0
Q:

# $\inline \frac{23\times 12+49\times 15}{(31)^{2}+50}=?$

 A) 0.5 B) 1 C) 2 D) 3

Explanation:

$\inline \frac{23\times 12+49\times 15}{(31)^{2}+50}= \frac{276+735}{961+50}=\frac{1011}{1011}=1$

Q:

Two parallel chords on the same side of the centre of a circle are 5 cm apart. If the chords are 20 and 28 cm long, what is the radius of the circle?

 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

1 15
Q:

Hemavathi gets 3 marks for each right sum and loses 2 marks for each wrong sum. He attempts 35 sums and obtains 60 marks. The number of sums attempted correctly is ?

 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.

1 4
Q:

The average temperature of Monday to Wednesday was 37 C and of Tuesday to Thursday was 34 C. If the temperature on Thursday was 4/5 th of that of Monday, the temperature on Thursday was ?

 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

3 18
Q:

A secret can be told to only 3 persons in 3 minutes. Each person in turn tells 3 other persons in the next 3 minutes and the processes continues accordingly. In 30 minutes how many persons can be told this secret in this way ?

 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 = $\inline \fn_jvn \small 3+3^{2}+3^{3}+3^{4}+.....+3^{9}+3^{10}$

Now it forms a geometric progression,

Sum to n terms is S= $\inline&space;\fn_jvn&space;\small&space;\frac{a(r^{n}-1)}{r-1}$

Here a = 3, r = 3

S = $\inline \fn_jvn \small \frac{3(3^{10}-1)}{3-1}$
=> 59048 x 3 /2

= 88572.

3 22
Q:

In a party there are male and female members. If 15 female quit then the number of females will become double the number of males. If 45 males quit no. of female becomes five times the number of males. Find the number of females ?

 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.