objective Ques (45 results)
SSC CGL 20221)In the given figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 54°, then ∠OBA = ________.
27°
SSC CGL 20222)In the figure BCDE is a square and ABC is an equilateral triangle then ∠ADC is:
15°
SSC CGL 20223)A triangle and a parallelogram have the same base 28 cm and the same area. If the height of the parallelogram is 12 cm, then find the length of the altitude of the triangle.
24 cm
SSC CGL 20224)In the given figure, ∠ABC = 81° and ∠ACB = 9°. What is the value of ∠BDC?
90°
SSC CGL 20225)In the given figure, if KI = IT and EK = ET, then ∠TEI = .
105°
6)The value of 80° in radian is
\(( {4 \pi \over 9})^c\)
SSC CGL 20227)PQRS is a cyclic quadrilateral and PQ is a diameter of the circle. If ∠RPQ = 23°, then what is the measure of ∠PSR?
113°
SSC CGL 20228)A circle is circumscribed on a quadrilateral ABCD. If ∠DAB = 100°, ∠ADB = 35° and ∠CDB = 40°, then find the measure of ∠DBC.
60°
SSC CGL 20229)In a quadrilateral ABCD, the bisectors of ∠C and ∠D meet at point E. If ∠CED = 57° and ∠A = 47°, then the measure of ∠B is:
67°
SSC CGL 202210)A cyclic quadrilateral ABCD is drawn in a circle with center O. A and C are joined O. If ∠ABC = 2p and ∠ADC = 3p, what is the measure (in degrees) of the ∠AOC reflex?
216
SSC CPO 202011)PQRS is a cyclic quadrilateral. If ∠P is 4 times ∠R, and ∠S is 3 times ∠Q, then the average of ∠Q and ∠R is:
40.5°
SSC CPO 202012)ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 118°. What is the measure of ∠BAC?
28°
SSC CPO 202013)ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and∠ADC = 148°. What is the measure of the∠BAC?
58°
SSC CPO 202014)The sides of a triangle are 24 cm, 26 cm and 10 cm. At each of its vertices, circles of radius 4.2 cm are drawn. What is the area (in sqcm ) of the triangle, excluding the portion covered by the section of the circles?
92.28
SSC CHSL 202115)In a trapezium ABCD, DC || AB, AB = 16 cm and DC = 11.2 cm. What is the length (in cm) of the line segment joining the mid points of its diagonals?
2.4
SSC CHSL 202116)The sum of the square of the sides of a rhombus is 1600 cm2. What is the side of the rhombus?
20 cm
SSC CHSL 202117)The in-radius and circumradius of a right-angled triangle is 3 cm and 12.5 cm, respectively. The area of the triangle is:
84 cm2
SSC CHSL 202118)In a circle with centre O, chord AB and diameter CD intersect each other at point E, inside the circle. If ∠AOD = 42° and ∠BOC = 104°, then what is the measure (in degrees) of ∠AED?
73
SSC CHSL 202119)Chords AB and CD of a circle intersect externally at P. If CD = 11.6 cm, PD = 6.4 cm and PB = 7.2 cm, then AB (in cm) is equal to:
8.8
SSC CHSL 202120)BD and CE are the medians of Δ ABC, right angled at A. If \(CE =\frac{{5\sqrt {13} }}{2}\) cm, BC = 10 cm, then the length of BD is:
\(\frac{5}{2}\sqrt {7}\) cm
SSC CHSL 202121)In a circle with centre O, PA and PB are the tangents at A and B, respectively, from an external point P. If ∠APB = 42° then what will be the measure of ∠AOB ?
138°
SSC CHSL 202122)A rhombus of side 28 cm has one angle of 60°. What is the length of the larger diagonal?
28√3 cm
SSC CHSL 202123)Two chords AB and CD of a circle intersect at O. If CO = 4 cm, OD = 3.75 cm, and AB = 8 cm, then what is the length (in cm) of the smaller among AO and OB?
3
SSC CHSL 202124)In triangle ABC, if BD and CD bisect ∠B and ∠C , respectively, and ∠BDC = 135°, then find the measure of ∠BAC .
90°
SSC CHSL 202125)PQRS is a cyclic quadrilateral with QR as the diameter of the circle. If ∠SQR = 24°, then what will be the measure of ∠QPS?
114°
SSC CHSL 202126)ABCD is a cyclic quadrilateral whose diagonals intersect at P. If ∠DBC = 72° and ∠BAC = 42°, then the measure of ∠BCD (in degrees) is:
66
SSC CHSL 202127)PQRS is a cyclic quadrilateral. If ∠P is four time ∠R and ∠S is three times ∠Q, then sum of the measures of ∠S and ∠R will be:
171°
SSC CHSL 202128)A circle touches all four sides of a quadrilateral PQRS. If PQ = 11 cm. QR = 12 cm and PS = 8 cm. then what is the length of RS ?
9 cm
SSC CHSL 202129)ABCD is cyclic quadrilateral with AB as a diameter of the circle. If ∠ADC = 118o,, then the measure (in degrees) of ∠BAC is:
28
SSC CGL 202030)Sides AB and DC of cyclic quadrilateral ABCD are produced to meet at E, and sides AD and BC are produced to meet at F. If \(\angle ADC = 75^\circ\) and \(\angle BEC =52^\circ\), then the difference between \(\angle BAD\) and \(\angle AFB \) is:
\(31^0\)
ABCD is a cyclic quadrilateral. \(\angle ADC = 75^\circ\) ;
∴\(\angle ABC + ∠ADC=180^0\) ;
⇒ \(∠ABC = 180^0 − 75^0=105^0\) ;
⇒ \(∠CBE = 180^0 − 105^0=75^0\) ;
\(\therefore ∠BCE = 180-(52+75)=53^0\);
\(\angle BCD=180-53=127^0\) ;
\(\because \angle BCD+\angle BAD=180^0\) ; ⇒ \(\angle BAD = 53^0\);
\(\angle AFB = 180-(105+53)=22^0\) ;
Required difference = \(53^0-22^0=31^0\)
SSC CGL 202031)ABCD is a cyclic quadrilateral which sides AD and BC are produced to meet at P, and sides DC and AB meet at Q when produced. If \(\angle A = 60^\circ\) \( and\space \angle ABC = 72^\circ,\)\( then\space \angle DPC - \angle BQC = ?\)
\(36^0\)
Since ABCD is a cyclic quadrilateral. \(\angle A+\angle C = 180 \) & \(\angle B +\angle D = 180^0\) ;
\(\therefore \angle C = 120^0\) & \(\angle D = 108^0\) ;
In \(\triangle PDC\) ⇒ \(\angle PDC = 180-108=72^0\) & \(\angle PCD = 180-120=60^0\) ;
\(\therefore \angle P = 180-72-60=48^0\) ;
Similarly, In \(\triangle BCQ\) ⇒ \(\angle Q = 12^0\) ; Now \(\angle P-\angle Q= 48^0-12^0=36^0\)
SSC CGL 201632)In a trapezium ABCD, AB || CD, AB < CD, CD = 6 cm and distance between the parallel sides is 4 cm. If the area of ABCD is 16 cm2, then AB is
2 cm
SSC CGL 202033)The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Its area is :
\(96\space cm^2\)
Area of rhombus = \(1\over2\) x first diagonal x second diagonal = \({1\over2}\times16\times12=96\space cm^2\)
SSC CGL 202034)In the figure. if \(\angle A = 100^0\) then \(\angle C = ?\)
\(80^0\)
ABCD is a cyclic quadrilateral. \(\angle A = 100^0\); \(\angle A + \angle C=180^0\); ⇒ \(\angle C = 180^0-100^0=80^0\)
SSC CGL 202035)In quadrilateral PQRS, \(RM\perp QS\), \(PN\perp QS\) and QS = 6 cm. If RM = 3 cm and PN = 2 cm, then the area of PQRS is
\(15cm^2\)
Area of quadrilateral PQRS = Area of \(\triangle PQS\) + Area of \(\triangle QRS\) =\({1\over2}\times QS\times PN + {1\over2}\times QS\times RM={1\over2}\times QS(PN + RM)={1\over2}\times6(2+3)=15 cm^2\)
SSC CGL 201936)A circle is inscribed in a quadrilateral ABCD touching AB, BC, CD and AD at the points P, Q, R and S, respectively, and \(\angle B=90^0\). If AD = 24 cm, AB = 27 cm and DR = 6 cm, then what is the circumference of the circle?
\(18\pi cm.\)
SSC CGL 201937)In a quadrilateral ABCD, the bisectors of \(\angle C\) and \(\angle D\) meet at E. If \(\angle CED=56^0\) and \(\angle A = 49^0\), then the measure of \(\angle B\) is:
\(63^0\)
SSC CGL 201938)The sum of the interior angles of a regular polygon is \(1260^0\). What is the difference between an exterior angle and an interior angle of the polygon?
\(100^0\)
SSC CGL 201939)If the measure of each exterior angle of a regular polygon is \((51\frac{3}{7})^0\), then the ratio of the number of its diagonals to the number of its sides is:
2 : 1
As we know,
Number of sides in the polygon = 360/exterior angle = \({360 \over 51\frac{3}{7}^0} = 7\)
Number of diagonal = [n (n – 3)]/2 = [7 (7 – 3)]/2 = [7 × 4]/2 =14
Required ratio = 14 : 7 = 2 : 1
SSC CGL 201940)In quadrilateral ABCD, \(\angle C=72^0\) and \(\angle D = 28^0\). The bisectors of \(\angle A\) and \(\angle B\) meet at O. What is the measure of \(\angle AOB\)?
\(50^0\)
SSC CGL 201941)In a circle with centre O, ABCD is a cyclic quadrilateral and AC is the diameter. Chords AB and CD are produced to meet at E. If \(\angle CAE = 34^0\) and \(\angle E = 30^0\), then \(\angle CBD\) is equal to :
\(26^0\)
By the exterior angle property, \(\angle DCA=30 +34=64\); \(\angle DCA=180-90-64=26\); \(\angle DAC=\angle CBD\); \(\angle CBD=26^0\)
SSC CGL 201942)In quadrilateral ABCD, the bisectors of\( \angle A \)and \(\angle B\) meet at O and \(\angle AOB = 64^\circ\).\( \angle C + \angle D\) is equal to:
\(128^0\)
In \(\triangle AOB\),
\(\angle OAB + \angle OBA + \angle O = 180\);
\(\angle OAB + \angle OBA = 180 - 64 = 116^0\);
\(\angle OAB \)and\( \angle OBA \) is the bisector of\( \angle A and \angle B\).
So,
\(\angle A + \angle B = 2 \times 116 = 232^0;\)
\(\angle A + \angle B + \angle C + \angle D = 360;\)
\(\angle C + \angle D = 360 - 232 = 128^0\)
SSC CGL 201943)If each interior angle of a regular polygon is \( \left(128\frac{4}{7}\right)^\circ\) , then what is the sum of the number of its diagonals and the number of its sides?
21
Interior angle = \(180 - \frac{360}{n}\);
\(128\frac{4}{7}^\circ = 180 - \frac{360}{n}\);
\(\frac{900}{7}^\circ = 180 - \frac{360}{n}\);
\( \frac{360}{n} = 180 - \frac{900}{7}\);
\( \frac{360}{n} = \frac{360}{7} \); Side(n) = 7;
Number of diagonals =\( \frac{n(n - 3)}{2} = \frac{7(7 - 3)}{2} = \frac{28}{2} = 14 \); Sum of the number of its diagonals and the number of its sides = 7 + 14 = 21
SSC CGL 201944)PQRS is a cyclic quadrilateral in which PQ = 14.4 cm. QR = 12.8 cm and SR = 9.6 cm. If PR bisects QS, what is the length of PS?
19.2 cm
By the property,
\(PQ \times QR = RS \times PS\);
\(14.4 \times 12.8 = 9.6 \times x;\)
9.6x = 184.32;
x = 19.2 cm
SSC CGL 202045)Triangle PDC is drawn inside the square ABCD of side 24cm where P lies on AB. What is the area of the triangle ?
288\(cm^2\)
since ABCD is a square, Area of triangle PDC = \( {1 \over 2}\times CD \times PE\) = \( {1 \over 2}\times 24 \times 24 = 288 cm^2\)
