A) 14.69 cm | B) 15.69 cm |

C) 18.65 cm | D) 16.42 cm |

Explanation:

Draw the two chords as shown in the figure. Let O be the center of the circle. Draw OC

perpendicular to both chords. That divides the two chords in half.

So CD = 10 and AB = 14. Draw radii OA and OD, both equal to radius r.

We are given that BC = 5, the distance between the two chords. Let

OB = x.

We use the Pythagorean theorem on right triangle ABO

AO² = AB² + OB²

r² = 14² + x²

We use the Pythagorean theorem on right triangle DCO

DO² = CD² + OC²

We see that OC = OB+BC = x+5, so

r² = 10² + (x+5)²

So we have a system of two equations:

r² = 14² + x²

r² = 10² + (x+5)²

Since both left sides equal r², set the right sides

equal to each other.

14² + x² = 10² + (x+5)²

196 + x² = 100 + x² + 10x + 25

196 = 125 + 10x

71 = 10x

7.1 = x

r² = 14² + x²

r² = 196 + (7.1)²

r² = 196 + 50.41

r² = 246.41

r = √246.41

r = 15.69745202 cm

A) 23 | B) 24 |

C) 25 | D) 26 |

Explanation:

Let, Hema attempted 'k' sum correctly, then

k x 3 -2 x(35-k) = 60

5k = 130

k = 26

so 26 correct sums.

A) 35 c | B) 36 c |

C) 34 c | D) 32 c |

Explanation:

Monday + Tuesday + Wednesday = 37 x 3 -----------(1)

Tuesday + Wednesday + Thursday = 34 x 3---------(2)

Thursday = 4/5 of Monday ------------------(3)

subtract eqn (1) from (2) we get,

Thursday - Monday = -9

=> Monday - Thursday = 9.......(4)

From (3) & (4), we get

So,Thursday = 36 C

A) 88572 | B) 77854 |

C) 99584 | D) 55654 |

Explanation:

Given a secret is told to 3 persons in 3 minutes.

And if the process continues with each person saying 3 other persons,

In 30 minutes => the rocess for 10 times because each person time is 3 minutes.

Required number of persons =

Now it forms a geometric progression,

Sum to n terms is S=

Here a = 3, r = 3

S =

=> 59048 x 3 /2

= 88572.

A) 175 | B) 145 |

C) 165 | D) 135 |

Explanation:

Let the number of males be 'M'

Let the number of females be 'F'

From the given conditions,

(F-15)=2M.....(i)

F=5(M-45).....(ii)

By solving the equations (1) & (2) we get M = 80

Then substitute M = 80 in (1)

F = 2M + 15

F = 2 x 80 + 15

=> F = 175

Therefore, number of males = 80 and females = 175 in the party.