Shashikant Kumar: Your Dedicated Tutoring Resource

Answer

Let the remainder is 'r'. Then by remainder theorem,we can write, P(x)=x^3-6x^2+ax-6=m(x-2)+r, and Q(x)=x^3+(5-a)x^2+12x-8=n(x-2)+r. Where m and r are quotients of the polynomial respectively and m#n. P(x)-Q(x)=x^2(a-11)+(a-12)x+2=(m-n)(x-2). Now put x=2 in above equation,we get P(2)-Q(2)=4(a-11)+(a-12)2+2=0 On solving we get a=11.

Answer

Given, (t1+t2+t3) empty 1 tank in 3 hrs. so in 1 hr (t1+t2+t3) will empty 1/3 tank. ----------(eq1) Similarly. In 1 hr t1 will empty 1/6 tank. ---------(eq2) In 1 hr t2 will empty 1/9 tank. ----------(eq3) Now, let t3 takes x hr to empty 1 tank so in 1 hr t3 will empty 1/x tank. --------(eq4) Now, 1/3=(1/6)+(1/9)+1/x or, 1/x=(1/3)-(1/6)-(1/9)=15/54=5/18 or, x=(18/5) hr=3.6 hr Thus third tap will take 3.6 hr to empty a tank.

Answer

let x be the speed of boy in stiil water.So along the current his speed will be (x+4) and against the current his speed will be (x-4). Since the time is fixed, so (3*s/x+4)=(s/x-4) upon solving we get x=8 km/hr. Here s is the distance when he swims against the stream.

Answer

let x be the breadth. Then length=x+8. Now perimeter of rectangle =64, i.e 2(length+breadth)=64 or, 2(x+8+x)=64 or, 2x+8=32 or, x=12. Thus breadth=12 cm and length =20 cm

Answer

H is father-in-law of I.