SSC CGL Tier l 2023 Question Paper Shift 3 (July 17th)

If a $$\cot \theta + b \cosec \theta = p$$ and $$b \cot \theta + a \cosec \theta = q$$ then $$p^{2} - q^{2}$$ is equal to __________.

What is the value of the given expression?
$$(a + b + c)^{2}-a^{2}-b^{2}- c^{2}$$

Study the given table and answer the question that follows.
The table shows the classification of 100 students based on the marks obtained by them in Statistics and Mathematics in an examination out of 50.

If at least 60% marks in Mathematics are required for pursuing higher studies in Mathematics, then how many students will be eligible to pursue higher studies in Mathematics?

After allowing a discount of 15%, the value of a washing machine is ₹29,750. If no discount is allowed, then the shopkeeper gains 12%. The cost price of the washing machine is:

Pratima and Diksha can complete a typing work separately in 10 hours and 15 hours, respectively. After typing for 4 hours alone, Pratima leaves the work. In how many hours will Diksha complete the remaining typing work?

What is the volume of a cube if the perimeter of one face of the cube is 40 cm?

The following table gives the information of the number of students (in thousands) placed in five different companies during six different years.

What is the difference (in thousands) between the students placed in all companies in the year 2014 and 2012?

One quality of rice at ₹45 per kg is mixed with another quality at a certain rate in the ratio of 3 : 2. If the mixture so formed is worth ₹50 per kg, what is the rate per kg of the second quality of rice?

What is the radius of circle which circumscribes the triangle ABC whose sides are 16, 30, 34 units, respectively?

How many of the following numbers are divisible by 132?
660, 754, 924, 1452, 1526, 1980, 2045 and 2170