Maths Mock Test

In triangle ABC, points D and E are on sides BC and AB respectively, such that angle ACB = angle DEB. If AB = 12 cm, BE = 5 cm, and BD:CD = 1:2, what is the length of BC?

A well with an inner radius of 3 m is dug 6 m deep. The soil taken out is spread evenly around it to form an embankment with a width of 2 m. What is the height of the embankment?

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

In 2020, the ratio of incomes of A and B was 5:4. In 2020 and 2021, their individual income ratios were 4:5 and 2:3, respectively. If the total income of A and B in 2021 was Rs. 7,05,600, what was B's income in 2021?

If $x = 32.5$, $y = 34.6$, and $z = 30.9$, then the value of $x^3 + y^3 + z^3 - 3xyz$ is $0.98k$. What is the value of k?

The base of a right prism is a triangle with sides 8 cm, 15 cm, and 17 cm, and its lateral surface area is 480 cm². What is the volume of the prism?

What is the value of the expression $11.4 + 22.5 \times 6/7 - 33.5 \div 9$?

In a class of 45 students, 33 1/3% are boys, and the rest are girls. The average score of the girls in Science is 66 2/3% more than that of the boys. If the average score of all students is 78, what is the average score of the girls?

A car travels at 75 km/hr. The driver sees a bus 80 m ahead moving in the same direction. After 15 seconds, the bus is 40 m behind the car. What is the speed of the bus?

Three numbers are in the ratio 1/2 : 2/3 : 3/4. If the difference between the largest and smallest number is 33, what is the HCF of the three numbers?

Simplify the expression: $(\tan \theta + \cot \theta) (\sec \theta + \tan \theta) (1 - \sin \theta)$ where $0° < \theta < 90°$.

In a medical transaction, 17 times the cost price equals 8 times the sum of the cost price and selling price. What is the gain or loss percentage?

P alone can complete a work in 18 days. P worked for 5 days, then Q joined him and together they completed the rest of the work in 6 2/5 days. How many days will Q take to complete 66 2/3% of the same work?

Rs. 5,000 is divided into two parts. The simple interest on the first part for $4\frac{1}{2}$ years at $6\frac{2}{3}%$ p.a. is double the simple interest on the second part for $2\frac{1}{4}$ years at 4% p.a. Find the ratio of the second part to the first part.

If $847 \times 385 \times 675 \times 3025 = 3^a \times 5^b \times 7^c \times 11^d$, what is the value of ab - cd?

A circle is inscribed in triangle PQR, touching the sides QR, PR, and PQ at points S, U, and T, respectively. Given PQ = (QR + 5) cm, PQ = (PR + 2) cm, and the perimeter of triangle PQR is 32 cm. What is the length of PR?

What is $\frac{1 + cos \theta - sin^2 \theta}{sin \theta (1 + cos \theta)} \times \frac{\sqrt{sec^2 \theta + cosec^2 \theta}}{tan \theta + cot \theta}$ equal to, given $0° < \theta < 90°$?

An article was sold for Rs. 716 after a discount of 10.5%. If a discount of 6.5% is given instead, for how much should the article be sold?

If the 10-digit number 75462A97B6 is divisible by 72, then what is the value of $\sqrt{8A - 4B}$?

A starts a business with Rs. 54,000. B and C join after 4 and 6 months, respectively. At the end of the year, the profit is divided among the three in the ratio 1:4:5. What is the sum of the capitals invested by B and C?