For Basic and Standard Levels 1. The sum of two numbers is 105 ... | Filo (2024)

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Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficientsq(x)=3​x2+10x+73​

If sin3A=cos(A−26∘) where 3A is an acute angle, find the value of A.

A bag contains 5 red, 8 white and 7 black balls. A ball is drawn at random from the bag. Find the probability that the drawn ball is neither white nor black.

A man in a boat rowing away from a light house 100m high takes 2 minutes to change the angle of elevation of the top of the light house from 60∘ to 30∘. Find the speed of the boat in metres per minute. [ Use 3​=1.732]

6. The length of the minu minute hand in 5 minutes.Section - C(3.) If α and β are the zeroes of the polynomial 2x2−5x+7, then find a (3x) quadratic polynomial whose zeroes are (3α+4β) and (4α+3β)−34b. On comparing the ratio a2​a1​​,b2​b1​​ and c2​c1​​, find out whether the pair of linear equation are consistent, or inconsistent. 30. Had she got 2 marks more in M marks in Mathematics and English is the product of their marks would hathematics and 3 marks less in English, d. The altitude of a right triangle is 7cm less than its base. If the hypotenuse is 13cm, find the other two sides. If the 3dd and the 9th term of an AP are 4 and −8 respectively, which term ofthe coordinates of the points of trisection of the line segment joining (4,−1)3​ and (−2,−3)−P−175⊗2.9. Answer any 2 out of 4 questions:a. In △ PQR, right angled at Q. PR+QR=25cm and PQ=5cm) (2) values of sinP,cosP and tanP. PR−25cm and PQ−5cm. Determine theb. Prove that: secA1+secA​=1−cosAsin2A​ [Hint: Simplify LHS and RHS separately] −D−203.e. Evaluate: sec30∘+cos60∘+cot45∘sin30∘+tan45∘−cosec60∘​−195d. The angle of elevation of the top of a building from the foot of the tower is 30∘ and the angle of elevation of the top of the tower from the foot of the building is 60∘. If the tower is 50m high, find the height of the building.10. a. Construct an isosceles triangle whose base is 8cm and altitude is 4cm and then another triangle whose sides are 121​ times the corresponding sides of the isosceles triangle. −p−230⩽44.Orb. Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4cm and 3cm. Then construct another triangle whose sides are 35​ times the corresponding sides of the given triangle. −p−230p of 311. A lot consist of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives to her. What is the probability that:i. She will buy it?

questions of 5 marks eachOr A right angled triangle whose sides are 3cm and 4cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. [choose the value of π as found appropriate]

6. Explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers.

value of x. EN8. Solve : x−5(x+2)(2x−3)−2x2+6​=2.Sol. The given equation is⇒⇒​x−5(x+2)(2x−3)−2x2+6​=2x−52x2+4x−3x−6−2x2+6​=2x−5x​=12​​Cross multiplying, 1×x=2(x−5)⇒x=2x−10⇒x−2x=−10⇒−x=−10⇒x=10.EXERCISE 7 (A)k your answer :(ii) 7+2(a+1)−3a=5a(iii) 4(x+3)−2(x−1)=3x+33. (i) 4y+5y​=21(ii) 32m​+43m​=17=53x−5​−256. 103x−2​−7x+3​+34x−7​=x−1=8−0.45x9. 61​(4y+5)−32​(2y+7)=23​