1. Find the 10th term of the AP: 3, 7, 11, 15, ... (F) (a) 35 (b) 37 (c) 39 (d) 41 2. Find the sum of the first 20 terms of the AP: 2, 5, 8, 11, ... (F) (a) 590 (b) 600 (c) 610 (d) 620 3. Find the 6th term of the GP: 2, 6, 18, 54, ... (F) (a) 450 (b) 468 (c) 486 (d) 500 4. Find the sum of the GP 3, 6, 12, 24, ... up to 6 terms. (F) (a) 180 (b) 185 (c) 189 (d) 195 5. The sum of the first n natural numbers is 210. Find n. (F) (a) 18 (b) 19 (c) 20 (d) 21 6. Find the sum of

1. Find the length of the median to the hypotenuse of a right triangle with legs 6 cm and 8 cm. (A) (a) 4 cm (b) 4.5 cm (c) 5 cm (d) 5.5 cm 2. Two tangents are drawn from an external point P to a circle with centre O, touching it at points A and B. If angle APB = 60°, find angle AOB. (A) (a) 100° (b) 110° (c) 120° (d) 130° 3. In triangle ABC, angle A = 90°, and AD is the altitude to BC. If BD = 4 and DC = 9, find AD. (A) (a) 5 (b) 5.5 (c) 6 (d) 6.5 4. Find the length of

1. [CAT 2021, Slot 1] A circle of diameter 8 inches is inscribed in a triangle ABC where angle ABC = 90°. If BC = 10 inches, find the area of the triangle (in square inches). (P) (a) 100 (b) 110 (c) 120 (d) 130 2. [CAT 2023, Slot 1] In a right-angled triangle ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are two points on BC such that the areas of triangles ABP, ABQ, and ABC are in arithmetic progression. If the area of triangle ABC is 1.5 times the area of

1. Find the sum of interior angles of a hexagon. (F) (a) 540° (b) 600° (c) 720° (d) 900° 2. In a triangle, the angles are in the ratio 2:3:4. Find the largest angle. (F) (a) 60° (b) 70° (c) 80° (d) 90° 3. Find the length of the hypotenuse of a right triangle with legs 9 cm and 12 cm. (F) (a) 13 cm (b) 14 cm (c) 15 cm (d) 16 cm 4. Two triangles are similar with a ratio of corresponding sides 3:5. Find the ratio of their areas. (F) (a) 3:5 (b) 6:10 (c) 9:25 (d) 9:15 5. Find

Q1. A trader has 100 kg of rice, part of which he sells at a profit of 10% and the rest at a loss of 5%. If his overall profit on the whole 100 kg is 4%, find the ratio of the quantities sold at profit and at loss. (A) (a) 2:3 (b) 3:2 (c) 1:2 (d) 4:1 Q2. A shopkeeper buys two grades of rice at ₹40/kg and ₹60/kg, mixes them, and sells the mixture at ₹57.50/kg, earning a profit of 15%. Find the ratio in which the two grades were mixed. (A) (a) 1:1 (b) 2:1 (c) 1:2 (d) 3:2 Q3.

Q1. [CAT 2025] A mobile phone was sold at a loss of 5%. Had it been sold for ₹90 more, the seller would have made a profit of 1%. Find the cost price of the phone. (P) (a) ₹1,200 (b) ₹1,350 (c) ₹1,500 (d) ₹1,650 Q2. [CAT 2020, Slot 1] A person spent ₹50,000 to buy a desktop computer and a laptop computer. He sold the desktop at a 20% profit and the laptop at a 10% loss. If overall he made a 2% profit, find the purchase price of the desktop. (P) (a) ₹15,000 (b) ₹18,000 (c)

1. A shopkeeper buys an item for ₹450 and sells it for ₹540. Find the profit percentage. (F) (a) 15% (b) 18% (c) 20% (d) 25% 2. A man sells a table at a loss of 8%. If he had sold it for ₹120 more, he would have gained 4%. Find the cost price. (F) (a) ₹800 (b) ₹900 (c) ₹1,000 (d) ₹1,200 3. By selling a pen for ₹90, a shopkeeper gains 20%. Find the cost price. (F) (a) ₹70 (b) ₹72 (c) ₹75 (d) ₹80 4. A trader marks his goods 40% above cost price and allows a discount of 10%.

1. Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works every day. Anu works only on alternate days starting from the first day, while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is [CAT 2021, Slot 1] (a) 8 (b) 6 (c) 5 (d) 7 2. Amar, Akbar and Anthony are working on a project. Working together, Amar and Akbar can complete the project in 1 year, Akbar and

Q1. Renu would take 15 days working 4 hours per day to complete a certain task, whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work is [CAT 2024, Slot 1] (TITA – enter the numeric answer; no

1. Two workers, A and B, can finish a job in 15 days and 20 days respectively. If they work together for 4 days, what fraction of the job will still remain unfinished? (F) (a) 7/15 (b) 8/15 (c) 9/20 (d) 11/20 2. A can lay railway track between two stations in 16 days, while B can do the same in 12 days. With the help of C, they complete the work in just 4 days. How long would C alone take to finish the job? (F) (a) 9 days (b) 8 days (c) 10 days (d) 12 days 3. A, B, and C ca

1. A bus starts at 9 am and follows a fixed route every day. One day, it traveled at a constant speed of 60 km/h and reached its destination 3.5 hours later than its scheduled arrival time. Next day, it traveled two-thirds of its route in one-third of its total scheduled travel time, and the remaining part of the route at 40 km/h to reach just on time. The scheduled arrival time of the bus is [CAT 2024, Slot 2] (a) 7 pm (b) 9 pm (c) 10:30 pm (d) 7:30 pm 2. A boat takes 2 hou

1. Two places A and B are 45 km apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km/h, is [CAT 2024, Slot 1] (a) 16 (b) 12 (c) 18 (d) 14 2. A train travelled a certain distance at a uniform speed. Had the speed been 6 km/h more, it would have needed 4 hours less. Had

1. Convert a speed of 90 km/h into metres per second. (F) (a) 20 m/s (b) 25 m/s (c) 30 m/s (d) 18 m/s 2. A train 150 m long crosses a pole in 15 seconds. Find its speed in km/h. (F) (a) 30 km/h (b) 32 km/h (c) 36 km/h (d) 40 km/h 3. A car travels 60 km at 30 km/h and returns the same distance at 60 km/h. Find its average speed for the entire journey. (R) (a) 40 km/h (b) 45 km/h (c) 42 km/h (d) 36 km/h 4. Walking at 5 km/h, a man reaches his office 6 minutes late; walking a