General Mathematics

                                              Term: III
Time:  2 hours 30 mins         Total Marks: 75
Subject:  General 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. Encircle the correct option.
Q. No. 1 Encircle the correct option.

i.   is  a surd of order:
⦁ zero b.   1 c.   2 d.    ½

ii.   = …………..
⦁ 2 (a2 + b2) b.  4 ab c.  ̶  4ab    d.  a2  + b2

iii. If  is a factor of P (x), then P (a) = …………..
⦁ 0 b.   1 c.   ̶   a d.    a
iv.   Formula of the area of a circle is:
a.  b.    c.      d. 
v.    The medians of a triangle are:
⦁ concurrent b.  collinear c.  non-concurrent   d.    congruent

vi.    Length of a line segment joining the centre to any point on the circle is called:
⦁ Segment b.   Sector c.  Radius d.    Diameter


vii. The value of the variable which makes the equation a true statement is called the:
a)   Equation b) In equation c)  Solution d)  Constant
viii. A quadratic equation has a degree:
a)  1 b)   2 c) 3    d)   0
ix. In matrices (A + B)t  = ?
a)  At b)   Bt c)   At + Bt d)   At Bt
x. Solution set of (x  ̶  2)2 = 4 is:
    a)  {2, 6 } b)  { 0,  ̶  4} c) {2, ̶  6 }  d)   { 0, 4}
xi. The number of ways to find L.C.M are:
a)  2 b)  3 c) 4 d)  5
xii. Two angles with common vertex and a common side are called:
a)  Vertical angles b) Supplementary angles
c)  Adjacent angles d)  Complementary angles

xiii. If x > y, then ( ̶ 2) x  _________  ( ̶  2) y.
a)  > b)  < c)  ≥ d)    ≤
xiv. Circles with equal radii and equal diameters are called:

a)  Concentric circles b)   Semi-circles
c) Equal circles d)   Concyclic points.

xv.    is called:

a)  Distance formula b)   Collinear points
c)  Non-Collinear points d)   Equal points





Subjective
Part -I
Time Allowed: 2 hours 10 mins Marks: 60

Note: Use separate sheets for subjective section.
Q. No. 2   Write short answers to any six (6) questions. /12

⦁ What is meant by real numbers?
⦁ Solve 
⦁ Express   with rational denominator.
⦁ What is absolute value?
⦁ Factorize 
⦁ Find the square root of  .
⦁ Define linear equations.
⦁ State remainder theorem.
⦁ Find LCM of: 

Q. No. 3   Write short answers to any six (6) questions. /12

⦁ What is meant by quadratic equation?
⦁ Solve  .
⦁ Solve by using factorization method: 
⦁ Find the determinant of metrix   
⦁ Factorize 
 Define rectangular matrix.
⦁ If   then find P-1 if possible.
⦁ Find the value of ‘x’ in the given triangle. 
⦁ Define quadrilaterals.





Q. No. 4   Write short answers to any six (6) questions. /12
⦁ Define altitude of a triangle.
⦁ What is meant by medians of a triangle?

iii. Find the area of a circle whose circumference is 
iv. Draw a triangle ABC in which  .
v. The sum of two angles is 1000, the supplement of the first angle exceeds the supplement of the second angle by 400. Find the angles.
vi. Draw and define right angles triangle.
    vii. The sides of a triangle are 5 cm and 12 cm. Find the hypotenuse.
   viii.     What is meant by abscissa and ordinate?
ix. Find the area of a triangle whose sides are 5, 12 and 13.

























Part -II

Note: Attempt three questions.
Q. No. 5   (a)  Simplify:    /04
     (b)   Factorize: /04
 
Q. No. 6
(a) Simplify:    . /04

(b) Solve:   . /04
                                   
Q. No. 7
  (a) Solve by completing the square method:   . /04 (b) Solve by Cramer’s rule:    /04

 Q. No. 8  (a) Find the value of ‘x’ in the given triangle.  /04





     (b)  Draw an equilateral triangle with length of each side’s 6 cm. /04

                       
Q. No. 9
(a)    If the legs of a right triangle are ‘ ’ and ‘ ’ , prove that the            hypotenuse is  . /04

(b) What kind of a triangle has vertices A (6,  ̶  2),  B (1,  ̶  2) and C (  ̶  2, 2).  /04




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