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Question Number 19192 Answers: 0 Comments: 2

Find a natural number ′n′ such that 3^9 + 3^(12) + 3^(15) + 3^n is a perfect cube of an integer.

$Find a natural number^{'} n^{'} such that$ $3^{9} + 3^{12} + 3^{15} + 3^{n} is a perfect cube of$ $an integer .$

Question Number 19262 Answers: 1 Comments: 0

Let p, q, r be three mutually perpendicular vectors of the same magnitude. If a vector x satisfies the equation p ×{x−q)×p}+q×{x−r)×q} + r×{x−p)×r}=0, then x is given by

$Let p, q, r be three mutually perpendicular$ $vectors of the same magnitude . If a vector$ $x satisfies the equation$ $p \times {x - q) \times p} + q \times {x - r) \times q}$ $+ r \times {x - p) \times r} = 0, then x is$ $given by$

Question Number 19182 Answers: 2 Comments: 0

Find all three digit numbers abc (with a ≠ 0) such that a^2 + b^2 + c^2 , is divisible by 26.

$Find all three digit numbers a b c (with$ $a \neq 0) such that a^{2} + b^{2} + c^{2}, is divisible$ $by 26 .$

Question Number 19171 Answers: 1 Comments: 1

log_(√2) (√(2(√(2(√(2(√(2 ))))))))

${l o g}_{\sqrt{2}} \sqrt{2 \sqrt{2 \sqrt{2 \sqrt{2}}}}$

Question Number 19154 Answers: 0 Comments: 0

If f(x) = (9^x /(9^x + 3)), find the value f((1/(2007))) + f((2/(2007))) + f((3/(2007))) + ... + f(((2006)/(2006)))

$If f (x) = \frac{9^{x}}{9^{x} + 3}, find the value$ $f (\frac{1}{2007}) + f (\frac{2}{2007}) + f (\frac{3}{2007}) + . . . + f (\frac{2006}{2006})$

Question Number 19150 Answers: 1 Comments: 4

A semicircle is tangent to both legs of a right triangle and has its centre on the hypotenuse. The hypotenuse is partitioned into 4 segments, with lengths 3, 12, 12, and x, as shown in the figure. Determine the value of ′x′.

$A semicircle is tangent to both legs of a$ $right triangle and has its centre on the$ $hypotenuse . The hypotenuse is$ $partitioned into 4 segments, with lengths$ $3, 12, 12, and x, as shown in the figure .$ $Determine the value of^{'} x^{'} .$

Question Number 19148 Answers: 1 Comments: 0

If f(x)= determinant (((sin x+sin2x+sin 3x),(sin 2x),(sin 3x)),(( 3+4 sin x),( 3),(4 sin x)),(( 1+sin x),( sin x),( 1))) then the value of ∫_( 0) ^(π/2) f(x) dx is

$If$ $f (x) = | \begin{matrix} \sin x + \sin 2 x + \sin 3 x & \sin 2 x & \sin 3 x \\ 3 + 4 \sin x & 3 & 4 \sin x \\ 1 + \sin x & \sin x & 1 \end{matrix} |$ $then the value of \underset{0}{\int^{π / 2}} f (x) d x is$

Question Number 19140 Answers: 0 Comments: 9

A racing car travels on a track (without banking) ABCDEFA. ABC is a circular arc of radius 2R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The co-efficient of friction on the road is μ = 0.1. The maximum speed of the car is 50 ms^(−1) . Find the minimum time for completing one round.

$A racing car travels on a track (without$ $banking) A B C D E F A . A B C is a circular$ $arc of radius 2 R . C D and F A are$ $straight paths of length R and D E F is$ $a circular arc of radius R = 100 m . The$ $co - efficient of friction on the road is μ =$ $0.1 . The maximum speed of the car is$ $50 {ms}^{- 1} . Find the minimum time for$ $completing one round .$

Question Number 19137 Answers: 1 Comments: 1

Figure shows (x, t), (y, t) diagram of a particle moving in 2-dimensions. If the particle has a mass of 500 g, find the force (direction and magnitude) acting on the particle.

$Figure shows (x, t), (y, t) diagram of a$ $particle moving in 2 - dimensions . If the$ $particle has a mass of 500 g, find the$ $force (direction and magnitude) acting$ $on the particle .$

Question Number 19135 Answers: 1 Comments: 0

solve for x: 2^(∣x+2∣) −∣2^(x+1) −1∣=2^(x+1) +1

$s o l v e f o r x :$ $2^{∣ x + 2 ∣} - ∣ 2^{x + 1} - 1 ∣= 2^{x + 1} + 1$

Question Number 19134 Answers: 1 Comments: 0

If (1/((243)^x )) = (729)^y = 3^3 , then find the value of 5x + 6y.

$If \frac{1}{{(243)}^{x}} = {(729)}^{y} = 3^{3}, then find the$ $value of 5 x + 6 y .$

Question Number 19127 Answers: 0 Comments: 0

Question Number 19123 Answers: 1 Comments: 0

{ ((xf(x)−g(x)+h(x)=2x+1)),((f(x)−(2x−2)g(x)−3h(x)=x)),((ln (x)f(x)−(x−3)h(x)=1)) :} Find f(x),g(x),h(x)

${\begin{cases} xf (x) - g (x) + h (x) = 2 x + 1 \\ f (x) - (2 x - 2) g (x) - 3 h (x) = x \\ \ln (x) f (x) - (x - 3) h (x) = 1 \end{cases}$ $Find f (x), g (x), h (x)$

Question Number 19122 Answers: 1 Comments: 0

Prove that r_1 + r_2 + r_3 = 4R + r

$Prove that r_{1} + r_{2} + r_{3} = 4 R + r$

Question Number 19121 Answers: 0 Comments: 0

Question Number 19118 Answers: 0 Comments: 0

Question Number 19104 Answers: 1 Comments: 1

Let ABC be an acute-angled triangle with AC ≠ BC and let O be the circumcenter and F be the foot of altitude through C. Further, let X and Y be the feet of perpendiculars dropped from A and B respectively to (the extension of) CO. The line FO intersects the circumcircle of ΔFXY, second time at P. Prove that OP < OF.

$Let ABC be an acute - angled triangle$ $with AC \neq BC and let O be the$ $circumcenter and F be the foot of$ $altitude through C . Further, let X and Y$ $be the feet of perpendiculars dropped$ $from A and B respectively to (the$ $extension of) CO . The line FO intersects$ $the circumcircle of Δ FXY, second time$ $at P . Prove that OP < OF .$

Question Number 19101 Answers: 0 Comments: 3

A polynomial f(x) with rational coefficients leaves remainder 15, when divided by x − 3 and remainder 2x + 1, when divided by (x − 1)^2 . Find the remainder when f(x) is divided by (x − 3)(x − 1)^2 .

$A polynomial f (x) with rational$ $coefficients leaves remainder 15, when$ $divided by x - 3 and remainder 2 x + 1,$ $when divided by {(x - 1)}^{2} . Find the$ $remainder when f (x) is divided by$ $(x - 3) {(x - 1)}^{2} .$