Class – 9 Maths (MCQs with answers) Important concepts

Q- 1 One of the factors of (x³ – 1) – (x – 1) is
(a) x² + 1
(b) x² – 1
(c) x – 1
(d) x + 4

Ans- (c) x – 1

Q- 2 Find the degree of polynomial √2 .
(a) 2
(b) 0
(c) 1
(d) 1/2

Ans – (b) 0

Q- 3 Find the coefficient of x² in (3x² – 5) (4 + 4x²).
(a) 12
(b) 5
(c) -8
(d) 9

Ans – (c) -8

Q- 4 Zero of the polynomial p(x) = cx + d is
(a) -d
(b) -c
(c) d/c

(d) -d/c

Ans – (d) -d/c

Q- 5 If the area of the rectangle is 4x² + 4x – 3, then find its possible dimensions.
(a) 2x – 3, 2x + 1
(b) 2x – 1, 2x + 3
(c) 3x + 1, 2x – 3
(d) 3x – 1, 2x + 3

Ans – (b) 2x – 1, 2x + 3

Q- 6 When p(x) is divided by ax – b, then the remainder is
(a) p(a + b)
(b) P(−b/a)
(c) p(a/b)
(d) p(b/a)

Ans – (d) p(b/a)

Q- 7 The value of

(a) 300                (b) 500                  (c) 400                 (d) 600

Ans – (b) 500

Q- 8  If x + y = 3, x2 + y2 = 5 then xy is

(a)   1

(b)   3

(c)   2

(d)   5

Ans – (c)   2

Q- 9  Identify the polynomial

(a)   x–2 + x–1 + 5

(b)

(c)

(d)   3x2 + 7

Ans – (d)   3x2 + 7

Q- 10 In ΔABC, the bisectors of ∠ABC and ∠BCA intersect each other at O. The measure of ∠BOC is
(a) 90° + ∠A        (b) 90° + ∠A/2             (c) 180 – ∠A              (d) 90° – ∠A/2

Ans – (b) 90° + ∠A/2

Q- 11 In figure if ∠A + ∠B + ∠C + ∠D + ∠E + ∠F = k right angles, then find value of k.

(a) 2        (b) 3                 (c) 4                        (d) 5

Ans – (c) 4

Q- 12 The angle of a triangle are in the ratio 5 : 3 : 7, the triangle is
(а) an acute-angled triangle     (b) an obtuse angled triangle
(c) an right angled triangle       (d) an isosceles triangle

Ans – (а) an acute-angled triangle

Q- 13 If one angle of triangle is equal to the sum of the other two, then the triangle is
(a) an isosceles triangle
(b) an obtuse-angled triangle
(c) an equilateral triangle
(d) a right triangle

Ans – (d) a right triangle

Q- 14 Given lines l1 || l2 and l2 || l3 in figure. The value of x is

(a) 40°            (b) 140°              (c) 50°               (d) 80°

Ans – (b) 140°

Q- 15 The diagonals of the rectangle ABCD intersect at O. If ∠COD = 78°, then ∠OAB is:
(a) 35o           (b) 51o                (c) 70o              (d) 110 o

Ans – (b) 51o

Q- 16 If AB = x + 3, BC = 2x and AC = 4x – 5, then for what value of ‘x’, B lies on AC?
(a) 2              (b) 3              (c) 5          (d) 8

Ans – (d) 8

Q- 17 In ΔABC, ∠C = ∠A and BC = 4 cm and AC = 5 cm, then find length of AB.
(a) 5 cm        (b) 3 cm             (c) 4 cm                (d) 2.5 cm

Ans – (c) 4 cm

Q- 18 In figure, D is the mid-point of side BC of a ΔABC and ∠ABD = 50°. If AD = BD = CD, then find the measure of ∠ACD.

(a) 30°         (b) 70°              (c) 80°            (d) 40°

Ans – (d) 40°

Q- 19 In figure, ABC is an isosceles triangle whose side AC is produce to E and through C, CD is drawn parallel to BA. Find the value of x.

(a) 52°              (b) 156°                (c) 76°                (d) 104°

Ans – (d) 104°

Q- 20 Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be
(a) 3.6 cm
(b) 4.1 cm
(c) 3.8 cm
(d) 3.4 cm

Ans – (d) 3.4 cm

Q- 21 In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are
(a) isosceles but not congruent
(b) isosceles and congruent
(c) congruent but not isosceles
(d) neither congruent nor isosceles

Ans – (a) isosceles but not congruent

Q- 22  In two triangles DEF and PQR, if DE = QR, EF = PR and FD = PQ, then
(a) ∆DEF ≅ ∆PQR          (b) ∆FED ≅ ∆PRQ
(c) ∆EDF ≅ ∆RPQ          (d) ∆PQR ≅ ∆EFD

Ans – (b) ∆FED ≅ ∆PRQ

Q- 23 All the medians of a triangle are equal in case of a:
(a) Scalene triangle             (b) Right angled triangle
(c) Equilateral triangle         (d) Isosceles triangle

Ans – (c) Equilateral triangle

Q- 24 The perimeter of an equilateral triangle is 60 m. The area is
(a) 10√3 m²      (b) 15√3 m²       (c) 20√3 m² (d) 100√3 m²

Ans – (d) 100√3 m²

Q- 25 The area of an equilateral triangle with side 2√3 cm is
(a) 5.196 cm²         (b) 0.866 cm²      (c) 3.496 cm²      (d) 1.732 cm²

Ans – (a) 5.196 cm²

Q- 26 The sides of a triangle are 35 cm, 54 cm and 61 cm. The length of its longest altitude is
(a) 16√5 cm             (b) 10√5 cm          (c) 24√5 cm         (d) 28 cm

Ans – (c) 24√5 cm