Mathematics

                                              Term: III
Time:  2 hours 30 mins         Total Marks: 75
Subject: Mathematics                                                                           Class: X
Name: ______________________                                      Date: ____________
Questions 1 2 3 4 5 6 7 8 9 Total Marks
Marks Obtained

Objective
Time Allowed: 20 min       Marks: 15
Instruction:
⦁ Fifteen (15) Multiple Choice Questions (MCQs) are given in this part. Attempt all questions. All questions carry equal marks.
Q. No. 1 Encircle the correct option.

i. Which is an open sentence?
a)  3 > 2 b)  x + 2 = 3 c)  ̶  3 <  ̶  8 d)   3y < 7y

ii. Product of cube roots of unity is:
a)   0 b)  1 c)  ̶  1 d)  3

iii.   Lowest class limit in the interval (15 - 19) is:
⦁ 15 b)  17 c)   19 d)  34
iv.   If x : 5 = 4 : 2 then x = ………..
a)  20 b)  10 c)  15 d)   5

v. If the two circles touch externally, then the distance between their centres is  equal to the:
a)  Difference of their radii    b)  Sum of their radii
c) Product of their radii d)   none of these

vi.   = _________________
a)    b)    c)    d)   

vii. The distance of any point of the circle to its centre is called:
a)   Radius b)  Diametre c)  A chord d)  An arc

viii. If  , then Alternendo property is:
    a)    b) 
    c)    d) 
ix. The solution set of the equation  is:
a)  {9, 5} b)  { ̶  5, 9} c) { 5,  ̶  9} d) { ̶  5,  ̶  9}
x. If number of elements in set A is 3 and set B is 2, then number of binary relation
A ×B is:
a)  23    b) 26  c) 28 d)  22

xi. In a right angle triangle base = 4 cm, perpendicular = 4 cm the hypotenuse will be equal to:
a)  8 cm b)     cm c)   cm     d)   12 cm
xii. Fourth proportional of 7, 21, 3 is:
a)   7 b)   8 c)   9 d)   10

xiii. How many common tangents can be drawn for two disjoint circles?

a)   Two b)   Three c)   Four d)   Five

xiv. Two chords of a circle which are equidistant from the centre are:

a)  Congruent b)  Concurrent c)  Similar d)  Greater
xv. In the figure, O is the centre of the circle, then the angle ‘x’ is:

a)  550 b)  1100 c)  2200 d)   1250




Subjective
Part -I
Time Allowed: 2 hour 10 min Marks: 60
Note: Use separate sheet for subjective section.

Q. No. 2   Write short answers to any six (6) questions. /12
⦁ Define compound open sentence and give example.
⦁ Find the solution set of 
⦁ Evaluate .
⦁ What do you know about Cartesian plane?
⦁ Solve  .
⦁ Define radical equation and give one example.
⦁ Define extraneous roots.
⦁ Find the solution set of 
⦁ Solve by factorization 
Q. No. 3   Write short answers to any six (6) questions. /12

⦁ What is meant by elimination and eliminant?
⦁ Eliminate “t” from equations   and  .
⦁ Write dividendo theorem.
⦁ Find value of “x” if 6 : 3 = 4 : x.
⦁ Write demerits of mode.
⦁ Find arithmetic mean for the information 
⦁ Eliminate ‘x’ by substitution method 
⦁ What is the difference between discrete and continuous variable.
⦁ Find the fourth proportional of 

Q. No. 4   Write short answers to any six (6) questions. /12
i. Define major arc of the circle.
ii. Draw a circle of radius 4 cm. Take a point ‘D’ on it and draw a tangent at it.
    iii. Construct a triangle if 
iv. Differentiate between a sector and a segment of a circle.
v. Prove that 
vi. If   , find  .
    vii. Define transverse common tangents.
   viii. Write trigonometric ratios of 300.
    ix.    Find the value of  .


Part -II

Note: Attempt three questions.
Q. No. 5
  (a)     Solve                          /04
(b) Find the solution set if  3 ≤ 2x   ̶  3  ≤ 5,  /04

Q. No. 6
(a) Eliminate ‘t’ from the following equations: /04

(b) Solve by completing square method:  /04
Q. No. 7
(a) If     (where a, b, c, p, q, r ≠ 0) then prove that /04
                   

(b) A set of data contains the values as: 148, 145, 160, 157, 156, 160.
Show that Mode > Median > Mean /04
 Q. No. 8
(a) A tree is 72 m high. Find the angle of elevation of its top 100 m away on the     ground level. /04
(b) Construct any  and draw its escribed circle (e-circle) opposite to vertex B. /04
Q. No. 9  Prove that two chords of a circle which are equidistant from the centre, are congruent. /08


Answer Key
Objective
Q. No. 1  Encircle the correct option.  
Q. No Answers
i. b
ii. b
iii. a
iv. b
v. b
vi. b
vii. c
viii. c
ix. c
x. b
xi. b
xii. c
xiii. c
xiv. a
xv. a