7. Let Px be a polynomial of degree n > 0 such that Px=x-α'Qx, where r ≥ 2 and α is a real number. Qx is a polynomial with real coefficients of degree q > 0 . Which of the following is the incorrect statement?
From the digits 0, 1, 2, 3, ………, 9 two digits are selected without replacement. If they are both odd digits, what is the probability that their sum is greater than 10? A. 35 B. 14 C. 25 D. 310
Draw a large neat sketch of the ellipse x225+Y225=1 labelling clearly the, the foci, the directices
In a class of 15 girls, one girl is chosen to be the referee and the other girls play 7 a side soccer. In how many ways can the referee and teams be chosen?
Two circles touch externally at A. A common tangent touches the circles at M and N respectively. Find the size of ∠MAN, giving reasons.
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The base of the solid is the region bounded by the parabola 𝑥 2 = 4𝑦 and the line 𝑦 = 1. Cross sections perpendicular to this base and the 𝑦 axis are parabolic segments with their vertices 𝑉 directly above the 𝑦 axis. The diagram shows a typical segment 𝑃𝑉𝑄. All the segments have the property that the vertical height VC is three times the base length 𝑃𝑄. Let 𝑃(𝑥, 𝑦) where 𝑥 ≥ 0 be a point on the parabola 𝑥 2 = 4𝑦 (i) Show that the area of the segment 𝑃𝑉𝑄 is 8𝑥 2. (ii) Hence, find the volume of the solid.
A solid is formed by rotating the region enclosed by the parabola y2 = 4ax, its vertex (0, 0) and the line x=a about the y axis. Which of the following integrals gives the volume of this area by slicing? (A) 2π a ∫0a z32 dz (B) 4π a ∫0a z32 dz (C) π∫02a a2-z416a2 dz (D) 2π∫02a a2-z416a2 dz
Two of the zeros of the polynomial Px=x4+bx3+cx2+dx+e b,c,d,e ∈IR are 2+i and 1-3i.Find the other two zeros and hence find b and e.
Let z = r(cosθ+i sinθ) where z≠0 and n≥1 for integer n. Use De Moivre's theorem to show zn -1zn = 2i sinθ for n≥ 1. (ii) You may assume z-1z5=z5 -1z5 -5z3 -1z3+10z -1z Show that sin5θ=116 (sin 5θ —5sin 3θ + 10 sin θ) . (iii) Hence solve sin5θ = 5sin3θ to the nearest radian for 0 ≤θ≤π . Tangents PA and PB are drawn to a circle. Point Q is on the minor arc AB. Perpendiculars QL, QM and QN are drawn from Q to PA, AB and PB respectively.
Show that △BNQ Ill △AMQ and △ALQ △BMQ . Hence show that QN, QM and QL form a geometric sequence Find a primitive function of 11+sinx
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