question_answer 1)
In the shown figure, two line segments PQ and RS intersect each other at the point O such that PO = 4.8, OS = 4.2 cm, RO = 3.2 cm and \[\angle \]ORP = \[\mathbf{65}{}^\circ \], \[\angle \]POR = \[80{}^\circ \] and \[\angle \]OSQ = 35°, then find the value of OQ.
A)
3 cm done
clear
B)
4.2 cm done
clear
C)
2.8 cm done
clear
D)
3.6 cm done
clear
E)
None of these done
clear
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question_answer 2)
Find the value of x for which PQ || RS in shown figure.
A)
3 done
clear
B)
4 done
clear
C)
5 done
clear
D)
6 done
clear
E)
None of these done
clear
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question_answer 3)
From a point P, inside of an equilateral triangle ABC, the perpendicular istances of the three sides are 4 cm, 6 cm and 7 cm respectively. Find the perimeter of the triangle.
A)
56\[\sqrt{3}\]cm done
clear
B)
24\[\sqrt{3}\]cm done
clear
C)
17\[\sqrt{3}\] done
clear
D)
34\[\sqrt{3}\]cm done
clear
E)
None of these done
clear
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question_answer 4)
In a triangle ABC, P is a point on BC and from point P lines parallel to AB and AC are drawn which intersects AB and AC at R and Q respectively If RQ meets BC produced in S. Then \[\mathbf{S}{{\mathbf{P}}^{\mathbf{2}}}\] equals to _______
A)
3SB \[\times \] SC done
clear
B)
SB \[\times \] SC done
clear
C)
2SR \[\times \] RQ done
clear
D)
2SB \[\times \] SC done
clear
E)
None of these done
clear
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question_answer 5)
Which one among the following statements is not true?
A)
In a triangle PQR, if S is a point on QR such that S divides QR in the ratio PQ : PR, then PS is the bisector of \[\angle \]P. done
clear
B)
In a triangle PQR, if PS is the bisector of the exterior of angle P and meets QR produced in S, then \[\frac{QS}{RS}=\frac{PQ}{PR}\] done
clear
C)
If a line through one vertex of a triangle divides the opposite sides in the ratio of other two sides, then the line bisects the angle at the vertex. done
clear
D)
In a \[\Delta \]PQR, in which S is a point on QR such that \[\frac{QS}{QR}=\frac{PQ}{PR}\], then PS is bisector of \[\angle \]P. done
clear
E)
None of these done
clear
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question_answer 6)
Find the length of altitude on the hypotenuse of a right angled triangle whose area is 60\[\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}\] and one of the sides containing the right angle is 15 cm.
A)
7.06 cm done
clear
B)
6.28 cm done
clear
C)
7.36 cm done
clear
D)
6.88 cm done
clear
E)
None of these done
clear
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question_answer 7)
In a \[\Delta \] PQR, the bisector of \[\angle \] Q meets PR at T. If a line MN is drawn parallel to PR which meets PQ, QR and QT at M, N and 0 respectively, then ________
A)
MO.QN = QM.ON done
clear
B)
QP.NR = PM.QR done
clear
C)
\[\frac{Area\text{ }of\text{ }\Delta QTP\text{ }}{Area\text{ }of\text{ }\Delta QTP\text{ }}=\frac{QR}{QP}\] done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer 8)
In a triangle PQR (as shown below), \[\angle \]PQR = \[\mathbf{90}{}^\circ \] and QS is its bisector. If SM\[\bot \]QR then SM\[\times \](PQ + QR) is equal to _________
A)
PS \[\times \] SR done
clear
B)
PQ \[\times \] QR done
clear
C)
2PS \[\times \] SR done
clear
D)
2PQ \[\times \] QR done
clear
E)
None of these done
clear
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question_answer 9)
In the shown figure, PQ || RS, find the value of x.
A)
3 done
clear
B)
7 done
clear
C)
5 done
clear
D)
8 done
clear
E)
None of these done
clear
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question_answer 10)
In a trapezium PQRS, PQ || RS and RS = 2PQ. MN drawn parallel to PQ meets PS in M and QR in N such that \[\frac{\mathbf{QN}}{\mathbf{NR}}\]=\[\frac{\mathbf{3}}{\mathbf{4}}\]. If diagonal QS intersects MN at O, then the ratio of \[\frac{\mathbf{MN}}{\mathbf{PQ}}\] is equal to
A)
\[\frac{7}{10}\] done
clear
B)
\[\frac{10}{7}\] done
clear
C)
\[\frac{4}{7}\] done
clear
D)
\[\frac{7}{4}\] done
clear
E)
None of these done
clear
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question_answer 11)
In the shown figure, if PS, UQ and RT are each perpendicular to PR, then _______
A)
\[\frac{1}{a}+\frac{1}{b}=\frac{1}{c}\] done
clear
B)
\[\frac{1}{b}+\frac{1}{c}=\frac{1}{a}\] done
clear
C)
\[\frac{1}{a}+\frac{1}{c}=\frac{1}{b}\] done
clear
D)
\[\frac{1}{c}+\frac{1}{a}=\frac{2}{b}\] done
clear
E)
None of these done
clear
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question_answer 12)
In the shown figure, if \[\Delta \]PQR is right angled at Q and TS \[\bot \] PR. Find the lengths of PS and ST respectively.
A)
\[\frac{30}{13}cm\,\,and\,\,\frac{36}{13}cm\] done
clear
B)
\[\frac{20}{13}cm\,\,and\,\,\frac{26}{15}cm\] done
clear
C)
\[\frac{15}{13}cm\,\,and\,\,\frac{17}{13}cm\] done
clear
D)
\[\frac{19}{13}cm\,\,and\,\,\frac{17}{13}cm\] done
clear
E)
None of these done
clear
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question_answer 13)
Which one among the following statements is correct?
A)
The area of the equilateral triangle described on the side of a square is equal to the area of the equilateral triangle described on its diagonal. done
clear
B)
If equilateral triangles are drawn on the sides of a right triangle then the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides. done
clear
C)
The line segments joining the mid-points of the sides of a triangle form four triangles, each of which is similar to the original triangle. done
clear
D)
both B and C done
clear
E)
None of these done
clear
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question_answer 14)
In the shown figure, ST || PR and ST divides triangular region PQR into two parts of equal area. Find the ratio of \[\frac{PS}{PQ}\].
A)
B)
\[\frac{\sqrt{2}\left( \sqrt{2}-2 \right)}{2}\] done
clear
C)
\[\sqrt{2}+1\] done
clear
D)
\[2-\sqrt{2}\] done
clear
E)
None of these done
clear
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question_answer 15)
In the shown figure, an equilateral triangle QRT surmounts square PQRS. Find the value of x + y.
A)
\[100{}^\circ \] done
clear
B)
\[110{}^\circ \] done
clear
C)
\[120{}^\circ \] done
clear
D)
\[120{}^\circ \] done
clear
E)
None of these done
clear
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question_answer 16)
In the shown figure, MN = QP and on producing MN & QP, they intersect at R. Also, MQ || NP. If \[\angle \]NMQ = 55°, then find \[\angle \] R.
A)
\[50{}^\circ \] done
clear
B)
\[70{}^\circ \] done
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C)
\[60{}^\circ \] done
clear
D)
\[80{}^\circ \] done
clear
E)
None of these done
clear
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question_answer 17)
PQR is a triangle in which\[\angle \]PQR = \[\mathbf{90}{}^\circ \] and a perpendicular is drawn from Q to PR which intersects PR at S. If PQ = a, QR = b, PR = c and QS = p, then which one of the following is true?
A)
\[cp=ab\] done
clear
B)
\[\frac{1}{{{p}^{2}}}=\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}\] done
clear
C)
\[\frac{1}{{{p}^{2}}}=\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}-\frac{1}{{{c}^{2}}}\] done
clear
D)
both A and B done
clear
E)
None of these done
clear
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question_answer 18)
In a right angled triangle PQR right angled at P, S and T are points on PQ and PR respectively, which divide these sides on the ratio 2 : 1, then which one of the following is correct?
A)
\[9(Q{{T}^{2}}+R{{S}^{2}})=13\,Q{{R}^{2}}\] done
clear
B)
\[9\,QT=9P{{Q}^{2}}+4\,P{{R}^{2}}\] done
clear
C)
\[9\,R{{S}^{2}}=4\,P{{Q}^{2}}+9\,P{{R}^{2}}\] done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer 19)
Which among the following statements is incorrect?
A)
Equal chords subtend equal angles at the centre of the circle. done
clear
B)
The opposite angles of a cyclic quadrilateral are supplementary. done
clear
C)
A line drawn through the end point of a radius of a circle and perpendicular to it is a tangent to the circle. done
clear
D)
The number of common tangents to two circles touching externally is four. done
clear
E)
None of these done
clear
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question_answer 20)
In the figure shown below, if PQ = 20 cm and \[\angle \]QPR =\[\angle \]SPR, then QR = ?
A)
6 cm done
clear
B)
8 cm done
clear
C)
10 cm done
clear
D)
12 cm done
clear
E)
None of these done
clear
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question_answer 21)
In the shown figure, if the angle between two chords PQ and PR is\[55{}^\circ \]then the angle between two tangents which are drawn at Q and R is ______
A)
\[50{}^\circ \] done
clear
B)
\[60{}^\circ \] done
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C)
\[70{}^\circ \] done
clear
D)
\[80{}^\circ \] done
clear
E)
None of these done
clear
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question_answer 22)
If PQRS is a trapezium, PR and QS are the diagonals intersecting each other at 0, then PR : QS = _______
A)
\[PO-RO:OQ-OS\] done
clear
B)
\[PO+PS:SR+QR\] done
clear
C)
\[P{{O}^{2}}:O{{Q}^{2}}\] done
clear
D)
\[PQ:RS\] done
clear
E)
None of these done
clear
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question_answer 23)
In the shown figure, if PQR is an equilateral triangle and square ABCD is inscribed in it whose side is 6 cm, then by how many \[\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}\] is the area of triangle more than that of the square?
A)
18\[\sqrt{3}\] done
clear
B)
21 done
clear
C)
21\[\sqrt{3}\] done
clear
D)
18 done
clear
E)
None of these done
clear
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question_answer 24)
If I is the in centre of a triangle PQR, where \[\angle \]PQR = \[\mathbf{65}{}^\circ \] and \[\angle \]PRQ = \[\mathbf{55}{}^\circ \], the \[\angle \]QIR is.
A)
\[140{}^\circ \] done
clear
B)
\[120{}^\circ \] done
clear
C)
\[110{}^\circ \] done
clear
D)
\[130{}^\circ \] done
clear
E)
None of these done
clear
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question_answer 25)
In a right angled triangle, the product of its two sides equals half of the square of the third side, where third side is the hypotenuse. One of the acute angles then must be
A)
\[15{}^\circ \] done
clear
B)
\[45{}^\circ \] done
clear
C)
\[30{}^\circ \] done
clear
D)
\[60{}^\circ \] done
clear
E)
None of these done
clear
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question_answer 26)
The sum of the three altitudes of a triangle is ______
A)
more than the sum of three sides of the triangle. done
clear
B)
equal to the half of the three sides of the triangle. done
clear
C)
less than the sum of three sides of the triangle. done
clear
D)
equal to the double of the three sides of the triangle. done
clear
E)
None of these done
clear
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question_answer 27)
In an isosceles triangle PQR, PQ < 6 cm and PR = 12 cm, then
A)
QR = PR done
clear
B)
QR < PR done
clear
C)
QR = PQ done
clear
D)
QR > PR done
clear
E)
None of these done
clear
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question_answer 28)
The lengths of 3 sides of a triangle are given as 12 cm, 9 cm and 15 cm. Find the length of the median to its greatest side.
A)
8.8 cm done
clear
B)
8.6 cm done
clear
C)
7.5 cm done
clear
D)
8.2 cm done
clear
E)
None of these done
clear
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question_answer 29)
Two equal circles of radius 14 cm intersect each other such that each passes through the centre of the other. The length of the common chord is
A)
12 cm done
clear
B)
12\[\sqrt{3}\]cm done
clear
C)
14\[\sqrt{3}\]cm done
clear
D)
15 cm done
clear
E)
None of these done
clear
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question_answer 30)
In a \[\Delta \]MMO, \[\angle \]MNO =\[\mathbf{90}{}^\circ \], MN: NP: PO = 3: 1: 3. If OM = 20 cm then what is the length of MP?
A)
\[2\sqrt{10}\]cm done
clear
B)
\[4\sqrt{10}\]cm done
clear
C)
\[3\sqrt{5}\]cm done
clear
D)
\[4\sqrt{5}\]cm done
clear
E)
None of these done
clear
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question_answer 31)
In the shown figure PQRS is a rectangle, where RQ = 24 cm, SU = 10 cm and RS = 15 cm, then PT + RT is equal to ________
A)
50 cm done
clear
B)
48 cm done
clear
C)
51 cm done
clear
D)
38 cm done
clear
E)
None of these done
clear
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question_answer 32)
PQR is an equilateral triangle of side 6 cm. If a circle of radius 1 cm is moving inside and along the sides of the triangle, then locus of the centre of the circle is an equilateral triangle of side _______
A)
5.5 cm done
clear
B)
\[(3-\sqrt{3)}\]cm done
clear
C)
\[(3+\sqrt{3)}\]cm done
clear
D)
\[\left( 6-2\sqrt{3} \right)\]cm done
clear
E)
None of these done
clear
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question_answer 33)
An equilateral triangle ABC is constructed on a side AB of a square MNAB. The measure of \[\angle \] MCN can be ______
A)
\[30{}^\circ \] done
clear
B)
\[15{}^\circ \] done
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C)
\[45{}^\circ \] done
clear
D)
\[60{}^\circ \] done
clear
E)
None of these done
clear
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question_answer 34)
Diagonal PR of a rectangle PQRS is produced to the point E such that PR: RE = 2: 1. If PQ = 8 cm and QR = 6 cm, then the length of SE is ________
A)
\[2\sqrt{5}cm\] done
clear
B)
\[3\sqrt{17}cm\] done
clear
C)
\[3\sqrt{15}cm\] done
clear
D)
\[4\sqrt{19}cm\] done
clear
E)
None of these done
clear
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question_answer 35)
In the shown figure, PQJ. RS and PS is the bisector of \[\angle \] QPM. If PQ = 3 cm and PR = 5 cm, then the length of RS is ______
A)
8 cm done
clear
B)
10 cm done
clear
C)
12 cm done
clear
D)
14 cm done
clear
E)
None of these done
clear
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question_answer 36)
In the shown figure, AB is a tangent to the circle at A. If \[\angle \]BAC = \[\mathbf{40}{}^\circ \] and AC = BC, then \[\angle \]AED = ________
A)
\[{{60}^{o}}\] done
clear
B)
\[80{}^\circ \] done
clear
C)
\[100{}^\circ \] done
clear
D)
\[85{}^\circ \] done
clear
E)
None of these done
clear
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question_answer 37)
In the shown figure, two circles having centres P and Q respectively intersect at R and S. The radii PR and PS are tangents to the other Tele and radii RQ and QS are tangents to the first circle. Find \[\frac{3}{5}\angle \,PMR\].
A)
\[35{}^\circ \] done
clear
B)
\[70{}^\circ \] done
clear
C)
\[{{60}^{o}}\] done
clear
D)
\[54{}^\circ \] done
clear
E)
None of these done
clear
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question_answer 38)
Two sides of a triangle are 12 cm and 5 cm lone. lf the measure of third side is an integer is an obtuse triangle' then how many such triangle are possible?
A)
5 done
clear
B)
6 done
clear
C)
7 done
clear
D)
8 done
clear
E)
None of these done
clear
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question_answer 39)
In a \[\Delta \]ABC, P lies on AC such that BC = AP = BP. If \[\angle \]PBC = \[40{}^\circ \], then \[\angle \]P =?
A)
\[25{}^\circ \] done
clear
B)
\[30{}^\circ \] done
clear
C)
\[35{}^\circ \] done
clear
D)
\[40{}^\circ \] done
clear
E)
None of these done
clear
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question_answer 40)
In the figure shown below, PQ is the diameter of the circle and \[\angle \]ORQ = \[\mathbf{30{}^\circ }\] then \[\angle \]SQR = ?
A)
\[{{72}^{o}}\] done
clear
B)
\[62{}^\circ \] done
clear
C)
\[38{}^\circ \] done
clear
D)
\[68{}^\circ \] done
clear
E)
None of these done
clear
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