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Case Study : Raghav is preparing for his forthcoming assignment on triangles. For which, he is solving the worksheet given by his teacher and comes across the following questions. He finds it difficult to answer and so he decides to get them clear by his teacher in the school by the next day. Answer these questions to test your understanding.

Which of the following is possible in a ΔPQR?

A PQ – QR > PR
B PQ + QR < PR
C PQ – QR < PR
D PQ + PR < QR

Case Study : Rohit, Arjun, Seema, Palak and Roshni were playing with some chits. In every chit, some numbers are written. They picked the chits one by one.
Based on the above information, answer the following questions.

If Arjun picked 2341178, Palak picked 1348321, Rohit picked 2178342, Roshni picked 1839753 and Seema picked 2454371, then who picked the second greatest number and the second smallest number?

A Arjun, Roshni
B Seema Palak
C Arjun, Palak
D Rohit, Roshni

Case Study : Anny and John were two friends who lived in USA. Once they visited India. Anny knew about Indian System of Numeration but John didn't know. John asked some questions to Anny about Indian and International System of Numeration.

The questions are listed below. Answer them.
Indian System of Numeration?

A Eighteen crore twenty two lakh three
B One crore eighty two lakh twenty thousand three
C Eighteen crore two lakh twenty thousand three
D One crore eight lakh twenty two thousand three

Passage-III : An equation involving trigonometric ratios of an angle θ is a trigonometric identity. If the L.H.S. of the equation = R.H.S. of the equation for all values of θ such that
sin θ sin (60° - θ) sin (60° + θ) =
cos θ cos (60° - θ) cos (60° + θ) =
The value of sin 20° sin 40° sin 60° sin 80° is equal to

A
B
C
D

In this section each question has two matching lists. Choices for the correct combination of elements from List-I and List-II are given as options (A),(B), (C) and (D) out of which one is correct.
In ΔABC, right angled at B and , then match the List

List-I	List-II
(P)	(1)
(Q) sin C + cos C + sinB	(2) 0
(R) sec2 A - cosec2 A + 2	(3)
(S) ∠ A - ∠ C	(4) 2

Case Study : In a classroom activity, teacher taught students about how to form numbers and then teacher writes all the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 on the board and asks some questions to the students.

Based on the above information, answer the following questions.
What is the smallest 7-digit odd number formed by the digits 2, 3, 1, 6, and 5 using each digit atleast once?

A 1112365
B 1123561
C 1235611
D 1111111

Only one of the four options is correct. Write the correct one.
Number of integers lying between –1 and 1 is

A1
B2
C3
D0

Case Study : Anuj was sitting in his garden with his father. There was one mango tree and one neem tree situated at each side of the garden. Anuj observed that on mango tree, honey bees have started making their house with 3 beautiful hexagonal patterns in one hour while his father observed that on neem tree, another honey bees also have started making their house with 5 hexagonal patterns in one hour.

Based on the above information, answer the following questions.
Number of hexagonal patterns made by honey bees on mango tree at the rate of power, raised to 5 after 5 hours, is

A 9
B 27
C 81
D 243

Case Study : One day, Ankur visited the library with his friends. He observed that 5 books and 5 paper sheets are placed in a stock. Each book has thickness 20 mm and each sheet has thickness 0.016 mm written on their back side.

Based on the above information, answer the following questions.
The total thickness of stock in standard form, is

A 10.08 × 10² mm
B 100.08 × 10² mm
C 1.0008 × 10² mm
D None of these

PASSAGE-I : and
where x and x are positive real numbers.
If andthen x⁴ + y⁴ =

A1538
B1200
C1048
D149