B(12, 17) in the ratio 2 : 7. (43) The cost of fencing a circular field at the rate of 24 per metre is 5280. The field is to be ploughed at the rate of 0.50 per m^2. Find the cost of ploughing the field. (^) Take π=^227
(44) The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. (45) A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (1) a two digit number, (2) a perfect square number and (3) a number divisible by 5. SECTION – D ’ Answer any five questions from the following eight questions with calculation. (Que. no. 46 to 53) (Each question carries 4 marks) [20]
(46) If DABC ~ DPQR, then prove that =^ ^ ^ =^ ^ ^ = ^
ABC AB 2 BC 2 AC^2
PQR PQ QR PR.
(47) State and prove Pythagoras theorem. (48) Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts. Write steps of construction. (49) Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60º. Write the steps of construction. (50) A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30º with it. The distance between the foot of the tree to the point where the top touches the ground is 8 cm. Find the height of the tree. (51) A gulab jamun, contains sugar syrup up to about 30 % of its volume. Find approximately how much syrup would be found in 45 gulab jamun, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.
12 (E) 5
(52) The median of the following data is 525. Find the values of x and y, if the total frequency is 100. Class interval Frequency 0 – 100 2 100 – 200 5 200 – 300 x 300 – 400 12 400 – 500 17 500 – 600 20 600 – 700 y 700 – 800 9 800 – 900 7 900 – 1000 4 (53) Consider the following distribution of daily wages of 50 workers of a factory. Daily wages (in ) Number of workers 500 – 520 12 520 – 540 14 540 – 560 8 560 – 580 6 580 – 600 10 Find the mean daily wages of the workers of the factory by using an appropriate method.
