question_answer 1)
It is known that if \[\mathbf{a}\text{ }+\text{ }\mathbf{b}\text{ }+\text{ }\mathbf{c}\text{ }=\text{ }\mathbf{18}\] then\[a + b + c +d= 18+d\]. The Euclid?s axiom that illustrates this statement is __________
A)
First axiom done
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B)
Second axiom done
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C)
Third axiom done
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D)
Fourth axiom done
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E)
None of these done
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question_answer 2)
In geometry, we take a point, a line and a plane (in Euclid's words a plane surface) as ________
A)
constant done
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B)
defined terms done
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C)
undefined terms done
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D)
variables done
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E)
None of these done
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question_answer 3)
In Indus Valley Civilization (about 3000 B.C.), the bricks used for construction work were having dimension in the ratio __________
A)
\[2\,\,:\,\,4\,\,:\,\,5\] done
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B)
\[3:2:1\] done
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C)
\[4:2:1~\] done
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D)
\[4:2:5\] done
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E)
None of these done
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question_answer 4)
In the shown figure, I is a straight line. Find the value of x.
A)
\[60{}^\circ \] done
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B)
\[30{}^\circ \] done
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C)
\[40{}^\circ \] done
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D)
Cannot be determined done
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E)
None of these done
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question_answer 5)
In the shown figure, \[\mathbf{OA}\text{ }\parallel \text{ }\mathbf{CD}\] and \[\angle \mathbf{OAB= 115{}^\circ }\] and\[\angle \mathbf{BCD}\text{ }=\text{ }\mathbf{125}{}^\circ \], find the value of\[\angle \mathbf{ABC}\].
A)
\[20{}^\circ \] done
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B)
\[60{}^\circ \] done
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C)
\[30{}^\circ \] done
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D)
\[45{}^\circ \] done
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E)
None of these done
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question_answer 6)
In which of the following figures, the given two lines will be parallel lines?
A)
B)
C)
D)
E)
None of these done
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question_answer 7)
In the shown figure, if \[\mathbf{PQ}\text{ }\parallel \text{ }\mathbf{MN}\] and\[\mathbf{NO}\text{ }\parallel \text{ }\mathbf{QR}\], then which of the following conditions can be true?
A)
\[x\text{ }=\text{ }y\] done
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B)
\[x+y=90{}^\circ \] done
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C)
\[x\text{ }+\text{ }y=180{}^\circ ~\] done
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D)
\[x=90{}^\circ +y\] done
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E)
None of these done
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question_answer 8)
In the following figure, \[\mathbf{AB}\text{ }\parallel \text{ }\mathbf{CD}\] and\[\angle \mathbf{ABR}\text{ }=\text{ }\mathbf{115}{}^\circ \], \[\angle \mathbf{BRC}\text{ }=\text{ }\mathbf{40}{}^\circ \] and\[\mathbf{1}.~~~~~~~~~~~\angle \mathbf{R}CD=\mathbf{x}{}^\circ \]. Find the value of x°.
A)
\[140{}^\circ \] done
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B)
\[25{}^\circ \] done
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C)
\[75{}^\circ \] done
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D)
\[155{}^\circ \] done
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E)
None of these done
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question_answer 9)
In the given figure, if \[\mathbf{a}\text{ }+\text{ }\mathbf{c}\text{ }=\text{ }\mathbf{205}{}^\circ \] and \[\mathbf{0}\text{ }=\text{ }\mathbf{80}{}^\circ \], also \[\mathbf{N}\text{ }=\text{ }\mathbf{a}\], then _______
A)
\[P=80{}^\circ \] done
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B)
\[M=105{}^\circ \] done
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C)
\[\frac{3}{5}(M+c)=105{}^\circ \] done
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D)
\[N+d=180{}^\circ \] done
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E)
None of these done
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question_answer 10)
ABC is a cyclic triangle and the bisectors of \[\angle \mathbf{BAC},\text{ }\angle \mathbf{ABC}\] and \[\angle \mathbf{BCA}\] me the circle at P, Q and R respectively. Then the angle \[\angle \mathbf{RQP}\] is __________.
A)
\[90{}^\circ +\frac{C}{2}\] done
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B)
\[90{}^\circ -\frac{A}{2}\] done
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C)
\[90{}^\circ +\frac{B}{2}\] done
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D)
\[90{}^\circ -\frac{B}{2}\] done
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E)
None of these done
clear
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question_answer 11)
In the shown figure, the value of a is equal to
A)
\[y+z\] done
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B)
\[x+y\] done
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C)
\[x+y+z\] done
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D)
\[~\frac{x+y+z}{2}\] done
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E)
None of these done
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question_answer 12)
In the shown figure, if \[\mathbf{PQ}\text{ }\parallel \text{ }\mathbf{BC}\] and \[\mathbf{AP}=\mathbf{5}.\mathbf{4}\text{ }\mathbf{cm}\],\[\text{ }\mathbf{AQ}=\left( \mathbf{x}+\mathbf{1} \right)\,\,\mathbf{cm},\]\[\mathbf{AB}=\mathbf{8}.\mathbf{1}cm\] cm and \[QC=(x-1)\]cm, then AC equals to _______
A)
12 cm done
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B)
6 cm done
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C)
3 cm done
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D)
4 cm done
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E)
None of these done
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question_answer 13)
In a \[\Delta \,\mathbf{ABC}\], if \[\angle \mathbf{A}\text{ }-\text{ }\angle \mathbf{B}\text{ }=\mathbf{35}{}^\circ \] and \[\angle \mathbf{C}\text{ }-\angle \mathbf{B}\text{ }=\mathbf{34}{}^\circ \], then
A)
\[\angle A=71{}^\circ \] done
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B)
\[\angle B=72{}^\circ \] done
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C)
\[\angle A+\angle B=109{}^\circ \] done
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D)
\[\angle A+\angle C=142{}^\circ \] done
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E)
None of these done
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question_answer 14)
In two triangles ACB and QPR if AB = QR, ZB = ZQ and CA = PR then ___
A)
\[\Delta \,ABC\cong \Delta \,PQR~\] done
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B)
\[\Delta \,ACB\cong \Delta \,RPQ~\] done
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C)
\[\Delta \,BAC\cong \Delta \,QRP~\] done
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D)
\[\Delta \,BAC\cong \Delta \,QPR~\] done
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E)
None of these done
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question_answer 15)
Two sides of a triangle are of lengths 6.2 cm and 3.5 cm. The length of the third side of the triangle cannot be ________
A)
9.2cm done
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B)
8.5cm done
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C)
2.8cm done
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D)
2.6cm done
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E)
None of these done
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question_answer 16)
Which among the following statements is correct?
A)
In a triangle PQR, if \[\angle Q<\angle P\] then\[PR\text{ }<\text{ }QR\]. done
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B)
\[\Delta \text{ }ABC\cong \Delta \text{ }PQR\] if \[\angle A\text{ }=\text{ }\angle P,\] and \[AC=\text{ }QR\]. done
clear
C)
In triangles PQR and STU if \[\angle P\text{ }=\text{ }\angle S,\] \[\angle Q\text{ }=\text{ }\angle T\] and \[PQ\text{ }=\text{ }TU\], then both the triangles are congruent. done
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D)
All the above done
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E)
None of these done
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question_answer 17)
S is a point on the side QR of a triangle PQR such that PS bisects\[\text{ }\angle QPR\] then _________
A)
\[QS=SR\] done
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B)
\[PR<RS\] done
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C)
\[PQ>QS\] done
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D)
Both B and C are true done
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E)
None of these done
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question_answer 18)
In the shown figure, the bisector of angle P is bisecting the opposite side QR. If \[\mathbf{PQ}\text{ }=\text{ }\mathbf{3}\text{ }\mathbf{cm}\] then the value of PR is _________
A)
3cm done
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B)
4cm done
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C)
6cm done
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D)
1.5cm done
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E)
None of these done
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question_answer 19)
If M is any point in the interior of \[\Delta \,\mathbf{ABC}\]then _______
A)
\[MC+MB>AC+AB\] done
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B)
\[MC+MB=AC+AB\] done
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C)
\[MC+MB=AC+AB\] done
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D)
\[MC+MB\ge AC+AB\] done
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E)
None of these done
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question_answer 20)
Which one among the following statements is correct?
A)
If ABCD is a rectangle such that BD bisects \[\angle B\]then it is also a rhombus. done
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B)
A rectangle is formed by the bisectors of the angles of a parallelogram. done
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C)
A square is formed by the mid points of the consecutive sides of a square. done
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D)
All the above done
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E)
None of these done
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question_answer 21)
In a triangle, other than an equilateral triangle, angle opposite to the largest side is _________
A)
lesser than \[\frac{2}{3}\]of a right angle. done
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B)
greater than \[\frac{2}{3}\]of a right angle. done
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C)
always greater than a right angle. done
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D)
lesser than\[\frac{1}{2}\]of a right angle. done
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E)
None of these done
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question_answer 22)
PQR is a triangle in which\[\angle \mathbf{Q}\text{ }=\text{ }\mathbf{2}\angle \mathbf{R}\]. If a line PS is drawn from vertex P such that it bisects \[\angle \mathbf{QPR}\] and cuts QR at S such that \[\mathbf{PQ}\text{ }=\text{ }\mathbf{RS}\], then \[\angle \mathbf{QPR}\text{ }+\text{ }\angle \mathbf{QRP}\] equals to __________
A)
\[72{}^\circ \] done
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B)
\[136{}^\circ \] done
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C)
\[108{}^\circ \] done
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D)
\[130{}^\circ \] done
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E)
None of these. done
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question_answer 23)
If PQR is a triangle and M is the mid-point of QR and the perpendiculars from M to PQ and PR are equal, then PQR is _______
A)
an equilateral triangle done
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B)
an isosceles triangle done
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C)
not an equilateral triangle done
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D)
not an isosceles triangle done
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E)
None of these done
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question_answer 24)
In the given triangle PQR, another triangle MLN is drawn by joining the mid-points of the sides of \[\Delta \]PQR. Based on this information choose the correct one among the following.
A)
\[\angle LMN=\angle QPR\] done
clear
B)
\[\angle LNM=\text{ }\angle RPQ\] done
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C)
\[\angle MLN=\angle QRP\] done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer 25)
MNOP is a rhombus in which the diagonal OM is produced to Q. If\[\angle \mathbf{POQ}=\text{ }\mathbf{140}{}^\circ \], then which one is correct?
A)
\[x=60{}^\circ \] done
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B)
\[y=50{}^\circ \] done
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C)
\[z=50{}^\circ \] done
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D)
All of the above done
clear
E)
None of these done
clear
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question_answer 26)
In the shown figure, PQRS is a trapezium where \[\mathbf{PQ}\text{ }\parallel \text{ }\mathbf{RS}\] and M and N are the mid-points of PR and SQ respectively. If \[\mathbf{PQ}\text{ }=\text{ }\mathbf{7}\text{ }\mathbf{cm}\]and \[\mathbf{RS}\text{ }=\text{ }\mathbf{3cm}\] then the length of MN is ________
A)
1 cm done
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B)
2 cm done
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C)
3 cm done
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D)
4 cm done
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E)
None of these done
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question_answer 27)
In the shown figure, PQRS is a trapezium and\[\mathbf{PQ}\text{ }\parallel \text{ }\mathbf{RS}\]. If M is the mid- point of PS such that \[\mathbf{MN}\text{ }\parallel \text{ }\mathbf{RS}\] and \[\mathbf{PQ}\text{ }=\text{ }\mathbf{8}\text{ }\mathbf{cm}\] and \[\mathbf{RS}=\text{ }\mathbf{12cm}\], then MN equals to ______
A)
6 cm done
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B)
8 cm done
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C)
10 cm done
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D)
8.5 cm done
clear
E)
None of these done
clear
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question_answer 28)
In the shown figure, N is the mid-point of QP. M is any point on QR. If \[\mathbf{OR}\text{ }\parallel \text{ }\mathbf{NM}\] meets PQ in O, then which one among the following is true?
A)
\[ar(\Delta QMO)=ar(\Delta QNR)\] done
clear
B)
\[ar\text{ }(\Delta \text{ }MNO)=ar\text{ }(\Delta \text{ }MRN)\] done
clear
C)
\[ar\text{ }(\Delta \text{ }QRN)=\frac{1}{2}ar\text{ }(\Delta \text{ PQR})\] done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer 29)
In the shown figure, PQRS is a parallelogram and if M and N are the mid- points of RQ and RS respectively, then ________
A)
\[Ar\text{ (}\Delta \text{ NMR)=}\frac{1}{4}\text{ A}r(\text{ }{{\parallel }^{gm}}PQRS)\] done
clear
B)
\[Ar\text{ (}\Delta \text{ PQM)=}\frac{1}{8}\text{ A}r(\,{{\parallel }^{gm}}PQRS)\] done
clear
C)
\[Ar\text{ (}\Delta \text{ PNM)=}\frac{3}{8}\text{ A}r\text{ }(\text{ }{{\parallel }^{gm}}PQRS)\] done
clear
D)
All of the above done
clear
E)
None of these done
clear
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question_answer 30)
In the shown triangle PQR, find the value of \[\alpha \]
A)
\[50{}^\circ \] done
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B)
\[65{}^\circ \] done
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C)
\[80{}^\circ \] done
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D)
\[100{}^\circ \] done
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E)
None of these done
clear
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question_answer 31)
Two concentric circles with centre 0 have P, Q, R, S as the points intersection with the line l as shown in the figure. If \[\mathbf{PS}\text{ }=\text{ }\mathbf{16}\text{ }\mathbf{cm}\] and \[\mathbf{QR}\text{ }=\text{ }12 \mathbf{cm}\] then the lengths of _________
A)
PQ is 3 cm done
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B)
PR is 12 cm done
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C)
SQ is 14 cm done
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D)
RS is 4 cm done
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E)
None of these done
clear
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question_answer 32)
PQ and RS are two chords of the circle such that \[\mathbf{PQ}\text{ }=\text{ }\mathbf{8}\text{ }\mathbf{cm}\] and \[\mathbf{RS}\text{ }=\text{ }\mathbf{16}\] \[\mathbf{PQ}\text{ }\parallel \text{ }\mathbf{RS}\]. If the distance between PQ and RS is 4 cm, then _________
A)
\[ON\text{ }=\text{ }5\text{ }cm\] done
clear
B)
\[radius\text{ }=\text{ }4\text{ }cm\] done
clear
C)
\[OM=8.5\,cm\] done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer 33)
In the shown figure, a circle with centre O and radius r is given with chords PQ and RS. Based on this information, which among the following statements is incorrect?
A)
If \[PQ\text{ }=\text{ }RS\] then\[\angle POQ\text{ }=\text{ }\angle ROS\]. done
clear
B)
If \[PQ<RS\] then PQ is nearer to the circle than RS. done
clear
C)
If\[PQ=\text{ }RS\], then both are equidistant from the centre of the circle 0 done
clear
D)
The perpendicular bisector of both the chords of the circle will pass through its centre. done
clear
E)
None of these done
clear
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question_answer 34)
In the shown figure, AB is a diameter of the circle with centre O. If AC is a chord and OM is perpendicular on it where \[\mathbf{AB}\text{ }=\text{ }\mathbf{13}\text{ }\mathbf{cm}\] and \[\mathbf{BC}\text{ }=\text{ }\mathbf{5}\text{ }\mathbf{cm}\], then the length of OM is ________
A)
6.25 cm done
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B)
3.25 cm done
clear
C)
3.5 cm done
clear
D)
2.5 cm done
clear
E)
None of these done
clear
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question_answer 35)
Two circles with centres O and O? and of radii 6 cm and 4 cm touch each other internally. If the perpendicular bisector of line segment OO? meets the bigger circle in M and N, then the length of MN is _______
A)
1cm done
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B)
\[2\sqrt{35\text{ }}cm\] done
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C)
\[3\sqrt{5\text{ }}cm\] done
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D)
\[\sqrt{35\text{ }}cm\] done
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E)
None of these done
clear
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question_answer 36)
The radius of the circle, in which an equilateral triangle of side 16 cm is inscribed, is _______
A)
\[\frac{8\sqrt{3}}{3}\]cm done
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B)
\[\frac{16\sqrt{3}}{3}\text{ cm}\] done
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C)
\[8\sqrt{3}\text{ cm}\] done
clear
D)
\[\frac{2\sqrt{3}}{3}\text{ cm}\] done
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E)
None of these done
clear
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question_answer 37)
In the shown figure, AD and BC are two chords of the circle with centre O, intersecting at E and \[\mathbf{AE}\text{ }=\text{ }\mathbf{6}\text{ }\mathbf{cm}\],\[\mathbf{BE}\text{ }=\text{ }\mathbf{5}\text{ }\mathbf{cm}\]. Find the value of _______\[\frac{EC+ED}{EC-ED}\].
A)
11 done
clear
B)
5 done
clear
C)
8 done
clear
D)
10 done
clear
E)
None of these done
clear
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question_answer 38)
A circle with centre O is inscribed in a quadrilateral PQRS as shown in the figure. Which one of the following statements is /are true?
(i) \[\angle POS\text{ }+\text{ }\angle QOR\text{ }=\text{ }180{}^\circ \]
(ii) \[\angle POQ\], and \[\angle ROS\] are complementary.
(iii) OP, OQ, OR and OS are the angle bisectors of \[\angle P,\text{ }\angle Q,\text{ }\angle R\text{ }and\text{ }\angle S\] respectively.
A)
both (i) and (ii) done
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B)
both (i) and (iii) done
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C)
both (ii) and (iii) done
clear
D)
All (i), (ii) and (iii) done
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E)
None of these done
clear
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question_answer 39)
In the shown figure, O is the centre of the circle and PT is a tangent to the circle at P. If\[\angle \mathbf{RPT}\text{ }=\text{ }\mathbf{15}{}^\circ \text{ }\mathbf{and}\text{ }\angle \mathbf{PTR}\text{ }=\text{ }\mathbf{65}{}^\circ \], then find the value of\[\angle \mathbf{PQO}\].
A)
\[15{}^\circ \] done
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B)
\[10{}^\circ \] done
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C)
\[25{}^\circ \] done
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D)
\[30{}^\circ \] done
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E)
None of these done
clear
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question_answer 40)
P, Q and R are on ML, NL and MN of the equilateral triangle MLN respectively. If \[\mathbf{MP}:\text{ }\mathbf{PL}\text{ }=\text{ }\mathbf{NQ}:\text{ }\mathbf{QL}\text{ }=\text{ }\mathbf{1}:\text{ }\mathbf{2}\] and G is the centroid of the triangle PQL and S is the mid-point of MN. Find LG: GS.
A)
\[2:3\] done
clear
B)
\[4:5\] done
clear
C)
\[3:4\] done
clear
D)
\[1:3\] done
clear
E)
None of these done
clear
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