1274 + Mcqs in Analytical Geometry in SRMJEEE Page 21 McqOptions

1001.	In ΔABC, ∠A = 50°. Its sides AB and AC are produced to the point D and E. If the bisectors of ∠CBD and ∠BCE meet at the point O, then ∠BOC is equal to∶
A.	75°
B.	65°
C.	55°
D.	40°
Answer» C. 55°

Discussion

1002.	Consider the following statements:(1) The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.(2) The point of intersection of the perpendicular drawn from the vertices to the opposite side of a triangle may lie on two sides.Which of the above statements is/are correct?
A.	1 only
B.	2 only
C.	Both 1 and 2
D.	Neither 1 and 2
Answer» D. Neither 1 and 2

Discussion

1003.	In the figure given below, M is the mid-point of AB and ∠DAB = ∠CBA and ∠AMC = ∠BMD. Then the triangle ADM is congruent to the triangle BCM by
A.	SAS rule
B.	SSS rule
C.	ASA rule
D.	AAA rule
Answer» D. AAA rule

Discussion

1004.	In the given figure, PQR is a triangle in which, PQ = 24 cm, PR = 12 cm and altitude PS = 8 cm. If PT is the diameter of the circumcircle, then what is the length (in cm) of circum-radius?
A.	15
B.	18
C.	20
D.	21
Answer» C. 20

Discussion

1005.	Given that ΔDEF ~ ΔABC. If the area of ΔABC is 9 cm2 and area of ΔDEF is 12cm2 , BC = 2.1 cm, then the length of EF is:
A.	\(\frac{8\sqrt3}{5}cm\)
B.	\(\frac{3\sqrt7}{5}cm\)
C.	\(\frac{4\sqrt7}{5}cm\)
D.	\(\frac{7\sqrt3}{5}cm\)
Answer» E.

Discussion

1006.	In a trapezium, the lengths of its parallel sides are a and b. The length of the line joining the midpoints of its non - parallel sides is
A.	\(\frac{a-b}{2}\)
B.	\(\frac{a+b}{2}\)
C.	\(\frac{ab}{2}\)
D.	\(\frac{ab}{a+b}\)
Answer» C. \(\frac{ab}{2}\)

Discussion

1007.	In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is
A.	\({\left( {\frac{\pi }{4}} \right)^{\frac{1}{2}}}\)
B.	\({\left( {\frac{\pi }{3\sqrt 3}} \right)^{\frac{1}{2}}}\)
C.	\({\left( {\frac{\pi }{6}} \right)^{\frac{1}{2}}}\)
D.	\({\left( {\frac{\pi }{4\sqrt3}} \right)^{\frac{1}{2}}}\)
Answer» C. \({\left( {\frac{\pi }{6}} \right)^{\frac{1}{2}}}\)

Discussion

1008.	If the ratio of the angles of a triangle is 3 : 5 : 7, find the value of the largest angle.A. 36°B. 60°C. 84°D. 15°
A.	B
B.	A
C.	C
D.	D
Answer» D. D

Discussion

1009.	ABC is a right angled triangle, right angled at A. A circle is inscribed in it. The lengths of two sides containing the right angle are 48 cm and 14 cm. The radius of the inscribed circle is:
A.	4 cm
B.	8 cm
C.	6 cm
D.	5 cm
Answer» D. 5 cm

Discussion

1010.	If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is:
A.	Isosceles
B.	Equilateral
C.	None of the above
D.	Right angled
Answer» B. Equilateral

Discussion

1011.	In the given figure, chords AB and CD are intersecting each other at point L. Find the length of AB
A.	23.5 cm
B.	21.5 cm
C.	22.5 cm
D.	24.5 cm
Answer» C. 22.5 cm

Discussion

1012.	PAQ is a line parallel to side BC of a triangle ABC. If ∠PAB = 55° and ∠ACB = 60°, then ∠CAB = _______.
A.	70°
B.	40°
C.	45°
D.	65°
Answer» E.

Discussion

1013.	In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is
A.	√13
B.	√ 14
C.	√11
D.	√12
Answer» B. √ 14

Discussion

1014.	PQRS is a trapezium with PQ \|\| RS. U and V are points on non-parallel sides PS and QR respectively such that UV is parallel to PQ, then
A.	SU . RV = UP . VQ
B.	SU . UP = RV . VQ
C.	\(\frac{SU}{RV} = \frac{UP}{VQ}\)
D.	\(\frac{SU}{VQ} = \frac{UP}{RV}\)
Answer» D. \(\frac{SU}{VQ} = \frac{UP}{RV}\)

Discussion

1015.	ΔABC is right angled at B. BD is an altitude. AD = 3 cm and DC = 9 cm. What is the value of AB (in cm)?
A.	6
B.	5
C.	4.5
D.	5.5
Answer» B. 5

Discussion

1016.	In the given figure \(\overline {DE} \parallel \overline {BC}\), AD = 6 cm and DB = 3 cm. What is the value of AM ∶ MN?
A.	2 ∶ 1
B.	3 ∶ 2
C.	3 ∶ 1
D.	2 ∶ 3
Answer» D. 2 ∶ 3

Discussion

1017.	AB is a chord of the circle and its center is “O”. ON is perpendicular to AB. If the length of AB = 20 cm, ON = (2√11) cm, find the radius (in cm) of the circle.
A.	10
B.	12
C.	13
D.	15
Answer» C. 13

Discussion

1018.	In the above figure, O is the centre of the circle. If ∠AOB = 110° and ∠AOC is a right angle, then the measure of ∠BAC is
A.	100°
B.	90°
C.	85°
D.	80°
Answer» C. 85°

Discussion

1019.	In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, is
A.	2.5
B.	3.5
C.	1.5
D.	0.5
Answer» E.

Discussion

1020.	ABCD is a cyclic quadrilateral of which AB is the diameter. Diagonals AC and BD intersect at E. If ∠DBC = 35°, then ∠AED measures
A.	35°
B.	45°
C.	55°
D.	90°
Answer» D. 90°

Discussion

1021.	A is a point at a distance 26 cm from the centre O of a circle of radius 10 cm. AP and AQ are the tangents to the circle at the point of contacts P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, then the perimeter of ΔABC is:
A.	48 cm
B.	46 cm
C.	42 cm
D.	40 cm
Answer» B. 46 cm

Discussion

1022.	If point C is equidistant from A (5, -6) and B (7, 8) co-ordinate of C will be
A.	(6, 3)
B.	(6, 7)
C.	(6, 1)
D.	(4, 3)
Answer» D. (4, 3)

Discussion

1023.	In ΔABC, P is a point on BC such that BP : PC = 4 : 11. If Q is the midpoint of BP, then ar(ΔABQ) : ar(ABC) is equal to:
A.	2 : 15
B.	3 : 13
C.	2 : 13
D.	2 : 11
Answer» B. 3 : 13

Discussion

1024.	Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to
A.	8.8
B.	7.2
C.	7.8
D.	6.6
Answer» B. 7.2

Discussion

1025.	If P is the circum-center in ΔABC, ∠BPC = 30°, then what is the value (in degrees) of ∠BAC?
A.	15
B.	60
C.	75
D.	105
Answer» B. 60

Discussion

1026.	In a circle with centre O, chords AB and CD are parallel chords on the opposite side of O. If AB = 20 cm, CD = 48 cm and the distance between the chords is 34 cm, then the diameter (in cm) of the circle is:
A.	26
B.	39
C.	42
D.	52
Answer» E.

Discussion

1027.	If P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively of a quadrilateral ABCD then the quadrilateral PQRS is a:
A.	Square
B.	Rhombus
C.	Rectangle
D.	Parallelogram
Answer» E.

Discussion

1028.	In a triangle ABC, AB = 12, BC = 18 and AC = 15. The medians AX and BY intersect sides BC and AC at X and Y respectively. If AX and BY intersect each other at O, then what is the value of OX?
A.	4√23
B.	√23
C.	2√2 3
D.	(√23)/(√2)
Answer» E.

Discussion

1029.	In a circle, if a chord AB is nearer to the center O than the chord CD, then:
A.	AB ≥ CD
B.	AC < CD
C.	AB > CD
D.	AB = CD
Answer» D. AB = CD

Discussion

1030.	In the diagram, M is the midpoint of \(\overline {YZ} ,\;\angle XMZ = 32^\circ,\) and ∠XYZ = 16°. The measure of ∠XZY is:
A.	68°
B.	84°
C.	81°
D.	74°
Answer» E.

Discussion

1031.	If triangles ∆A1 B1 C1 and ∆A2 B2 C2 are similar then:
A.	\(\frac{{{A_1}{B_1}}}{{{A_2}{B_2}}} = \frac{{{A_1}{C_1}}}{{{A_2}{C_2}}} = \frac{{{B_1}{C_1}}}{{{B_2}{C_2}}}\)
B.	\(\frac{{{A_1}{B_1}}}{{{A_2}{B_2}}} \ne \frac{{{A_1}{C_1}}}{{{A_2}{C_2}}} = \frac{{{B_1}{C_1}}}{{{B_2}{C_2}}}\)
C.	\(\frac{{{A_1}{B_1}}}{{{A_2}{B_2}}} = \frac{{{A_1}{C_1}}}{{{A_2}{C_2}}} \ne \frac{{{B_1}{C_1}}}{{{B_2}{C_2}}}\)
D.	\(\frac{{{A_1}{B_1}}}{{{A_2}{B_2}}} \ne \frac{{{A_1}{C_1}}}{{{A_2}{C_2}}} \ne \frac{{{B_1}{C_1}}}{{{B_2}{C_2}}}\)
Answer» B. \(\frac{{{A_1}{B_1}}}{{{A_2}{B_2}}} \ne \frac{{{A_1}{C_1}}}{{{A_2}{C_2}}} = \frac{{{B_1}{C_1}}}{{{B_2}{C_2}}}\)

Discussion

1032.	In ΔABC, D and E are points on AB and AC respectively such that DE is parallel to BC. If AD = 2 cm, BD = 3 cm, then \(\frac{{ar\left( {{\rm{\Delta }}ADE} \right)}}{{ar\left( {{\rm{\Delta }}ABC} \right)}}is:\)
A.	4/9
B.	16/81
C.	4/25
D.	2/5
Answer» D. 2/5

Discussion

1033.	If a point O in the interior of a rectangle ABCD is joined with each of vertices A, B, C and D, then OB2 + OD2 will be equal to
A.	2 OC2 + OA2
B.	OC2 - OA2
C.	OC2 + OA2
D.	OC2 + 2OA2
Answer» D. OC2 + 2OA2

Discussion

1034.	In the given figure, ABC is a triangle in which, AB = 10 cm, Ac = 6 cm and altitude AE = 4 cm. If AD is the diameter of the circumcircle, then what is the length (in cm) of circumradius?
A.	3
B.	7.5
C.	12
D.	15
Answer» C. 12

Discussion

1035.	An arc length of 16π units subtends an angle of 240 degrees. Find the radius (in units) of the circle.
A.	6
B.	12
C.	24
D.	36
Answer» C. 24

Discussion

1036.	ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 128° and ∠ECD = 25°, then what is the measure of ∠BAC?
A.	52°
B.	103°
C.	93°
D.	98°
Answer» C. 93°

Discussion

1037.	In the given figure, a circle inscribed in ∆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?
A.	PS = 6.5 cm, QT = 8.5 cm and RU = 3.5 cm
B.	PS = 3.5 cm, QT = 6.5 cm and RU = 8.5 cm
C.	PS = 8.5 cm, QT = 6.5 cm and RU = 3.5 cm
D.	PS = 8.5 cm, QT = 3.5 cm and RU = 6.5 cm
Answer» D. PS = 8.5 cm, QT = 3.5 cm and RU = 6.5 cm

Discussion

1038.	A circle touches the side PQ of a ΔAPQ at the point R and sides AP and AQ produced at the points B and C, respectively. If the perimeter of ΔAPQ = 30 cm, then the length of AB is∶
A.	12 cm
B.	15 cm
C.	10 cm
D.	20 cm
Answer» C. 10 cm

Discussion

1039.	Let ABC be a triangle in which AB = AC. Let L be the locus of points X inside or on the triangle such that BX = CX. Which of the following statements are correct?(1) L is a straight line passing through A and in-centre of triangle ABC is on L.(2) L is a straight line passing through A and orthocentre of triangle ABC is on L.(3) L is a straight line passing through A and centroid of triangle ABC is on L.Select the correct answer using the code given below.
A.	1 and 2 only
B.	2 and 3 only
C.	1 and 3 only
D.	1, 2 and 3
Answer» E.

Discussion

1040.	In ΔABC, ∠A = 70°. AB and AC are produced to points D and E respectively. If the bisectors of ∠CBD and ∠BCE meet at the point O, then ∠BOC is equal to∶
A.	95°
B.	105°
C.	70°
D.	55°
Answer» E.

Discussion

1041.	D and E are points on the sides AB and AC respectively of ΔABC such that DE is parallel to BC and AD : DB = 4 : 5, CD and BE intersect each other at F. Then the ratio of the areas of ΔDEF and ΔCBF
A.	16 : 25
B.	16 : 81
C.	81 : 1
D.	4 : 9
Answer» C. 81 : 1

Discussion

1042.	In triangle PQR, the internal bisectors of ∠Q and ∠R meet at O. If ∠QPR = 70°, then what is the value of ∠QOR?
A.	45°
B.	125°
C.	115°
D.	110°
Answer» C. 115°

Discussion

1043.	A circular coin of radius 1 cm is allowed to roll freely on the periphery over a circular disc of radius 10 cm. If the disc has no movement and the coin completes one revolution rolling on the periphery over the disc and without slipping, then what is the number of times the coin rotated about its centre?
A.	10
B.	10.5
C.	11
D.	12
Answer» B. 10.5

Discussion

1044.	ABCD is a rhombus with ∠ABC = 52°. The measure of ∠ACD is:
A.	48°
B.	54°
C.	64°
D.	26°
Answer» D. 26°

Discussion

1045.	AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length, in cm, of QB is nearest to
A.	8.5
B.	9.3
C.	9.1
D.	7.8
Answer» D. 7.8

Discussion

1046.	Find the value of ∠BOC in the given figure in which O is the center of the circle.
A.	100°
B.	130°
C.	110°
D.	120°
Answer» B. 130°

Discussion

1047.	If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?
A.	(5√3)/2
B.	4√3
C.	(3√6 )/2
D.	3√3
Answer» D. 3√3

Discussion

1048.	In the given figure, the ratio of the area of the largest square to that of the smallest square is:
A.	2 : 1
B.	√2 : 1
C.	4 : 1
D.	3 : 1
Answer» D. 3 : 1

Discussion

1049.	If a regular hexagon is inscribed in a circle of radius r, then its perimeter is
A.	6r
B.	3r
C.	9r
D.	12r
Answer» B. 3r

Discussion

1050.	In triangle ABC, a perpendicular line is drawn from the vertex A to a point D on BC. If BC = 9 cm and DC = 3 cm, then what is the ratio of the areas of triangle ABD and triangle ADC respectively?
A.	1 : 1
B.	2 : 1
C.	3 : 1
D.	4 : 1
Answer» C. 3 : 1

Discussion

Explore topic-wise MCQs in SRMJEEE .

In ΔABC, ∠A = 50°. Its sides AB and AC are produced to the point D and E. If the bisectors of ∠CBD and ∠BCE meet at the point O, then ∠BOC is equal to∶

In the figure given below, M is the mid-point of AB and ∠DAB = ∠CBA and ∠AMC = ∠BMD. Then the triangle ADM is congruent to the triangle BCM by

In the given figure, PQR is a triangle in which, PQ = 24 cm, PR = 12 cm and altitude PS = 8 cm. If PT is the diameter of the circumcircle, then what is the length (in cm) of circum-radius?

Given that ΔDEF ~ ΔABC. If the area of ΔABC is 9 cm2 and area of ΔDEF is 12cm2 , BC = 2.1 cm, then the length of EF is:

In a trapezium, the lengths of its parallel sides are a and b. The length of the line joining the midpoints of its non - parallel sides is

If the ratio of the angles of a triangle is 3 : 5 : 7, find the value of the largest angle.A. 36°B. 60°C. 84°D. 15°

ABC is a right angled triangle, right angled at A. A circle is inscribed in it. The lengths of two sides containing the right angle are 48 cm and 14 cm. The radius of the inscribed circle is:

If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is:

In the given figure, chords AB and CD are intersecting each other at point L. Find the length of AB

PAQ is a line parallel to side BC of a triangle ABC. If ∠PAB = 55° and ∠ACB = 60°, then ∠CAB = _______.

In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is

PQRS is a trapezium with PQ || RS. U and V are points on non-parallel sides PS and QR respectively such that UV is parallel to PQ, then

ΔABC is right angled at B. BD is an altitude. AD = 3 cm and DC = 9 cm. What is the value of AB (in cm)?

In the given figure \(\overline {DE} \parallel \overline {BC}\), AD = 6 cm and DB = 3 cm. What is the value of AM ∶ MN?

AB is a chord of the circle and its center is “O”. ON is perpendicular to AB. If the length of AB = 20 cm, ON = (2√11) cm, find the radius (in cm) of the circle.

In the above figure, O is the centre of the circle. If ∠AOB = 110° and ∠AOC is a right angle, then the measure of ∠BAC is

In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, is

ABCD is a cyclic quadrilateral of which AB is the diameter. Diagonals AC and BD intersect at E. If ∠DBC = 35°, then ∠AED measures

A is a point at a distance 26 cm from the centre O of a circle of radius 10 cm. AP and AQ are the tangents to the circle at the point of contacts P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, then the perimeter of ΔABC is:

If point C is equidistant from A (5, -6) and B (7, 8) co-ordinate of C will be

In ΔABC, P is a point on BC such that BP : PC = 4 : 11. If Q is the midpoint of BP, then ar(ΔABQ) : ar(ABC) is equal to:

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to

If P is the circum-center in ΔABC, ∠BPC = 30°, then what is the value (in degrees) of ∠BAC?

In a circle with centre O, chords AB and CD are parallel chords on the opposite side of O. If AB = 20 cm, CD = 48 cm and the distance between the chords is 34 cm, then the diameter (in cm) of the circle is:

If P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively of a quadrilateral ABCD then the quadrilateral PQRS is a:

In a triangle ABC, AB = 12, BC = 18 and AC = 15. The medians AX and BY intersect sides BC and AC at X and Y respectively. If AX and BY intersect each other at O, then what is the value of OX?

In a circle, if a chord AB is nearer to the center O than the chord CD, then:

In the diagram, M is the midpoint of \(\overline {YZ} ,\;\angle XMZ = 32^\circ,\) and ∠XYZ = 16°. The measure of ∠XZY is:

If triangles ∆A1 B1 C1 and ∆A2 B2 C2 are similar then:

In ΔABC, D and E are points on AB and AC respectively such that DE is parallel to BC. If AD = 2 cm, BD = 3 cm, then \(\frac{{ar\left( {{\rm{\Delta }}ADE} \right)}}{{ar\left( {{\rm{\Delta }}ABC} \right)}}is:\)

If a point O in the interior of a rectangle ABCD is joined with each of vertices A, B, C and D, then OB2 + OD2 will be equal to

In the given figure, ABC is a triangle in which, AB = 10 cm, Ac = 6 cm and altitude AE = 4 cm. If AD is the diameter of the circumcircle, then what is the length (in cm) of circumradius?

An arc length of 16π units subtends an angle of 240 degrees. Find the radius (in units) of the circle.

ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 128° and ∠ECD = 25°, then what is the measure of ∠BAC?

In the given figure, a circle inscribed in ∆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?

A circle touches the side PQ of a ΔAPQ at the point R and sides AP and AQ produced at the points B and C, respectively. If the perimeter of ΔAPQ = 30 cm, then the length of AB is∶

In ΔABC, ∠A = 70°. AB and AC are produced to points D and E respectively. If the bisectors of ∠CBD and ∠BCE meet at the point O, then ∠BOC is equal to∶

D and E are points on the sides AB and AC respectively of ΔABC such that DE is parallel to BC and AD : DB = 4 : 5, CD and BE intersect each other at F. Then the ratio of the areas of ΔDEF and ΔCBF

In triangle PQR, the internal bisectors of ∠Q and ∠R meet at O. If ∠QPR = 70°, then what is the value of ∠QOR?

ABCD is a rhombus with ∠ABC = 52°. The measure of ∠ACD is:

AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length, in cm, of QB is nearest to

Find the value of ∠BOC in the given figure in which O is the center of the circle.

If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?

In the given figure, the ratio of the area of the largest square to that of the smallest square is:

If a regular hexagon is inscribed in a circle of radius r, then its perimeter is

In triangle ABC, a perpendicular line is drawn from the vertex A to a point D on BC. If BC = 9 cm and DC = 3 cm, then what is the ratio of the areas of triangle ABD and triangle ADC respectively?