Explore topic-wise MCQs in Arithmetic Ability.

This section includes 924 Mcqs, each offering curated multiple-choice questions to sharpen your Arithmetic Ability knowledge and support exam preparation. Choose a topic below to get started.

551.

One side of a rectangle is 12 m and its diagonal is 13 m. Find its area.

A. 60 sq.m
B. 55 sq.m
C. 50 sq.m
D. 45 sq.m
Answer» B. 55 sq.m
Discussion
552.

Line segment AB is parallel to line segment CD. AD intersects BC in E. If lengths of AE, BC and ED are 12 cm, 12 cm and 18 cm respectively, what is the length of EC?

A. 4.8 cm
B. 9.3 cm
C. 8.1 cm
D. 7.2 cm
Answer» E.
Discussion
553.

One of the roots of the equation x2 - 6x + k = 0 is x = 2. The other root is_x005F_x000D_

A. x = -1
B. x = 4
C. x = -4
D. x = 1
Answer» C. x = -4
Discussion
554.

One of the internal angle of a rhombus is 60° and length of its shorter diagonal is 8 cm. What is the area of the rhombus?

A. 64√3 sq cm
B. 32√2 sq cm
C. 64√2 sq cm
D. 32√3 sq cm
Answer» E.
Discussion
555.

One angle of a triangle is 55 deg. If the other two angles are in the ratio 9:16, find the angles?

A. 65 and 115
B. 90 and 160
C. 55 and 165
D. 45 and 80
Answer» E.
Discussion
556.

Let O be the orthocentre of the triangle ABC. If ∠BOC = 150°, Then ∠BAC is

A. 30°
B. 60°
C. 90°
D. 120°
Answer» B. 60°
Discussion
557.

Length and breadth of a rectangle are 8 cm and 6 cm respectively. The rectangle is cut on its four vertices such that the resulting figure is a regular octagon. What is the side (in cm) of the octagon?

A. 3(√11) – 7
B. 5(√13) – 8
C. 4(√7) – 11
D. 6(√11) – 9
Answer» B. 5(√13) – 8
Discussion
558.

Length and breadth of a rectangle are increased by 40% and 70% respectively. What will be the percentage increase in the area of rectangle?

A. 118
B. 110
C. 138
D. 128
Answer» D. 128
Discussion
559.

In which quadrant, will the point (4, -2) be located?

A. I
B. II
C. III
D. IV
Answer» E.
Discussion
560.

In which of the following quadrilaterals both pairs of opposite sides are parallel?

A. Rhombus
B. Cyclic quadrilateral
C. Kite
D. Isosceles trapezium
Answer» B. Cyclic quadrilateral
Discussion
561.

In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases.

A. 0.54791666666667
B. 0.67291666666667
C. 0.63125
D. 0.58958333333333
Answer» C. 0.63125
Discussion
562.

In triangle XYZ, G is the centroid. If XY = 11 cm, YZ = 14 cm and XZ = 7 cm, then what is the value (in cm) of GM ?_x005F_x000D_ _x005F_x000D_

A. 6
B. 4
C. 2
D. 3
Answer» D. 3
Discussion
563.

In triangle PQR, C is the centroid. PQ = 30 cm, QR = 36 cm and PR = 50 cm. If D is the midpoint of QR, then what is the length (in cm) of CD?

A. (4√86)/3
B. (2√86)/3
C. (5√86)/3
D. (5√86)/2
Answer» B. (2√86)/3
Discussion
564.

In triangle DEF measure of angle E is 90 deg. If cotD = 5/12 and DE = 1 cm, then what is the length (in cm) of side EF?_x005F_x000D_  _x005F_x000D_

A. 2.4_x005F_x000D_
B. 2.6_x005F_x000D_
C. 1.5_x005F_x000D_
D. 2
Answer» B. 2.6_x005F_x000D_
Discussion
565.

In triangle ABC, AB = 8 cm, angle A is bisected internally to intersect BC at D. BD = 6 cm and DC = 7.5 cm. What is the length of CA?

A. 12 cm
B. 10 cm
C. 12.5 cm
D. 10.5 cm
Answer» C. 12.5 cm
Discussion
566.

In triangle ABC, AB = 10 cm. Angle A is bisected internally to intersect BC at D. BD = 6 cm and DC = 7.5 cm. What is the length of CA?

A. 12.5 cm
B. 10.5 cm
C. 12 cm
D. 10 cm
Answer» B. 10.5 cm
Discussion
567.

In the given figure, two squares of sides 8 cm and 20 cm are given. What is the area (in sq.cm) of the shaded part?_x005F_x000D_

A. 120/7
B. 160/7
C. 180/7
D. 240/13
Answer» C. 180/7
Discussion
568.

In the given figure, two identical circles of radius 4 cm touch each other. A and B are the centres of the two circles. If RQ is a tangent to the circle, then what is the length (in cm) of RQ?_x005F_x000D_

A. 3√3
B. 2√6
C. 4√2
D. 6√2
Answer» D. 6√2
Discussion
569.

In the given figure, PQRSTU is a regular hexagon of side 12 cm. What is the area (in sq.cm) of triangle SQU?_x005F_x000D_

A. 162√3
B. 216√3
C. 108√3
D. 54√3
Answer» D. 54√3
Discussion
570.

In the given figure, the angle bisectors of B and C of an isosceles triangle intersect at point O. Find the angle BOC (in degree), when ∠ABC = ∠ACB = 75°._x005F_x000D_

A. 105
B. 147.5
C. 160
D. 170
Answer» B. 147.5
Discussion
571.

In the given figure, PQRS is a square of side 8 cm. PQO = 60 deg. What is the area (in sq.cm) of the triangle POQ?_x005F_x000D_

A. 32√3
B. 24[(√3) – 1]
C. 48[(√3) – 1]
D. 16[3 – (√3)]
Answer» E.
Discussion
572.

In the given figure, ,PQRS is a square whose side is 8 cm. PQS and QPR are two quadrants. A circle isplaced touching both the quadrants and the square as shown in the figure. What is the area (in sq.cm) of the circle?_x005F_x000D_

A. 13/17
B. 41944
C. 19/31
D. 15/19
Answer» C. 19/31
Discussion
573.

In the given figure, PQRS is a square inscribed in a circle of radius 4 cm. PQ is produced till point Y. From Y a tangent is drawn to the circle at point R. What is the length (in cm) of SY ? _x005F_x000D_

A. 4√10
B. 2√10
C. 6√10
D. 3√5
Answer» B. 2√10
Discussion
574.

In the given figure, PQR is a triangle and quadrilateral ABCD is inscribed in it. QD = 2 cm, QC = 5 cm, CR = 3 cm, BR = 4 cm, PB = 6 cm, PA = 5 cm and AD = 3 cm. What is the area in sq.cm of the quadrilateral ABCD?_x005F_x000D_

A. (23√21)/4
B. (15√21)/4
C. (17√21)/5
D. (23√21)/5
Answer» D. (23√21)/5
Discussion
575.

In the given figure, PQRS is a rectangle and a semicircle with SR as diameter is drawn. A circle is drawn as shown in the figure. If QR = 7 cm, then what is the radius (in cm) of the small circle ?_x005F_x000D_  _x005F_x000D_

A. 21 + 14√2
B. 21 – 14√2
C. Both 21 + 14√2 and 21 – 14√2
D. None of these
Answer» C. Both 21 + 14√2 and 21 – 14√2
Discussion
576.

In the given figure, PQRS is a quadrilateral. If QR = 18 cmand PS = 9 cm,then what is the area (in sq. cm) of quadrilateral PQRS?_x005F_x000D_

A. (64√3)/3
B. (177√3)/2
C. (135√3)/2
D. (98√3)/3
Answer» D. (98√3)/3
Discussion
577.

In the given figure, PQR is a quadrant whose radius is 7 cm. A circle is inscribed in the quadrant as shown in the figure. What is the area (in sq.cm) of the circle?_x005F_x000D_  _x005F_x000D_

A. 385 – 221√2
B. 308 – 154√2
C. 154 – 77√2
D. 462 – 308√2
Answer» E.
Discussion
578.

In the given figure, PQ is a diameter of the semicircle PABQ and O is its center. AOB = 64 deg. BP cuts AQ at X. What is the value (in deg) of AXP?_x005F_x000D_

A. 36
B. 32
C. 58
D. 54
Answer» D. 54
Discussion
579.

In the given figure, OX, OY and OZ are perpendicular bisectors of the three sides of the triangle. If QPR = 65 deg and PQR = 60 deg, then what is the value (in deg) of QOR + POR ?_x005F_x000D_

A. 250
B. 180
C. 210
D. 125
Answer» B. 180
Discussion
580.

In the given figure, O is the centre of the circle and QOR = 50 deg, then what is the value of RPQ (in deg) ?_x005F_x000D_

A. 15
B. 25
C. 20
D. 30
Answer» C. 20
Discussion
581.

In the given figure, O is centere of the circle. Circle has 3 tangents. If angle QPR = 45 deg, then what is the value (in deg) of angle QOR ?_x005F_x000D_

A. 67.5
B. 72
C. 78.5
D. 65
Answer» B. 72
Discussion
582.

In the given figure, in a right angle triangle ABC, AB = 12 cm and AC = 15 cm. A square is inscribed in the triangle. One of the vertices of square coincides with the vertex of triangle. What is the maximum possible area (in cm.sq) of the square?_x005F_x000D_

A. 1296/49
B. 25
C. 1225/36
D. 1225/64
Answer» B. 25
Discussion
583.

In the given figure, if  QR/XY = 14/9 and PY = 18 cm, then what is the value (in cm) of PQ?_x005F_x000D_ _x005F_x000D_  _x005F_x000D_

A. 28
B. 18
C. 21
D. 24
Answer» B. 18
Discussion
584.

In the given figure, four identical semicircles are drawn in a quadrant. XA = 7 cm. What is the area (in sq.cm) of shaded region ?_x005F_x000D_  _x005F_x000D_

A. 70
B. 140
C. 77
D. 84
Answer» E.
Discussion
585.

In the given figure, ABCDEF is a regular hexagon of side 12 cm. P, Q and R are the mid points of the sides AB, CD and EF respectively. What is the area (in sq.cm) of triangle PQR?_x005F_x000D_

A. 27√6
B. 81√3
C. 54√3
D. 54√6
Answer» C. 54√3
Discussion
586.

In the given figure, ABCDEF is a regular hexagon whose side is 6 cm. APF, QAB, DCR and DES are equilateral triangles. What is the area (in sq.cm) of the shaded region?_x005F_x000D_

A. 24√3
B. 18√3
C. 72√3
D. 36√3
Answer» D. 36√3
Discussion
587.

In the given figure, ABCD is a square whose side is 4 cm. P is a point on the side AD. What is the minimum value (in cm) of BP + CP ?_x005F_x000D_

A. 4√5
B. 4√4
C. 6√3
D. 4√6
Answer» B. 4√4
Discussion
588.

In the given figure, ABCD is a square of side 14 cm. E and F are mid points of sides AB and DC respectively. EPF is a semicircle whose diameter is EF. LMNO is a square . What is the area (in sq.cm) of the shaded region?_x005F_x000D_  _x005F_x000D_

A. 108.5
B. 94.5
C. 70
D. 120
Answer» C. 70
Discussion
589.

In the given figure, AB = 30 cm and CD = 24 cm. What is the value (in cm) of MN?_x005F_x000D_

A. 18
B. 9
C. 12
D. 15
Answer» B. 9
Discussion
590.

In the given figure, ABCD is a square. EFGH is a square formed by joining mid points of sides of ABCD. LMNO is a square formed by joining mid points of sides of EFGH. A circle is inscribed inside EFGH. If area of circle is 38.5 sq.cm, the what is the area (in sq.cm) of square ABCD?_x005F_x000D_

A. 98
B. 196
C. 122.5
D. 171.5
Answer» C. 122.5
Discussion
591.

In the given figure, a circle inscribed in  triangle PQR touches its sides PQ, QR and RP at points S, T and U, respectively. If PQ = 15 cm, QR=10 cm, and RP = 12 cm, then find the lengths of PS, QT and RU?_x005F_x000D_  _x005F_x000D_

A. PS = 8.5 cm, QT = 3.5 cm and RU =6.5 cm_x005F_x000D_
B. PS = 8.5 cm, QT = 6.5 cm and RU = 3.5 cm_x005F_x000D_
C. PS = 6.5 cm, QT = 8.5 cm and RU =3.5 cm_x005F_x000D_
D. PS = 3.5 cm, QT = 6.5 cm and RU = 8.5 cm
Answer» C. PS = 6.5 cm, QT = 8.5 cm and RU =3.5 cm_x005F_x000D_
Discussion
592.

In the given figure, 3 semicircles are drawn on three sides of triangle ABC. Ab = 21 cm, BC = 28 cm and AC = 35 cm. What is the area (in sq.cm) of the shaded part?_x005F_x000D_

A. 588
B. 324
C. 294
D. 286
Answer» D. 286
Discussion
593.

In the figure,  PA is a tangent from an external point P to the circle with centre O. If  Angle POB = 110 Deg, then the measure of Angle APO  is:_x005F_x000D_

A. 25 deg
B. 40deg
C. 20deg
D. 30deg
Answer» D. 30deg
Discussion
594.

In the circle below, chord is extended to meet the tangent at D. If = 24 cm and = 9 cm, what is the length of BD ?_x005F_x000D_  _x005F_x000D_ _x005F_x000D_  _x005F_x000D_

A. 46cm
B. 3 cm
C. 5 cm
D. 4 cm
Answer» C. 5 cm
Discussion
595.

In the figure given above, AF is a tangent to the circle at E, = 80° and . What is the measure of ∠BEA ?_x005F_x000D_  _x005F_x000D_ _x005F_x000D_

A. 30°
B. 45°
C. 40°
D. 35°
Answer» D. 35°
Discussion
596.

In the figure, B and C are the centres of the two circles. ADE is the common tangent to the two circles. If the ratio of the radius of both the circles is 3:5 and AC= 40, then what is the value of DE?_x005F_x000D_

A. 3√15
B. 5√15
C. 6√15
D. 4√15
Answer» E.
Discussion
597.

In the circle below, chord AB is extended to meet the tangent at DE. If = 9 cm and = 3 cm, find the length of DE._x005F_x000D_  _x005F_x000D_  _x005F_x000D_

A. 5 cm
B. 4 cm
C. 27 cm
D. 6 cm
Answer» E.
Discussion
598.

In the circle above, chord AB is extended to meet the tangent DE at D. If AB = 12 cm and DE = 8 cm, find the length of BD._x005F_x000D_

A. 4 cm
B. 5 cm
C. 6 cm
D. 7 cm
Answer» B. 5 cm
Discussion
599.

In figure 'O' is the centre of a circle. The area of sector OAPB is 5/18. of the area of the circle find 'x'._x005F_x000D_  _x005F_x000D_ _x005F_x000D_

A. 120 deg
B. 100 deg
C. 115 deg
D. 125 deg
Answer» C. 115 deg
Discussion
600.

In measuring the sides of a rectangle, one side is taken 5% in excess and the other 4% in deficit. Find the error percent in the area, calculate from the those measurements.

A. 0.007
B. 0.008
C. 0.009
D. 0.003
Answer» C. 0.009
Discussion