If 5 x + 9 + 5 x − 9 = 3 ( 2 + 2 ) \sqrt{5x+9} + \sqrt{5x - 9} = 3(2 + \sqrt{2}) 5 x + 9 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> + 5 x − 9 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> = 3 ( 2 + 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> ) , then 10 x + 9 \sqrt{10x+9} 1 0 x + 9 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> is equal to

3 7 3\sqrt{7} 3 7 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z">

3 31 3\sqrt{31} 3 3 1 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z">

4 5 4\sqrt{5} 4 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z">

2 7 2\sqrt{7} 2 7 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z">

If x is a positive real number such that x 8 + ( 1 x ) 8 = 47 x^8 + \left(\frac{1}{x}\right)^8 = 47 x 8 + ( x 1 ) 8 = 4 7 , then the value of x 9 + ( 1 x ) 9 x^9 + \left(\frac{1}{x}\right)^9 x 9 + ( x 1 ) 9 is

34 5 34\sqrt{5} 3 4 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z">

40 5 40\sqrt{5} 4 0 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z">

30 5 30\sqrt{5} 3 0 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z">

36 5 36\sqrt{5} 3 6 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z">

For all real values of x, the range of the function f ( x ) = x 2 + 2 x + 4 2 x 2 + 4 x + 9 f(x)=\frac{x^{2}+2x+4}{2x^{2}+4x+9} f ( x ) = 2 x 2 + 4 x + 9 x 2 + 2 x + 4 is:

[ 3 7 , 1 2 ) [\frac{3}{7},\frac{1}{2}) [ 7 3 , 2 1 )

[ 4 9 , 8 9 ] [\frac{4}{9},\frac{8}{9}] [ 9 4 , 9 8 ]

[ 3 7 , 8 9 ) [\frac{3}{7},\frac{8}{9}) [ 7 3 , 9 8 )

( 3 7 , 1 2 ) (\frac{3}{7},\frac{1}{2}) ( 7 3 , 2 1 )

If x = ( 4096 ) 7 + 4 3 x=(4096)^{7+4\sqrt{3}} x = ( 4 0 9 6 ) 7 + 4 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> , then which of the following equals to 64?

x 7 2 x 2 3 \frac{x^{\frac{7}{2}}}{x^{2{\sqrt{3}}}} x 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> x 2 7

x 7 x 2 3 \frac{x^{7}}{x^{2\sqrt{3}}} x 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> x 7

x 7 2 x 4 3 \frac{x^{\frac{7}{2}}}{x^{\frac{4}{\sqrt{3}}}} x 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> 4 x 2 7

x 7 x 4 3 \frac{x^{7}}{x^{4\sqrt{3}}} x 4 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> x 7

For real x, the maximum possible value of x 1 + x 4 \frac{x}{\sqrt{1+x^{4}}} 1 + x 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> x is

1 2 \frac{1}{\sqrt{2}} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> 1

1 3 \frac{1}{\sqrt{3}} 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"> 1

CAT Higher Order Equations Practice Questions With Solutions

CAT Quant Higher Order Equations Practice Questions

VARC DILR

Question 1.

CAT Higher Order Equations Practice Questions With Solutions

CAT Quant Higher Order Equations Practice Questions

Question 1.

If 5x+9+5x−9=3(2+2)\sqrt{5x+9} + \sqrt{5x - 9} = 3(2 + \sqrt{2})5x+9​+5x−9​=3(2+2​), then 10x+9\sqrt{10x+9}10x+9​ is equal to

Question 2.

If xxx and yyy are real numbers such that x2+(x−2y−1)2=−4y(x+y)x^{2} + (x - 2y - 1)^{2} = -4y(x + y)x2+(x−2y−1)2=−4y(x+y), then the value x−2yx - 2yx−2y is

Question 3.

The sum of all possible values of x satisfying the equation 24x2−22x2+x+16+22x+30=02^{4x^{2}}-2^{2x^{2}+x+16}+2^{2x+30}=024x2−22x2+x+16+22x+30=0, is

Question 4.

If p2+q2−29=2pq−20=52−2pqp^{2}+q^{2}-29=2pq-20=52-2pqp2+q2−29=2pq−20=52−2pq, then the difference between the maximum and minimum possible value of (p3−q3)(p^{3}-q^{3})(p3−q3)

Question 5.

If x is a positive real number such that x8+(1x)8=47x^8 + \left(\frac{1}{x}\right)^8 = 47x8+(x1​)8=47, then the value of x9+(1x)9x^9 + \left(\frac{1}{x}\right)^9x9+(x1​)9 is

Question 6.

Let a and b be natural numbers. If a2+ab+a=14a^2 + ab + a = 14a2+ab+a=14 and b2+ab+b=28b^2 + ab + b = 28b2+ab+b=28, then (2a+b)(2a + b)(2a+b) equals

Question 7.

Let r and c be real numbers. If r and -r are roots of 5x3+cx2−10x+9=05x^{3} + cx^{2} - 10x + 9 = 05x3+cx2−10x+9=0, then c equals

Question 8.

If c=16xy+49yxc=\frac{16x}{y}+\frac{49y}{x}c=y16x​+x49y​ for some non-zero real numbers x and y, then c cannot take the value

Question 9.

If x0=1,x1=2x_0 = 1, x_1 = 2x0​=1,x1​=2, and xn+2=1+xn+1xn,n=0,1,2,3,......,x_{n + 2} = \frac{1 + x_{n + 1}}{x_n}, n = 0, 1, 2, 3, ......,xn+2​=xn​1+xn+1​​,n=0,1,2,3,......, then x2021x_{2021}x2021​ is equal to

Question 10.

For all real values of x, the range of the function f(x)=x2+2x+42x2+4x+9f(x)=\frac{x^{2}+2x+4}{2x^{2}+4x+9}f(x)=2x2+4x+9x2+2x+4​ is:

Question 1.

For a sequence of real numbers x1,x2,...xnx_{1},x_{2},...x_{n}x1​,x2​,...xn​, If x1−x2+x3−....+(−1)n+1xn=n2+2nx_{1}-x_{2}+x_{3}-....+(-1)^{n+1}x_{n}=n^{2}+2nx1​−x2​+x3​−....+(−1)n+1xn​=n2+2n for all natural numbers n, then the sum x49+x50x_{49}+x_{50}x49​+x50​ equals

Question 2.

Consider the pair of equations: x2−xy−x=22x^{2}-xy-x=22x2−xy−x=22 and y2−xy+y=34y^{2}-xy+y=34y2−xy+y=34. If x>yx>yx>y, then x−yx-yx−y equals

Question 3.

The number of real-valued solutions of the equation 2x+2−x=2−(x−2)22^{x}+2^{-x}=2-(x-2)^{2}2x+2−x=2−(x−2)2 is:

Question 4.

How many disticnt positive integer-valued solutions exist to the equation (x2−7x+11)(x2−13x+42)=1(x^{2}-7x+11)^{(x^{2}-13x+42)}=1(x2−7x+11)(x2−13x+42)=1 ?

Question 5.

If x=(4096)7+43x=(4096)^{7+4\sqrt{3}}x=(4096)7+43​, then which of the following equals to 64?

Question 6.

For real x, the maximum possible value of x1+x4\frac{x}{\sqrt{1+x^{4}}}1+x4​x​ is

Question 7.

In how many ways can a pair of integers (x , a) be chosen such that x2−2∣x∣+∣a−2∣=0x^{2}-2\mid x\mid+\mid a-2\mid=0x2−2∣x∣+∣a−2∣=0 ?

Question 8.

If x1=−1x_1=-1x1​=−1 and xm=xm+1+(m+1)x_m=x_{m+1}+(m+1)xm​=xm+1​+(m+1) for every positive integer m, then X100X_{100}X100​ equals

Question 9.

If the population of a town is p in the beginning of any year then it becomes 3 + 2p in the beginning of the next year. If the population in the beginning of 2019 is 1000, then the population in the beginning of 2034 will be

Question 10.

The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers is

Other Topics of that Section

Quick Links

Still have questions about CAT ? Ask us.

Related News

Related Articles

Popular Degrees

Popular Specializations

Management Colleges in States

Management Colleges in Cities

Popular Management Exams

Management Colleges by College Type

If $\sqrt{5x+9} + \sqrt{5x - 9} = 3(2 + \sqrt{2})$ , then $\sqrt{10x+9}$ is equal to

If $x$ and $y$ are real numbers such that $x^{2} + (x - 2y - 1)^{2} = -4y(x + y)$ , then the value $x - 2y$ is

The sum of all possible values of x satisfying the equation $2^{4x^{2}}-2^{2x^{2}+x+16}+2^{2x+30}=0$ , is

If $p^{2}+q^{2}-29=2pq-20=52-2pq$ , then the difference between the maximum and minimum possible value of $(p^{3}-q^{3})$

If x is a positive real number such that $x^8 + \left(\frac{1}{x}\right)^8 = 47$ , then the value of $x^9 + \left(\frac{1}{x}\right)^9$ is

Let a and b be natural numbers. If $a^2 + ab + a = 14$ and $b^2 + ab + b = 28$ , then $(2a + b)$ equals

Let r and c be real numbers. If r and -r are roots of $5x^{3} + cx^{2} - 10x + 9 = 0$ , then c equals

If $c=\frac{16x}{y}+\frac{49y}{x}$ for some non-zero real numbers x and y, then c cannot take the value

If $x_0 = 1, x_1 = 2$ , and $x_{n + 2} = \frac{1 + x_{n + 1}}{x_n}, n = 0, 1, 2, 3, ......,$ then $x_{2021}$ is equal to

For all real values of x, the range of the function $f(x)=\frac{x^{2}+2x+4}{2x^{2}+4x+9}$ is:

For a sequence of real numbers $x_{1},x_{2},...x_{n}$ , If $x_{1}-x_{2}+x_{3}-....+(-1)^{n+1}x_{n}=n^{2}+2n$ for all natural numbers n, then the sum $x_{49}+x_{50}$ equals

Consider the pair of equations: $x^{2}-xy-x=22$ and $y^{2}-xy+y=34$ . If $x>y$ , then $x-y$ equals

The number of real-valued solutions of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is:

How many disticnt positive integer-valued solutions exist to the equation $(x^{2}-7x+11)^{(x^{2}-13x+42)}=1$ ?

If $x=(4096)^{7+4\sqrt{3}}$ , then which of the following equals to 64?

For real x, the maximum possible value of $\frac{x}{\sqrt{1+x^{4}}}$ is

In how many ways can a pair of integers (x , a) be chosen such that $x^{2}-2\mid x\mid+\mid a-2\mid=0$ ?

If $x_1=-1$ and $x_m=x_{m+1}+(m+1)$ for every positive integer m, then $X_{100}$ equals