UP TGT 2024 Mini Mock (Math): 13

If α and β are the roots of the equation x²- 5x + 25= 0, then what is the value of α³+β³?

A shopkeeper offers 25% discount on the Marked Price Another shopkeeper offers three successive discounts of 5%, 12% and 10% on the same Marked Price. The difference between the discounts given by two shopkeepers is:

The perimeter of a circular garden is 506 m. The cost (in Rs.) of levelling it at Rs. 14/m² is:  (Take π = 22/7)

If x% of 240 is equal to 60% of (x + 450), then 20% of (x + 50) is what percentage less than 40% of x?

A large container has a 50 litre mixture of juice and water in the ratio 3 : 2. To this, a 60 litre juice and water mixture is added, that has a juice to water ratio of 2 : 1. After this, 11 litres of the solution is replaced with pure juice. What is the ratio of water to juice in the final mixture?

What will be the average of first four positive multiples of 8?

Annual production of four different types of cold drinks has been tabulated below. Which of these cold-drinks has encountered maximum percentage increment in production?

If the angles of a triangle are (x – 46) degrees, (x + 96) degrees and 8x degrees, then what is the value of 2x?

Points A and B are on a circle with centre O. Point C is o the major arc AB. If ∠OAC = 35° and ∠OBC = 45°, then what is the measure (in degree) of the angle subtended by the minor arc AB at the centre?

Find the area of a trapezium whose parallel sides are of length 15 cm and 20 cm, respectively, and whose distance between the parallel sides is 12 cm.

Find the unit digit of 4 + 9² + 4³ + 9⁴ + 4⁵ + 9⁶ + ……….. + 4⁹⁹ + 9¹⁰⁰

One card is drawn from a well shuffled deck of 52 cards. Calculate the probability that the card will be a red Ace.

What is the value of sin² 21 + sin² 69?

The H.C.F. of two numbers, each having three digits, is 17 and their L.C.M. is 714. The sum of the numbers will be: