Question : Let $0^{\circ}<\theta<90^{\circ}$, $\left(1+\cot ^2 \theta\right)\left(1+\tan ^2 \theta\right) × (\sin \theta-\operatorname{cosec} \theta)(\cos \theta-\sec \theta)$ is equal to:

Option 1: $ \sin \theta+\cos \theta$

Option 2: $\sin \theta \cos \theta$

Option 3: $\sec \theta \operatorname{cosec} \theta$

Option 4: $\sec \theta+\operatorname{cosec} \theta$

Question : Sentences of a paragraph are given below in jumbled order. Arrange the sentences in the correct order to form a meaningful and coherent paragraph.
A. But, while the court's action solved one problem, it created another and because of the closure, many workers lost their jobs.
B. For instance, the courts directed industries in residential areas in Delhi to close down or shift out of the city.
C. In recent years, while the courts have come out with strong orders on environmental issues, these have sometimes affected people's livelihoods adversely.
D. Several of these industries were polluting the neighbourhood and discharge from these industries was polluting the river Yamuna because they had been set up without following the rules.

Option 1: CBDA

Option 2: BDCA

Option 3: CDAB

Option 4: BCAD

Question : If $\cos \theta=\frac{12}{13}$, then the value of $\frac{\sin \theta(1-\tan \theta)}{\tan \theta(1+\operatorname{cosec} \theta)}$ is:

Option 1: $\frac{25}{78}$

Option 2: $\frac{35}{234}$

Option 3: $\frac{35}{108}$

Option 4: $\frac{25}{156}$

Question : Directions: Study the given pattern carefully and select the number that can replace the question mark (?) in it.
First row – 15, 11, 43
Second row – 13, 8, 48
Third row – 9, 7, ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying, etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is NOT allowed.)

Option 1: 23

Option 2: 30

Option 3: 27

Option 4: 26

Question : Directions: A # B means A is the brother of B. A @ B means A is the daughter of B. A & B means A is the husband of B and A % B means A is the wife of B. If D @ N @ H & Y @ F % V, then how is N related to F?

Option 1: Daughter's daughter

Option 2: Daughter

Option 3: Sister's daughter

Option 4: Son's wife

Question : Comprehension:
In the given passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each number.

In August every year, thousands of twins descend on a town in Ohio called Twinsburg, named by identical twin brothers 1.________ two centuries ago. The Twins Days Festival is a three-day 2.________ consisting of talent shows and look-alike 3.__________ that has become one of the world's 4.___________ gatherings of twins. There have been 5.____________festivals in Nigeria, a country where 1 in 22 births to the Yoruba people 6.____________ twins, identical or fraternal, which is a much higher 7. ___________than anywhere else in the world. This has been 8.___________ to the eating of yams, but the theory is 9.__________ Biomedical researchers attend these events, regarding them as a 10.____________ opportunity to conduct surveys and experiments.

Question:
Select the most appropriate option to fill in the blank No. 8.

Option 1: attributed

Option 2: indicated

Option 3: dedicated

Option 4: distributed

Question : Directions: Select the option that represents the correct order of the given words as they would appear in the English dictionary.
1. Warriors
2. Warehouse
3. Warcraft
4. Warranty
5. Wardrobe
6. Wardenship

Option 1: 3, 6, 5, 2, 1, 4

Option 2: 3, 5, 6, 2, 1, 4

Option 3: 3, 5, 6, 2, 4, 1

Option 4: 3, 6, 5, 2, 4, 1

Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer.

He completed all projects on time except for two of them which he found too difficult to ________.

Option 1: Embrace

Option 2: Comprehend

Option 3: Acknowledge

Option 4: Discern

Question : The value of $\operatorname{cosec}^{2}60°+\sec^{2}60°– \cot^{2}60°+\tan^{2}30°$ will be:

Option 1: $5$

Option 2: $5\frac{1}{2}$

Option 3: $5\frac{1}{3}$

Option 4: $5\frac{2}{3}$

Question : Directions: Select the figure from among the given options that can replace the question mark (?) in the following series.

Option 1:

Option 2:

Option 3:

Option 4: