22
Q:

# If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.

 A) 20 B) 30 C) 40 D) 50

Explanation:

Let x and y be the length and breadth of the rectangle respectively.
Then, x - 4 = y + 3 or x - y = 7 ----(i)
Area of the rectangle =xy; Area of the square = (x - 4) (y + 3)
(x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(ii)
Solving (i) and (ii), we get x = 16 and y = 9.
Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.

Q:

A, B and C are three points on a circle such that the angles subtended by the chord AB and AC at the centre O are 110 and 130 deg, respectively. Then the value of angle BAC is:

 A) 70 deg B) 75 deg C) 60 deg D) 65 deg

Explanation:

0 27
Q:

In ABC, MN BC, the area of quadrilateral MBCN=130 sqcm. If AN : NC = 4 : 5, then the area of MAN is: A) 40 sq.cm B) 45 sq.cm C) 32 sq.cm D) 65 sq.cm

Explanation:

0 14
Q:

The radius of a circular garden is 42 m. The distance (in m) covered by running 8 rounds around it, is:

 A) 2112 B) 1124 C) 3248 D) 4262

Explanation:

0 13
Q:

Two chords AB and CD of a circle when produced, meet at a point P outside the circle. If AB = 6 cm, PB = 5 cm, PD = 4 cm, then CD is equalto:

 A) 7.5 cm B) 8.25 cm C) 9.75 cm D) 7.75 cm

Explanation:

0 34
Q:

In ABC, AD is a median and is a point on AD such that AP : PD = 3 : 4. Then ar( BPD) : ar( ABC)is equal to:

 A) 2 : 7 B) 4 : 7 C) 2 : 5 D) 1 : 3

Explanation:

0 25
Q:

The arc ABC of a circle with centre O subtends 132 at the centre. The chord AB is extended to the point P. The angle CBP is equal to

 A) 48 deg B) 66 deg C) 76 deg D) 68 deg

Explanation:

0 31
Q:

In a circle of radius 13 cm, a chord is at a distance of 5cm from its center. What is the length of the chord?

 A) 24 cm B) 18 cm C) 12 cm D) 20 cm

Explanation:

1 53
Q:

In ABC,P is a point on BC such that BP : PC = 3 : 4 and Q is the midpoint of AP. Then ar( ABQ): ar( ABC) is equal to:

 A) 3 : 8 B) 2 : 7 C) 1 : 4 D) 3 : 14