Geometry Set I(Exams > Cat > Quantitaitve Aptitude ) Questions and answers for exam Preparation

Exams > Cat > Quantitaitve Aptitude

GEOMETRY SET I MCQs

Total Questions : 110 | Page 11 of 11 pages

In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF. AE = 22, BE =16, CF = 16, CF = 16 and BF = 2. Find the length of the line joining the
mid-points of the sides AB and BC.
(CAT 1997)

4 $\sqrt{4}$
5
3.5
none of these

Discuss Question

Answer: Option B. -> 5
:
B

Option (b)

EF = AD = 8

(EADF is a rectangle)

CD = (22 – 16) = 6

So in the right angled triangle ADC, AD = 8 and CD = 6.

Therefore AC = 10

Therefore length of the line joining the mid – points of

AB and BC = $\frac{1}{2}$ (10) = 5

(length of the line joining the mid – point of two sides of a triangle is half the 3$^{rd}$

Question 102.

AB^ BC, BD^ AC and CE bisects $∠$ C, $∠$ A = 30 $^{\circ}$ . Then what is CED?
(CAT 1995)

30 $^{\circ}$
60 $^{\circ}$
45 $^{\circ}$
65 $^{\circ}$

Discuss Question

Answer: Option B. -> 60

^{\circ}

:
B

$∠$ ACB= 60

$∠$ DCE= $∠$ ECB= 30

Therefore, $∠$ CED= 60. Option (b)

Question 103.

Consider the five points comprising the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points? (CAT 1993)

Discuss Question

Answer: Option C. -> 8
:
C

The number of points will be $^5C_3$ - 2 = 8

(2 because of the 2 diagonals)

Question 104.

In the adjoining figure, points A, B, C and D lie on the circle, AD = 24 and BC = 12. What is the ratio of the area of triangle $Δ$ CBE to that of the triangle $Δ$ ADE ? (CAT 1997)

1:4
1:2
1:3
data insufficient

Discuss Question

Answer: Option A. -> 1:4
:
A

(b) In $Δ$ CBE and $Δ$ ADE

CBA = CDA

(a chord of a circle subtends equal angle an all its circumference)

Similarily BCD = BAD and BEC = AED

(opp. angles)

Therefore $Δ$ CBE $Δ$ ADE (AAA similarity rule)

Now $\frac{B C}{D A} = \frac{12}{24} = \frac{1}{2}$ Thus, ratios of areas = 1:4,

since Ratio of Areas of 2 similar triangles = Ratio of squares of the corresponding sides

Question 105.

Discuss Question

Answer: Option C. -> 93
:
C

Question 106.

Answer the questions based on the following information:
A rectangle PRSU is divided into two smaller rectangles PQTU, and QRST by the line TQ.PQ = 10cm. QR = 5 cm and Rs = 10cm. Points A, B, F are within rectangle PQTU, and points C, D, E are within the rectangle QRST. The closest pair of points among the pairs (A,C), (A,D), (A,E) (F,C), (F,E), (B,C), (B,D), (B,E) are 10√3 cm apart.
Which of the following statements is necessarily true?

The closest pair of points among the six given points cannot be (F, C).
Distance between A and B is greater than that between F and C.
The closest pair of points among the six given points is (C, D), (D, E) or (C, E).
None of the above

Discuss Question

Answer: Option A. -> The closest pair of points among the six given points cannot be (F, C).
:
A
The diagonal length of a rectancle PUSR =

5 \sqrt{13}

= 18 (approx)
Among given eight pairs the shortest distance =

10 \sqrt{3}

So, the six points A, B, F, C, D and E are near corner of rectangle PUSR.
So, (F,C) cannot be the shortest distance.

Question 107.

AB > AF > BF; CD > DE > CE; and BF = 6 $\sqrt{5}$ cm. which is the closest pair of points among all the six given points? (CAT 1999)

B ,F
C ,D
A ,B
None of these

Discuss Question

Answer: Option D. -> None of these
:
D

(d) Cannot be determined

Question 108.

ABCD is a rhombus with the diagonals AC and BD intersecting at the origin on the x y plane. The equation of the straight line AD is x + y =1. What is the equation of BC? (CAT 2000)

x + y = -1
x – y = -1
x + y = 1
None of these

Discuss Question

Answer: Option A. -> x + y = -1
:
A

Slope of line AD= -1

Hence, eqn of BC which passes through (0,-1) and (-1,0) and is parallel to x+y=1 is

(y-0)=-1(x+1)

Y=-x-1 $\Rightarrow$ x+y= -1. Option (a)

Question 109.

In triangle DEF shown below, points A, B and C are taken on DE, DF and EF respectively such that EC = AC and CF = BC. $∠$ D = 40 $^{\circ}$ then what is $∠$ ACB in degrees?(CAT 2001)

140 $^{\circ}$
70 $^{\circ}$
100 $^{\circ}$
None of these

Discuss Question

Answer: Option C. -> 100

^{\circ}

:
C

Option (c)

The angle in question is p

p+180-2x+180-2y=180 $^{\circ}$

thus p-2(x+y)= 180 $^{\circ}$ ……………..(1)

also, BDX = x+y (exterior angle= sum of 2 interior angles not adjacent to it)

x+y= 140 $^{\circ}$ ………(2)

using the 2 statements, p= 100 $^{\circ}$

Question 110.

A ladder leans against a vertical wall. The top of the ladder is 8m above the ground. When the bottom of the ladder is moved 2m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder ?
(CAT 2001)

Discuss Question

Answer: Option D. -> 17m
:
D

Option (d)