Mathematics Question for revision There will be 15 questions and timing will be 1.5 hour. 1. Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically. 2. On comparing the ratios a1/a2 , b1/b2 , c1/c2 find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident: (i) 5x – 4y + 8 = 0 7x + 6y – 9 = 0 (ii) 9x + 3y + 12 = 0 18x + 6y + 24 = 0 (iii) 6x – 3y + 10 = 0 2x – y + 9 = 0 3. Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73. 4. If the 3rd and the 9th terms of an A.P. are 4 and − 8 respectively. Which term of this A.P. is zero. 5. Which term of the A.P. 3, 15, 27, 39,.. will be 132 more than its 54th term? 6. Determine if the points (1, 5), (2, 3) and (-2, -11) are c...

Probability and Application of Trigonometry Question There will be 15 questions and timing will be 1.5 hour. 1. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red ? (ii) not red? 2. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) the queen of diamonds 3. 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one. 4. A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divis...

Trigonometry Test There will be 25 questions and timing will be 2 hour. 1. In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A (ii) sin C, cos C 2. If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B. 3. If 3 cot A = 4, check whether (1 – tan 2 A)/(1 + tan 2 A) = cos 2 A – sin 2 A or not. 4. In triangle PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P. 5. Show that : (i) tan 48° tan 23° tan 42° tan 67° = 1 (ii) cos 38° cos 52° – sin 38° sin 52° = 0 6. Prove the identities: (i) √[1 + sinA/1 – sinA] = sec A + tan A (ii) (1 + tan 2 A/1 + cot 2 A) = (1 – tan A/1 – cot A) 2 = tan 2 A 7. If sin θ + cos θ = √3, then prove that tan θ + cot θ = 1. 8. Prove that (sin A – 2 sin 3 A)/(2 cos 3 A – cos A) = tan A. 9. Prove that (1 – cos 2 A) cosec 2 A = 1 10. Prove that (sec 2 θ − 1)(cosec 2 θ − 1) = 1 11. Prove that (1 – sin θ) / (1 + sin θ) = (sec θ...

Difference between Environment , Ecology and Ecosystem Here's a simple breakdown of ecosystem, ecology, and environment: 1.Ecosystem An ecosystem is a specific area where living organisms (plants, animals, microorganisms) interact with each other and with their non-living surroundings (like soil, water, air, and sunlight).It's a system of interconnected relationships. Examples: A forest, a pond, or even a desert can be ecosystems. 2. Ecology Ecology is the scientific study of how living organisms interact with each other and their environment.It focuses on understanding relationships and processes within ecosystems. It includes topics like food chains, species distribution, and population dynamics. 3.Environment The environment refers to all the external conditions and factors—both biotic (living) and abiotic (non-living)—that influence an organism's life.It’s everything around us.The air you breathe, the water you drink, and the trees i...

Start the test Question no. 1 Suppose, ω and ω 2 are two distinct cube roots of unity different from 1. Then, what is (ω 1 - ω 2 ) 2 equal to? 3   1   -1   -3 Question no. 2 What is the argument of the complex number (−1 − i) , where i = √(−1)?   5π/4   -5π/4   3π/4 None of these Question no. 3 What is one of the square roots of 3 + 4i, where i = √(−1)? 2+i   2-i   -2 + i   -3 - i Question no. 4 Consider the following statements I. ( ω 10 +1) 7 + ω = 0 II. ( ω 105 +1) 10 = p 10 for some prime number p, where, ω ≠ 1 is a cubic root of unity. Which of the above statement(s) is/are correct? Only I   Only II   Both I and II   Neither I nor II Question no. 5 The origin and the roots of the equation z 2 + pz + q = 0 form an equilateral triangle, if p 2 = q ...

Biochemical oxygen demand Biochemical Oxygen Demand (BOD) is a way to measure how much oxygen is needed by microorganisms to break down organic material in water. Think of it as a test to see how "dirty" the water is with organic waste. The higher the BOD, the more polluted the water is, because it means there's a lot of organic matter that needs to be broken down. How does BOD affect aquatic life? High Biochemical Oxygen Demand (BOD) levels can significantly impact aquatic life. The following are: Oxygen Depletion: When BOD is high, it means there’s a lot of organic matter in the water that microorganisms need to break down. This process consumes a lot of oxygen, reducing the amount available for fish and other aquatic organisms. Stress on Aquatic Life: Low oxygen levels can stress aquatic organisms, making it difficult for them to survive. Fish, in particular, need a certain amount of dissolved oxygen to breathe. Death of Aquatic Organisms: If ...

Probability ⚫What is Probability ? ⚪ Probability is a measure of chance that tells us how likely an event is to happen. It’s always represented as a number between 0 and 1, inclusive. ⚪ In probability , Experiment is refered as action and event can be termed as the required action. ⚪ Suppose Event = E and Sample Space = S , the probability is : ⚪ If P(E) = 0 , it means it is null , happening of this event is impossible. Similarly, If P(E) = 1 , it is sure that event will happen (100% chance). ⚪ ⚪                     ⚪ Independent Probability: Probability of A when A event is independent of B (doesn't depend on B) ⚪ Conditional Probability : The probability of B event , when A events already happens (Event A and B are dependent) ⚪ Probability of happening at least one of independent event : Let P 1 , P 2 ....... P n are the probability ...