Maths Imp Mains Questions PDF

## Question 1: If P(AUB) = P(Ā∪B) = 1, and P(A) = 27/38, then find the odds against event B. ## Question 2: A vessel A contains an 80 liter mixture of spirit and water in the ratio 7:9. 20 liters of the mixture is transferred to another vessel B. Then vessel A is filled up with 20 liters of wat...

## Question 1: If P(AUB) = P(Ā∪B) = 1, and P(A) = 27/38, then find the odds against event B. ## Question 2: A vessel A contains an 80 liter mixture of spirit and water in the ratio 7:9. 20 liters of the mixture is transferred to another vessel B. Then vessel A is filled up with 20 liters of water. Then 32 liters of mixture is again transferred from vessel A to vessel B. What is the ratio of water to spirit in vessel B? ## Question 3: A and B together can complete a work in 12.5 days; B and C together can complete the same work in 18.75 days; whereas C and A together can complete the same work in 15 days. In how many days can A, B and C together complete the same work with D, who is only 40% as efficient as C? ## Question 4: Three cards are drawn from a deck of cards with replacement, one after another. What is the probability of getting a Jack on the first draw, a black card on the second draw, and an even-numbered card on the third draw? ## Question 5: There are 8 shots, out of which a person can hit 5 on target. If he fires 10 shots, what is the probability that he will hit the target twice? ## Question 6: If the inner angle of a regular polygon is equal to one-fifth of one of the inner angles of a regular decagon, then find the number of diagonals of the polygon. ## Question 7: If a cot 0 + b cosec 0 = p and b cot 0 + a cosec 0 = q then what is the value of p²-q²? ## Question 8: The base of a pyramid is an equilateral triangle of side 8 cm. Its slant edge is 24 cm. What is the total surface area (in cm²) of the pyramid?) ## Question 9: If the highest common factor (HCF) of x and y is 15, then 36x² - 81y² and 81x² - 9y² are divisible by: ## Question 10: Find the number of diagonals of a regular polygon whose sum of internal angles is 2700° ## Question 11: The product of two numbers is 1500 and their highest common factor is 10. How many such possible pairs are there? ## Question 12: A vessel contains 40 liters of milk. 4 liters of milk is drawn out and replaced by water. This process is repeated twice. How much milk is now present in the vessel? ## Question 13: The letters of the word ‘ARTICLE’ are arranged randomly. What is the probability of vowels occupying even places? ## Question 14: Find the value of the expression: 2/1x3 + 2/3x5 + 2/5x7 + .... + 2/99x101 ## Question 15: The marked price of a crockery was 15400/- rupees and a 12% discount was being given on it. Harsh bargained with the shopkeeper for a further discount and bought the crockery for 10164/- rupees. What was the further discount given by the shopkeeper? ## Question 16: In a cyclic quadrilateral ABCD, ∠DCB = 60°, side BC = 10 cm, CD = 15 cm and AD = 20 cm. DB is the diagonal of quadrilateral ABCD. If the area of ADCB is 75% of the area of ADAB, then find the length (in cm) of AB. ## Question 17: In △ABC, M is the mid-point of side AB. Point N lies inside △ABC such that CN is the angle bisector of ∠C and CN ⊥ NB. If BC = 10 cm and AC = 15 cm, then find the length of MN. ## Question 18: A shopkeeper buys 12 fans for ₹24,000. He marks up each fan 25% above its cost price. If he sells all fans with a 10% discount, then what is his total profit (in ₹)?