MCQOPTIONS
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MCQOPTIONS
This section includes 192 Mcqs, each offering curated multiple-choice questions to sharpen your Arithmetic Ability knowledge and support exam preparation. Choose a topic below to get started.
| 101. |
Angle between the internal bisectors of two angles of a triangle ∠B and ∠C is 120°, then ∠A is : |
| A. | 0° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» D. 0° | |
| 102. |
In a triangle ABC, ∠A = 90°, ∠C = 55°, $${AD}$$ ⊥ $${BC}$$. What is the value of ∠BAD ? |
| A. | 5° |
| B. | 0° |
| C. | 5° |
| D. | 5° |
| Answer» E. | |
| 103. |
The angle between the external bisectors of two angles of a triangle is 60°. Then the third angle of the triangle is |
| A. | 0° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» D. 0° | |
| 104. |
In ΔABC ∠A = 90° and AD ⊥ BC where D lies on BC. If BC = 8 cm, AD = 6 cm, then arΔABC : arΔACD = ? |
| A. | : 3 |
| B. | 5 : 16 |
| C. | 6 : 9 |
| D. | 5 : 9 |
| Answer» D. 5 : 9 | |
| 105. |
In a triangle ABC, AB = AC, ∠BAC = 40° then the external angle at B is : |
| A. | 0° |
| B. | 0° |
| C. | 10° |
| D. | 0° |
| Answer» D. 0° | |
| 106. |
ABC is an isosceles triangle such that AB = AC and ∠B = 35°, AD is the median to the base BC. Then ∠BAD is |
| A. | 0° |
| B. | 5° |
| C. | 10° |
| D. | 5° |
| Answer» E. | |
| 107. |
In a triangle ABC, AB + BC = 12 cm, BC + CA = 14 cm and CA + AB = 18 cm. Find the radius of the circle (in cm) which has the same perimeter as the triangle |
| A. | $\frac{5}{2}$$ |
| B. | $\frac{7}{2}$$ |
| C. | $\frac{9}{2}$$ |
| D. | $\frac{{11}}{2}$$ |
| Answer» C. $\frac{9}{2}$$ | |
| 108. |
The length of the two sides forming the right angle of a right angled triangle are 6 cm and 8 cm. The length of its circum-radius is : |
| A. | cm |
| B. | cm |
| C. | cm |
| D. | 0 cm |
| Answer» B. cm | |
| 109. |
If in a triangle, the orthocentre lies on vertex, then the triangle is |
| A. | cute angled |
| B. | sosceles |
| C. | ight angled |
| D. | quilateral |
| Answer» D. quilateral | |
| 110. |
ABC is a right angled triangled, right angled at C and P is the length of the perpendicular from C on AB. If a, b and c are the length of the sides BC, CA and AB respectively, then |
| A. | $\frac{1}{{{p^2}}} = \frac{1}{{{b^2}}} - \frac{1}{{{a^2}}}$$ |
| B. | $\frac{1}{{{p^2}}} = \frac{1}{{{a^2}}} + \frac{1}{{{b^2}}}$$ |
| C. | $\frac{1}{{{p^2}}} + \frac{1}{{{a^2}}} =- \frac{1}{{{b^2}}}$$ |
| D. | $\frac{1}{{{p^2}}} = \frac{1}{{{a^2}}} - \frac{1}{{{b^2}}}$$ |
| Answer» C. $\frac{1}{{{p^2}}} + \frac{1}{{{a^2}}} =- \frac{1}{{{b^2}}}$$ | |
| 111. |
In ΔABC, ∠BAC = 90° and AB = $$\frac{1}{2}$$ BC, Then the measure of ∠ACB is : |
| A. | 0° |
| B. | 0° |
| C. | 5° |
| D. | 5° |
| Answer» C. 5° | |
| 112. |
D is any point on side AC of ΔABC. If P, Q, X, Y are the mid-point of AB, BC, AD and DC respectively, then the ratio of PX and QYis |
| A. | : 2 |
| B. | : 1 |
| C. | : 1 |
| D. | : 3 |
| Answer» C. : 1 | |
| 113. |
For a triangle base is 6$$\sqrt 3 $$ cm and two base angles are 30° and 60°. Then height of the triangle is |
| A. | $$\sqrt 3 $$ cm |
| B. | .5 cm |
| C. | $$\sqrt 3 $$ cm |
| D. | $$\sqrt 3 $$ cm |
| Answer» C. $$\sqrt 3 $$ cm | |
| 114. |
I is the incentre of a triangle ABC. If ∠ACB = 55°, ∠ABC = 65° then the value of ∠BIC is |
| A. | 30° |
| B. | 20° |
| C. | 40° |
| D. | 10° |
| Answer» C. 40° | |
| 115. |
In a triangle ABC, incentre is O and ∠BOC= 110°, then the measure of ∠BAC is: |
| A. | 0° |
| B. | 0° |
| C. | 5° |
| D. | 10° |
| Answer» C. 5° | |
| 116. |
In a right angled ΔABC, ∠ABC = 90°, AB = 3, BC = 4, CA = 5; BN is perpendicular to AC, AN : NC is |
| A. | : 4 |
| B. | : 16 |
| C. | : 16 |
| D. | : 4 |
| Answer» C. : 16 | |
| 117. |
If the circumcentre of a triangle lies outside it, then the triangle is |
| A. | quilateral |
| B. | cute angled |
| C. | ight angled |
| D. | btuse angled |
| Answer» E. | |
| 118. |
Let O be the in-centre of a triangle ABC and D be a point on the side BC of ΔABC, such that OD ⊥ BC. If ∠BOD = 15°, then ∠ABC = ? |
| A. | 5° |
| B. | 5° |
| C. | 50° |
| D. | 0° |
| Answer» D. 0° | |
| 119. |
In a triangle ABC, ∠BAC = 90° and AD is perpendicular to BC. If AD = 6 cm and BD = 4 cm then the length of BC is: |
| A. | cm |
| B. | 0 cm |
| C. | cm |
| D. | 3 cm |
| Answer» E. | |
| 120. |
If ΔABC is an isosceles triangle with ∠C = 90° and AC = 5 cm then AB is: |
| A. | cm |
| B. | 0 cm |
| C. | $$\sqrt 2 $$ cm |
| D. | .5 cm |
| Answer» D. .5 cm | |
| 121. |
O is the incentre of ΔABC and ∠A = 30°, then ∠BOC is |
| A. | 00° |
| B. | 05° |
| C. | 10° |
| D. | 0° |
| Answer» C. 10° | |
| 122. |
The orthocentre of a right angled triangle lies |
| A. | utside the triangle |
| B. | t the right angular vertex |
| C. | n its hypotenuse |
| D. | ithin the triangle |
| Answer» C. n its hypotenuse | |
| 123. |
ΔABC be a right-angled triangle where ∠A = 90° and AD ⊥ BC. If ar (ΔABC) = 40 cm2, ar (ΔACD) = 10 cm2 and AC = 9 cm, then the length of BC is |
| A. | 2 cm |
| B. | 8 cm |
| C. | cm |
| D. | cm |
| Answer» C. cm | |
| 124. |
If the incentre of an equilateral triangle lies inside the triangle and its radius in 3 cm, then the side of the equilateral triangle is |
| A. | $$\sqrt 3 $$ cm |
| B. | $$\sqrt 3 $$ cm |
| C. | $$\sqrt 3 $$ cm |
| D. | cm |
| Answer» C. $$\sqrt 3 $$ cm | |
| 125. |
The circumcentre of a triangle ABC is O. If ∠BAC = 85° and ∠BCA = 75°, then the value of ∠OAC is |
| A. | 0° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» D. 0° | |
| 126. |
If the length of the three sides of a triangle are 6 cm, 8 cm and 10 cm, then the length of the median to its greatest side is - |
| A. | cm |
| B. | cm |
| C. | cm |
| D. | .8 cm |
| Answer» D. .8 cm | |
| 127. |
I is the incentre of ΔABC, ∠ABC = 60° and ∠ACB = 50°, Then ∠BIC is |
| A. | 5° |
| B. | 25° |
| C. | 0° |
| D. | 5° |
| Answer» C. 0° | |
| 128. |
If the circumradius of an equilateral triangle be 10 cm, then the measure of its in-radius is |
| A. | cm |
| B. | 0 cm |
| C. | 0 cm |
| D. | 5 cm |
| Answer» B. 0 cm | |
| 129. |
In ΔABC, AD is the internal bisector of ∠A, meeting the side BC at D. If BD = 5 cm, BC = 7.5 cm, then AB : AC is |
| A. | : 1 |
| B. | : 2 |
| C. | : 5 |
| D. | : 5 |
| Answer» B. : 2 | |
| 130. |
The sides of a triangle are in the ratio 3 : 4 : 6. The triangle is: |
| A. | cute-angled |
| B. | ight-angled |
| C. | btuse-angled |
| D. | ither acute-angled or right-angled |
| Answer» D. ither acute-angled or right-angled | |
| 131. |
The in-radius of an equilateral triangle is of length 3 cm. Then the length of each of its medians is |
| A. | 2 cm |
| B. | $\frac{9}{2}$$ cm |
| C. | cm |
| D. | cm |
| Answer» E. | |
| 132. |
A triangle cannot be drawn with the following three sides |
| A. | m, 3m, 4m |
| B. | m, 4m, 8m |
| C. | m, 6m, 9m |
| D. | m, 7m, 10m |
| Answer» C. m, 6m, 9m | |
| 133. |
In the adjoining figure AB, EF and CD are parallel lines. Given that GE = 5 cm, GC = 10 cm and DC = 18 cm, then EF is equal to: |
| A. | 1 cm |
| B. | cm |
| C. | cm |
| D. | cm |
| Answer» E. | |
| 134. |
In ΔABC, AD ⊥ BC, then |
| A. | B2 - BD2 = AC2 - CD2 |
| B. | B2 + BD2 = AC2 - CD2 |
| C. | B2 - BD2 = AC2 + CD2 |
| D. | B2 - AC2 = BD2 + CD2 |
| Answer» B. B2 + BD2 = AC2 - CD2 | |
| 135. |
Consider the following statements :I. Three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent.II. If three angles of a triangle are respectively equal to three angles of another triangle, then the two triangles are congruent.Of these statements : |
| A. | and II both are true |
| B. | is true and II is false |
| C. | is false and II is true |
| D. | one of these |
| Answer» C. is false and II is true | |
| 136. |
BL and CM are medians of ΔABC right-angled at A and BC = 5 cm. If BL = $$\frac{{3\sqrt 5 }}{2}$$ cm, then the length of CM is |
| A. | $2\sqrt 5 $$cm |
| B. | $5\sqrt 2 $$cm |
| C. | $10\sqrt 2 $$cm |
| D. | $4\sqrt 5 $$cm |
| Answer» B. $5\sqrt 2 $$cm | |
| 137. |
In a ΔABC ∠A : ∠B : ∠C = 2 : 3 : 4. A line CD drawn || to AB, then the ∠ACD is : |
| A. | 0° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» B. 0° | |
| 138. |
In a right-angled triangle, the product of two sides is equal to half of the square of the third side i.e., hypotenuse. One of the acute angle must be |
| A. | 0° |
| B. | 0° |
| C. | 5° |
| D. | 5° |
| Answer» D. 5° | |
| 139. |
In ΔABC, ∠B = 60° and ∠C = 40°. If AD and AE be respectively the internal bisector of ∠A and perpendicular on BC, then the measure of ∠DAE is |
| A. | ° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» C. 0° | |
| 140. |
The sum of three altitudes of a triangle is |
| A. | qual to the sum of three sides |
| B. | ess than the sum of sides |
| C. | reater than the sum of sides |
| D. | wice the sum of sides |
| Answer» C. reater than the sum of sides | |
| 141. |
Two right angled triangles are congruent if :I. The hypotenuse of one triangle is equal to the hypotenuse of the other.II. A side for one triangle is equal to the corresponding side of the other.III. Sides of the triangles are equal.IV. An angle of the triangle are equal.Of these statements, the correct ones are combination of: |
| A. | and II |
| B. | I and III |
| C. | and III |
| D. | V only |
| Answer» B. I and III | |
| 142. |
In ΔPQR, PS is the bisector of ∠P and PT ⊥ OR, then ∠TPS is equal to: |
| A. | Q + ∠R |
| B. | 0° + $$\frac{1}{2}$$ ∠Q |
| C. | 0° - $$\frac{1}{2}$$ ∠R |
| D. | $\frac{1}{2}$$ (∠Q - ∠R) |
| Answer» E. | |
| 143. |
In a triangle ABC, the internal bisector of the angle A meets BC at D. If AB = 4, AC = 3 and ∠A = 60°, then length of AD is : |
| A. | $2\sqrt 3 $$ |
| B. | $\frac{{12\sqrt 3 }}{7}$$ |
| C. | $\frac{{15\sqrt 3 }}{8}$$ |
| D. | $\frac{{6\sqrt 3 }}{7}$$ |
| E. | one of these |
| Answer» C. $\frac{{15\sqrt 3 }}{8}$$ | |
| 144. |
Consider the triangle shown in the figure where BC = 12 cm, Db = 9 cm, CD = 6 cm andWhat is the ratio of the perimeter of the triangle ADC to that of the triangle BDC ? |
| A. | : 9 |
| B. | : 9 |
| C. | :9 |
| D. | : 9 |
| E. | one of these |
| Answer» B. : 9 | |
| 145. |
The side QR of an equilateral triangle PQR is produced to the point S in such a way that QR = RS and P is joined to S. Then the measure of ∠PSR is |
| A. | 0° |
| B. | 5° |
| C. | 0° |
| D. | 5° |
| Answer» B. 5° | |
| 146. |
AD is the median of a triangle ABC and O is the centroid such that AO = 10 cm. The length of OD (in cm) is |
| A. | cm |
| B. | cm |
| C. | cm |
| D. | cm |
| Answer» C. cm | |
| 147. |
ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect at D. If ∠BDC = 50°, then ∠A is |
| A. | 00° |
| B. | 0° |
| C. | 20° |
| D. | 0° |
| Answer» B. 0° | |
| 148. |
ΔABC is an isosceles triangle and $$\overline {AB} $$= $$\overline {AC} $$= 2a unit, $$\overline {BC} $$= a unit. Draw $$\overline {AD} $$ ⊥ $$\overline {BC} $$ , and find the length of $$\overline {AD} $$ |
| A. | $\sqrt {15} $$ a unit |
| B. | $\frac{{\sqrt {15} }}{2}$$ a unit |
| C. | $\sqrt {17} $$ a unit |
| D. | $\frac{{\sqrt {17} }}{2}$$ a unit |
| Answer» C. $\sqrt {17} $$ a unit | |
| 149. |
If ABC is an equilateral triangle and D is a point of BC such that AD ⊥ BC, then |
| A. | B : BD = 1 : 1 |
| B. | B : BD = 1 : 2 |
| C. | B : BD = 2 : 1 |
| D. | B : BD = 3 : 2 |
| Answer» D. B : BD = 3 : 2 | |
| 150. |
ABC is an isosceles triangle with AB = AC. The side BA is produced to D such that AB = AD. If ∠ABC = 30°, then ∠BCD is equal to |
| A. | 5° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» C. 0° | |