Question : In a test consisting of 120 questions, Anuradha answered 65% of the first 60 questions correctly. What percentage of the remaining questions does she need to answer correctly to score 75% in the test?

Option 1: 80

Option 2: 85

Option 3: 84

Option 4: 90

Question : The value of $\frac{\sin ^2 30^{\circ}+\cos ^2 60^{\circ}+\sec 45^{\circ} × \sin 45^{\circ}}{\sec 60^{\circ}+{\text{cosec}} 30^{\circ}}$ is:

Option 1: $\frac{1}{4}$

Option 2: $-\frac{3}{8}$

Option 3: $\frac{3}{8}$

Option 4: $-\frac{1}{4}$

Question : If $a-\frac{1}{a-5}=10$, then the value of $(a-5)^3-\frac{1}{(a-5)^3}$ is:

Option 1: 140

Option 2: 70

Option 3: 100

Option 4: 120

Question : The HCF of $\frac{3}{4}, \frac{7}{8}$, and $\frac{13}{14}$ is:

Option 1: $\frac{1}{36}$

Option 2: $\frac{1}{56}$

Option 3: $\frac{1}{70}$

Option 4: $\frac{1}{60}$

Question : The ratio of the number of boys and girls in a school is 3 : 4 respectively. If the number of boys increases by 10% and the number of girls increases by 15%, what will be the new ratio of the number of boys to the number of girls?

Option 1: $\frac{33}{45}$

Option 2: $\frac{35}{46}$

Option 3: $\frac{33}{46}$

Option 4: $\frac{46}{33}$