Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

101.

If ΔABC ∼ ΔPQR, area of ΔABC/area of ΔPQR = 900/1225 and value of side PR = 7 cm, find the value of side AC. 1. 10 cm2. 5 cm3. 6 cm4. 30 cm

Answer» Correct Answer - Option 3 : 6 cm

Given:

ΔABC ∼ ΔPQR

Area of ΔABC/Area of ΔPQR = 900/1225

Value of side PR = 7 cm.

Concepts used:

If ΔABC ∼ ΔPQR,

Area of ΔABC/Area of ΔPQR = (AC/PR)2 =  (AB/PQ)2 = (BC/QR)2 

Calculation:

As ΔABC ∼ ΔPQR,

⇒ Area of ΔABC/Area of ΔPQR = (AC/PR)2 =  (AB/PQ)2 = (BC/QR)2

⇒ 900/1225 = (AC/PR)2 

⇒ √900/√1225 = AC/PR

⇒ 30/35 = AC/7 cm

⇒ AC = (30 × 7)/35 cm

⇒ AC = 210/35 cm

⇒ AC = 6 cm.

∴ The value of side AC is 6 cm. 
Discussion
102.

Which of the following statement is correct about SSS congruence of triangles?1. Two triangles are congruent if two sides of one triangle are congruent to the corresponding sides of another and the angles include between them are congruent2. Two triangles are congruent if three sides of one triangle are congruent to the corresponding sides of the other triangle3. Two triangles are congruent if two angles of one triangle are congruent to the corresponding angles of the other triangle and the sides include between them are congruent4. Two right-angled triangle are congruent if the hypotenuse and one side of one triangle are respectively congruent to the hypotenuse and the corresponding side of the other

Answer» Correct Answer - Option 2 : Two triangles are congruent if three sides of one triangle are congruent to the corresponding sides of the other triangle
Congruence of triangles: Two triangles are said to be congruent if their all sides and angles are equal corresponding to the other triangle’s all sides and angles. There are four ways in which a triangle can be proved or said congruent.
  • SSS (Side-Side-Side) Rule: It is when we are given that all the three sides of one triangle are equal to three sides of another triangle correspondingly.
  • SAS (Side-Angle-Side) Rule: It states that two sides and the angle included between those sides of one triangle are equal to two sides and the angle included between them of the other triangle.
  • ASA (Angle-Side-Angle) Rule: If the two angles and one side between them of one triangle is equal to the corresponding angles and side, the triangle is said to be congruent.
  • AAS (Angle-Angle-Side) Rule: It states that if two consecutive angles and one adjacent side of a triangle is equal to two consecutive angles and one adjacent side of another triangle.
  • Right- Hand Side (RHS) Rule: It states that if in two right-angled triangles, the length of the hypotenuse and one of the sides of one triangle is equal to the length of the hypotenuse and one of the sides of another triangle, the triangle is said to be congruent.
Discussion
103.

In triangle ABC AD is median on side BC. Find the length of AD if AB = 8 cm, BC = 10 cm and AC = 6?1. 5 cm2. 6 cm3. 7 cm4. 8 cm

Answer» Correct Answer - Option 1 : 5 cm

Given:

In triangle ABC, AD is median on side BC where AB = 8 cm, BC = 10 cm and AC = 6

Concept Used:

According to Apollonius theorem the sum of squares of any of the two sides of a triangle equals to twice its square on half of the third side, along with the twice of its square on the median bisecting the third side

Calculation:

Let ABC is a triangle with AD is median on BC then by Apollonius theorem

∴ (AB2 + AC2) = 2 × (BD2 + AD2)

∴ ((8)2 + (6)2) = 2 × ((5)2 + AD2)

⇒ 64 + 36 = 50 + 2 × AD2

⇒ AD2 = 25

⇒ AD = 5 cm

Hence, option (1) is correct
Discussion
104.

Consider the following statements:I. The orthocenter of right-angle triangle lies on the vertex of the triangleII. In right-angle triangle the median drawn on the base of a triangle is not half of its base.Which of the given statements is/are incorrect?1. Only 12. 2 only3. Both 1 and 24. Neither 1 nor 2

Answer» Correct Answer - Option 2 : 2 only

Given:

Two statements are given

Concept Used:

Basic concepts of triangle and circle

Calculation:

Orthocenter is the point of intersection of line perpendicular on the side of triangle and as we know that the two side of right angle triangle is perpendicular to each other so orthocenter will lie on the vertex of right angle triangle.

∴ Statement 1 is correct

Now, we know that in right angle triangle if the median drawn on the hypotenuse of the triangle is always half of the hypotenuse.

∴ Statement 2 is Incorrect

Hence, option (2) is correct
Discussion
105.

ABC = DCB  by SAS.  Which of the following is not a matching part? (i) AB = DC (ii) <ABC = <DCB (iii) AC = DB (iv) BC = CB (a) Both (i) & (ii) are correct (b) Only (ii) is correct (c) Only (iii) is correct (d) Only (iv) is correct

Answer» (d) BC = CB [Common is both the triangles]
Discussion
106.

In a ΔABC, 3∠A + 2∠B = 275° and 2∠B + 3∠C = 325°, value of ∠B is.1. 30°2. 60°3. 40°4. 50°

Answer» Correct Answer - Option 2 : 60°

Given:

3∠A + 2∠B = 275° and 2∠B + 3∠C = 325°

Calculations:

In ΔABC,

∠A + ∠B + ∠C = 180° (sum of all the angles of a Δ is 180°)

3∠A + 2∠B = 275°      ----(1)

2∠B + 3∠C = 325°      ----(2)

Adding eq. (1) and eq. (2)

3∠A + 2∠B + 2∠B + 3∠C = 275° + 325° 

⇒ 3∠A + 3∠B + 3∠C + ∠B = 600° 

⇒ 180° × 3 + ∠B = 600°

⇒ ∠B = 600° - 540°

⇒ ∠B = 60° 

∴ The value of ∠B is 60°.
Discussion
107.

In a quadrilateral ABCD, ∠C is a right angle, ∠ A is thrice of ∠ B and ∠D is 70°. Find ∠A and ∠B : 1. 120˚ and 80˚2. 110˚ and 90˚3. 150˚ and 50˚4. 140˚ and 60˚

Answer» Correct Answer - Option 3 : 150˚ and 50˚

Given: 

ABCD is a quadrilateral,  ∠C = 90° and ∠D = 70°   

Concept: 

The sum of all angles in a quadrilateral is 360°.

Calculation:

Let assume that ∠B = x

So, ∠A = 3x

⇒ The sum of all angles in a quadrilateral is 360°.

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ 3x + x + 90° + 70° = 360°

⇒ 4x + 160˚ = 360°

⇒ 4x = 200° 

⇒ x = 50° 

∴ ∠B = x = 50°

And,  ∠A = 3x = 50° × 3 =150°

The Correct option is 3 i.e. 150° and 50°
Discussion
108.

In a quadrilateral ABCD, if ∠A = 80°, ∠B = 100°, ∠C = 50°, then ∠D = _____.       1. 130° 2. 100° 3. 110° 4. 120°

Answer» Correct Answer - Option 1 : 130° 

Given:

∠A = 80°, ∠B = 100°, ∠C = 50°

Concept used:

The sum of interior angles in a quadrilateral is 360°.

Calculation:

∠A + ∠B + ∠C + ∠D = 360°

⇒ 80° + 100° + 50° + ∠D = 360°

⇒ ∠D = 360° - 230°

⇒ ∠D = 130°

∴ The value of ∠D = 130°.
Discussion