CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables VBQs Set 09

Multiple Choice Questions (MCQs)

Question. The lengths of the diagonals of a rhombus are 24 cm and 32 cm. The perimeter of the rhombus is :
(a) 9 cm
(b) 128 cm
(c) 80 cm
(d) 56 cm
Answer: (c) 80 cm

Question. In an isosceles \( \Delta ABC \) if \( AC = BC \) and \( AB^2 = 2AC^2 \), then \( \angle C \) is equal to :
(a) \( 45^\circ \)
(b) \( 60^\circ \)
(c) \( 30^\circ \)
(d) \( 90^\circ \)
Answer: (d) \( 90^\circ \)

Question. If in \( \Delta ABC \) and \( \Delta DEF \), \( \frac{AB}{DE} = \frac{BC}{FD} \), then they will be similar if:
(a) \( \angle B = \angle E \)
(b) \( \angle A = \angle D \)
(c) \( \angle B = \angle D \)
(d) \( \angle A = \angle F \)
Answer: (c) \( \angle B = \angle D \)

Question. In \( \Delta LMN, \angle L = 60^\circ, \angle M = 50^\circ \). If \( \Delta LMN \sim \Delta PQR \), then the value of \( \angle R \) is
(a) \( 40^\circ \)
(b) \( 30^\circ \)
(c) \( 70^\circ \)
(d) \( 110^\circ \)
Answer: (c) \( 70^\circ \)

Question. The area of two similar triangles \( ABC \) and \( PQR \) are 25 \( cm^2 \), 49 \( cm^2 \). If \( QR = 9.8 \) cm, then \( BC \) is :
(a) 9.8 cm
(b) 7 cm
(c) 49 cm
(d) 25 cm
Answer: (b) 7 cm

Question. If \( \Delta ABC \) is right angled at A, then value of \( \tan B \times \tan C \) is :
(a) 0
(b) 1
(c) -1
(d) None of the options
Answer: (b) 1

Question. If \( ABC \) and \( DEF \) are similar triangles such that \( \angle A = 47^\circ \) and \( \angle B = 83^\circ \), then \( \angle F \) is
(a) \( 60^\circ \)
(b) \( 70^\circ \)
(c) \( 50^\circ \)
(d) \( 80^\circ \)
Answer: (c) \( 50^\circ \)

Question. If \( \Delta ABC \) and \( \Delta PQR \) are similar triangles such that \( \angle A = 32^\circ \) and \( \angle R = 65^\circ \), then \( \angle B \) is
(a) \( 83^\circ \)
(b) \( 32^\circ \)
(c) \( 65^\circ \)
(d) \( 97^\circ \)
Answer: (a) \( 83^\circ \)

Question. Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio :
(a) 2 : 3
(b) 4 : 9
(c) 81 : 16
(d) 16 : 81
Answer: (d) 16 : 81

Question. If \( \Delta ABC \cong \Delta RQP, \angle A = 80^\circ, \angle B = 60^\circ \), then the value of \( \angle P \) is
(a) \( 60^\circ \)
(b) \( 50^\circ \)
(c) \( 40^\circ \)
(d) \( 30^\circ \)
Answer: (c) \( 40^\circ \)

Question. \( \Delta ABC \sim \Delta PQR \). If \( ar(ABC) = 2.25\ m^2, ar(PQR) = 6.25\ m^2, PQ = 0.5 \) m, then length of \( AB \) is:
(a) 30 cm
(b) 0.5 m
(c) 50 cm
(d) 3 m
Answer: (a) 30 cm

Question. If \( \Delta ABC \sim \Delta DEF, BC = 4 \) cm, \( EF = 5 \) cm and \( ar(\Delta ABC) = 80\ cm^2 \), the \( ar(\Delta DEF) \) is :
(a) \( 100\ cm^2 \)
(b) \( 125\ cm^2 \)
(c) \( 150\ cm^2 \)
(d) \( 200\ cm^2 \)
Answer: (b) \( 125\ cm^2 \)

Question. If the ratio of the corresponding sides of two similar triangles is 2 : 3, then the ratio of their corresponding altitude is:
(a) 3 : 2
(b) 16 : 81
(c) 4 : 9
(d) 2 : 3
Answer: (d) 2 : 3

Question. Which of the following are not the sides of a right triangle
(a) 9 cm, 15 cm, 12 cm
(b) 2 cm, 1 cm, \( \sqrt{5} \) cm
(c) 400 mm, 300 mm, 500 mm
(d) 9 cm, 5 cm, 7 cm
Answer: (d) 9 cm, 5 cm, 7 cm

Question. \( \Delta ABC \sim \Delta PQR \). M is the mid point of BC and N is the mid point of QR. If the area of \( \Delta ABC = 100 \) sq. cm and the area of \( \Delta PQR = 144 \) sq. cm. If \( AM = 4 \) cm then \( PN \) is :
(a) 4.8 cm
(b) 12 cm
(c) 4 cm
(d) 5.6 cm
Answer: (a) 4.8 cm

Question. The perimeters of two similar triangles \( ABC \) and \( LMN \) are 60 cm and 48 cm respectively. If \( LM = 8 \) cm, length of \( AB \) is
(a) 10 cm
(b) 8 cm
(c) 5 cm
(d) 6 cm
Answer: (a) 10 cm