Question 1 |

An opaque pyramid (shown below), with a square base and isosceles faces, is
suspended in the path of a parallel beam of light, such that its shadow is cast on a
screen oriented perpendicular to the direction of the light beam. The pyramid can
be reoriented in any direction within the light beam. Under these conditions, which
one of the shadows P, Q, R, and S is NOT possible?

P | |

Q | |

R | |

S |

Question 2 |

How many pairs of sets (S,T) are possible among the subsets of {1, 2, 3, 4, 5, 6}
that satisfy the condition that S is a subset of T?

729 | |

728 | |

665 | |

664 |

Question 2 Explanation:

Take one element {1}

T=\phi ,S=\phi \rightarrow (\phi, \phi ) \Rightarrow 1\; pair

T=1,S=\phi \rightarrow (\phi, 1 ),(1,1) \Rightarrow 2\; pair

For 1 element total pair = 3^1

Similarly

For 2 element total pair = 3^2

For 3 element total pair = 3^3

For 4 element total pair = 3^4

For 5 element total pair = 3^5

For 6 element total pair = 3^6=729

T=\phi ,S=\phi \rightarrow (\phi, \phi ) \Rightarrow 1\; pair

T=1,S=\phi \rightarrow (\phi, 1 ),(1,1) \Rightarrow 2\; pair

For 1 element total pair = 3^1

Similarly

For 2 element total pair = 3^2

For 3 element total pair = 3^3

For 4 element total pair = 3^4

For 5 element total pair = 3^5

For 6 element total pair = 3^6=729

Question 3 |

Consider the following inequalities

p^2-4q \lt 4

3p+2q \lt 6

where p and q are positive integers.

The value of (p+q) is _______.

p^2-4q \lt 4

3p+2q \lt 6

where p and q are positive integers.

The value of (p+q) is _______.

2 | |

1 | |

3 | |

4 |

Question 3 Explanation:

\begin{aligned}
p^2-4q &\lt 4 \\
p^2-4&\ lt 4q \;\;...(i)\\
3p+2Q& \lt 6 \\
6p-12 &\lt -4q\;\;...(ii)\\
&\text{by equation (i) + (ii)} \\
p^2+6p-16 &\lt 0 \\
(p+8)(p-2)& \lt 0 \\
\therefore \; p&\in (-8,2)
\end{aligned}

Given p is positive integer

\therefore \;p=1

Now, from equation (i), 1-4 \lt 4q

q \gt \frac{-3}{4}

from equation (ii),

q \lt 3/2

\therefore \; \frac{-3}{4} \lt q \lt \frac{3}{2}

Given q is positive integer

\therefore \;\; q=1

Thus p + q = 1+1 = 2

Given p is positive integer

\therefore \;p=1

Now, from equation (i), 1-4 \lt 4q

q \gt \frac{-3}{4}

from equation (ii),

q \lt 3/2

\therefore \; \frac{-3}{4} \lt q \lt \frac{3}{2}

Given q is positive integer

\therefore \;\; q=1

Thus p + q = 1+1 = 2

Question 4 |

The minute-hand and second-hand of a clock cross each other _______ times
between 09:15:00 AM and 09:45:00 AM on a day.

30 | |

15 | |

29 | |

31 |

Question 4 Explanation:

After 09:15:00 AM every minute, minute and second
hand cross each other once (1) times.

So, 09:16:00 to 09:45:00 minute hand and second hand cross each other 30 times.

So, 09:16:00 to 09:45:00 minute hand and second hand cross each other 30 times.

Question 5 |

A certain country has 504 universities and 25951 colleges. These are categorised into
Grades I, II, and III as shown in the given pie charts.

What is the percentage, correct to one decimal place, of higher education institutions (colleges and universities) that fall into Grade III?

What is the percentage, correct to one decimal place, of higher education institutions (colleges and universities) that fall into Grade III?

22.7 | |

23.7 | |

15 | |

66.8 |

Question 5 Explanation:

Percentage of grade III

\frac{ \text{7\% of 504 + 23 \% of 25951} }{504 + 25951}=22.7 \%

\frac{ \text{7\% of 504 + 23 \% of 25951} }{504 + 25951}=22.7 \%

There are 5 questions to complete.

Answer to 113 question is option b plz correct it

Thank You Hania,

We have updated the answer.

for question 22 the options dosent has the right option it shall 80/81 rather than 81/80

mistake in question 25 , as per solution the data for april second row (second row last column) should be 70 but here its given as 170

ques no. 65 ans should be “c”…..

We have updated the Answer as (C).