Question : If $\cos x+\sec x=\frac{7}{2 \sqrt{3}}$, then the value of $\cos ^2 x+\sec ^2 x$ will be_____.

Option 1: $\frac{15}{12}$

Option 2: $\frac{10}{12}$

Option 3: $\frac{25}{10}$

Option 4: $\frac{25}{12}$

Question : Directions: In this question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) which may improve the sentence. Choose the correct alternative. In case, no improvement is needed your answer is (4).

Come quickly if you will catch the train.

(1) you want to

(2) you shall

(3) you could

(4) No Improvement

Option 1: (1)

Option 2: (2)

Option 3: (3)

Option 4: (4)

Question : Directions: Select the Venn diagram that best represents the relationship between the following classes.
Insects, Animals, Poisonous

Option 1:

Option 2:

Option 3:

Option 4:

Question : Comprehension:
Read the given passage and answer the questions that follow.
Her name was Sulekha, but since her childhood, everyone had been calling her Bholi, the simpleton. She was the fourth daughter of Ramlal. When she was ten months old, she had fallen off the cot on her head and perhaps it had damaged some part of her brain. That was why she remained a backward child and came to be known as Bholi, the simpleton. At birth, the child was very fair and pretty. But when she was two years old, she had an attack of smallpox. Only the eyes were saved, but the entire body was permanently disfigured by deep black pockmarks. Little Sulekha could not speak till she was five as she was a slow learner, and when at last she learned to speak, she stammered. The other children often made fun of her and mimicked her. As a result, she talked very little. Ramlal had seven children - three sons and four daughters, and the youngest of them was Bholi. It was a prosperous farmer's household and there was plenty to eat and drink. All the children except Bholi were healthy and strong. The sons had been sent to the city to study in schools and later in colleges. Of the daughters, Radha, the eldest, had already been married. The second daughter Mangla's marriage had also been settled, and when that was done, Ramlal would think of the third, Champa. They were good-looking, healthy girls, and it was not difficult to find bridegrooms for them. But Ramlal was worried about Bholi. She had neither good looks nor intelligence. From her very childhood, Bholi was neglected at home. She was seven years old when Mangla was married. The same year a primary school for girls was opened in their village. The Tehsildar sahib came to perform its opening ceremony. He said to Ramlal, "As a revenue official you are the representative of the government in the village and so you must set an example to the villagers. You must send your daughters to school." That night when Ramlal consulted his wife, she cried, "Are you crazy? If girls go to school, who will marry them?" But Ramlal had not the courage to disobey the Tehsildar. At last, his wife said, "I will tell you what to do. Send Bholi to school. As it is, there is little chance of her getting married, with her ugly face and lack of sense. Let the teachers at school worry about her."

Question:
Who was invited to inaugurate the girls' school?

Option 1: Tehsildar

Option 2: Revenue official

Option 3: Village head

Option 4: School Headmaster

Question : For what value of k will the expression x⁶ – 18x³ + k be a perfect square?

Option 1: –9

Option 2: –81

Option 3: 9

Option 4: 81

Question : Direction: A bar graph showing the heights of six mountain peaks is given below. Study the bar graph and answer the question.

When the heights of the given peaks are written in ascending order, what is the average of the middle two peaks?

Option 1: 7950 m

Option 2: 7560 m

Option 3: 7650 m

Option 4: 7850 m

Question : Select the correct direct form of the given sentence.

She asked her mother why she was so upset that day.

Option 1: She said to her mother, “Why you are so upset today?”

Option 2: She said to her mother, “Why were you so upset that day?”

Option 3: She said to her mother, “Why are you so upset today?”

Option 4: She said to her mother, “Are you upset today?”

Question : $3\left[\mathrm{a}-\frac{1}{\mathrm{a}}\right]+\left[\mathrm{a}-\frac{1}{\mathrm{a}}\right]^3=?$

Option 1: $a^2-\frac{1}{a^3}$

Option 2: $a^3-\frac{1}{a^3}$

Option 3: $a^3+\frac{1}{a^3}$

Option 4: $a^2-\frac{1}{a^2}$

Question : Directions: If A – B means that A is the brother of B, A + B means that A is the sister of B, and A ÷ B means that A is the father of B, then which of the following expressions shows that P is the paternal uncle of R?

Option 1: P + Q ÷ R

Option 2: P ÷ Q – R

Option 3: P – Q ÷ R

Option 4: P – Q + R

Question : Directions: Which two signs should be interchanged to make the given equation correct?
588 ÷ 28 × 32 + 72 – 160 = 760

Option 1: – and +

Option 2: ÷ and –

Option 3: + and ×

Option 4: ÷ and +