Quiz about XAT Functions questions

Question 1

Consider the equation $\log_5(x - 2) = 2 \log_{25}(2x - 4)$ , where x is a real number.
For how many different values of x does the given equation hold?

Accepted Answer

0

Answer

1

Answer

2

Answer

4

Answer

Infinitely many

Question 2

The roots of the polynomial $\log_5(x - 2) = 2 \log_{25}(2x - 4)$ are the radii of three concentric circles.
The ratio of their area, when arranged from the largest to the smallest, is:

Accepted Answer

36:16:1

Answer

6:2:1

Answer

9:4:1

Answer

16:6:3

Answer

None of the remaining options is correct.

Question 3

Given $\log_5(x - 2) = 2 \log_{25}(2x - 4)$ . The maximum value of $|A|$ is:

Accepted Answer

9

Answer

111

Answer

6

Answer

3

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∞</mi></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math>∞

Question 4

ABC is a triangle and the coordinates of A, B and C are (a, b-2c), (a, b+4c) and (-2a,3c) respectively where a, b and c are positive numbers.
The area of the triangle ABC is:

Accepted Answer

9ac

Answer

6abc

Answer

9abc

Answer

6bc

Answer

None of the above

Question 5

Consider $\log_5(x - 2) = 2 \log_{25}(2x - 4)$ for $n = 1,2, ....., 2008, 2009$ where $a_{1} = 1$ . Find the value of $a_{1}a_{2} + a_{2}a_{3} + a_{3}a_{4} + ... + a_{2008}a_{2009}$ .

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>2008</mn><mn>2009</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{2008}{2009}</annotation></semantics></math>20092008​

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>2009</mn><mn>1000</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{2009}{1000}</annotation></semantics></math>10002009​

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>2009</mn><mn>2008</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{2009}{2008}</annotation></semantics></math>20082009​

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>6000</mn><mn>2009</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{6000}{2009}</annotation></semantics></math>20096000​

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>2008</mn><mn>6000</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{2008}{6000}</annotation></semantics></math>60002008​

Question 6

Raju and Sarita play a number game. First, each one of them chooses a positive integer independently. Separately, they both multiply their chosen integers by 2, and then subtract 20 from their resultant numbers. Now, each of them has a new number. Then, they divide their respective new numbers by 5. Finally, they added their results and found that the sum is 16. What can be the maximum possible difference between the positive integers chosen by Raju and Sarita?

Accepted Answer

58

Answer

67

Answer

49

Answer

40

Answer

None of the above

Question 7

The sum of the cubes of two numbers is 128, while the sum of the reciprocals of their cubes is 2.
What is the product of the squares of the numbers?

Accepted Answer

16

Answer

64

Answer

256

Answer

48

Answer

32

Question 8

Consider the real-valued function $\log_5(x - 2) = 2 \log_{25}(2x - 4)$ Find the domain of f(x).

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mfrac><mn>7</mn><mn>3</mn></mfrac><mo separator="true">,</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\frac{7}{3},\infty)</annotation></semantics></math>(37​,∞)

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mo>−</mo><mrow><mo fence="true">{</mo><mfrac><mn>7</mn><mn>3</mn></mfrac><mo fence="true">}</mo></mrow></mrow><annotation encoding="application/x-tex">R-\left\{\frac{7}{3}\right\}</annotation></semantics></math>R−{37​}

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mo>−</mo><mrow><mo fence="true">{</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo separator="true">,</mo><mn>2</mn><mo fence="true">}</mo></mrow></mrow><annotation encoding="application/x-tex">R-\left\{\frac{3}{2},2\right\}</annotation></semantics></math>R−{23​,2}

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mo>−</mo><mrow><mo fence="true">{</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mfrac><mn>7</mn><mn>3</mn></mfrac><mo fence="true">}</mo></mrow></mrow><annotation encoding="application/x-tex">R-\left\{\frac{3}{2},2,\frac{7}{3}\right\}</annotation></semantics></math>R−{23​,2,37​}

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo separator="true">,</mo><mfrac><mn>7</mn><mn>3</mn></mfrac><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(-\infty,\frac{7}{3})</annotation></semantics></math>(−∞,37​)

Question 9

Let $\log_5(x - 2) = 2 \log_{25}(2x - 4)$ if $x eq 1, -1,$ and 1 if x = 1, -1. Let $g(x) = \frac{x + 1}{x - 1}$ if $x eq 1,$ and 3 if x = 1.
What is the minimum possible values of $\frac{f(x)}{g(x)}$ ?

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{3}</annotation></semantics></math>31​

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{2}</annotation></semantics></math>21​

Answer

-1

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{4}</annotation></semantics></math>41​

Answer

1

Question 10

The topmost point of a perfectly vertical pole is marked A. The pole stands on a flat ground at point D. The points B and C are somewhere between A and D on the pole. From a point E, located on the ground at a certain distance from D, the points A, B and C are at angles of 60, 45 and 30 degrees respectively. What is AB : BC : CD?

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>3</mn><mo>−</mo><msqrt><mn>3</mn></msqrt><mo stretchy="false">)</mo><mo>:</mo><mo stretchy="false">(</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>:</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">(3 - \sqrt 3) : (\sqrt 3 - 1) : 1</annotation></semantics></math>(3−3<svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em"><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"></path></svg>​):(3<svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em"><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"></path></svg>​−1):1

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>3</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo stretchy="false">)</mo><mo>:</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo stretchy="false">)</mo><mo>:</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">(3 + \sqrt 3) : (1 + \sqrt 3) : 1</annotation></semantics></math>(3+3<svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em"><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"></path></svg>​):(1+3<svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em"><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"></path></svg>​):1

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>3</mn><mo>−</mo><msqrt><mn>3</mn></msqrt><mo stretchy="false">)</mo><mo>:</mo><mn>1</mn><mo>:</mo><mo stretchy="false">(</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(3 - \sqrt 3) : 1 : (\sqrt 3 - 1)</annotation></semantics></math>(3−3<svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em"><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"></path></svg>​):1:(3<svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em"><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"></path></svg>​−1)

Answer

1 : 1 : 1

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>:</mo><mn>1</mn><mo>:</mo><mo stretchy="false">(</mo><mn>3</mn><mo>−</mo><msqrt><mn>3</mn></msqrt><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\sqrt 3 - 1) : 1 : (3 - \sqrt 3)</annotation></semantics></math>(3<svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em"><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"></path></svg>​−1):1:(3−3<svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em"><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"></path></svg>​)

Question 11

Consider the four variables A, B, C and D and a function Z of these variables, $\log_5(x - 2) = 2 \log_{25}(2x - 4)$ It is given that A, B, C and D must be non-negative integers and thatall of the following relationships must hold:
i) $2A + B \leq 2$
ii) $4A + 2B + C \leq 12$
iii) $3A + 4B + D \leq 15$
If Z needs to be maximised, then what value must D take?

Accepted Answer

12

Answer

15

Answer

0

Answer

10

Answer

5

Question 12

Consider the function f(x) = (x + 4)(x + 6)(x + 8) ⋯ (x + 98). The number of integers x for which f(x) < 0 is:

Accepted Answer

24

Answer

23

Answer

26

Answer

48

Answer

NA

Question 13

If $\log_5(x - 2) = 2 \log_{25}(2x - 4)$ , then $x^{2018} + x^{2019}$ equals which of the following:

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mi>x</mi></mrow><annotation encoding="application/x-tex">-x</annotation></semantics></math>−x

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">x+1</annotation></semantics></math>x+1

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math>x

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">x-1</annotation></semantics></math>x−1

Answer

NA

Question 14

We have two unknown positive integers m and n, whose product is less than 100.
There are two additional statement of facts available:
mn is divisible by six consecutive integers { j, j + 1,...,j + 5 }
m + n is a perfect square.
Which of the two statements above, alone or in combination shall be sufficient to determine the numbers m and n?

Accepted Answer

Both statements taken together are suﬃcient to answer the question, but neither statement alone is suﬃcient.

Answer

Each statement alone is suﬃcient to answer the question.

Answer

Statement 2 alone is suﬃcient, but statement 1 alone is not suﬃcient to answer the question.

Answer

Statements 1 and 2 together are not suﬃcient, and additional data is needed to answer the question.

Answer

Statement 1 alone is suﬃcient, but statement 2 alone is not suﬃcient to answer the question.

Question 15

Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B and C - all of them are positive integers. If (A + B + C) = 41 and the product of the roots of one of the equations is 35, which of the following options is definitely correct?

Accepted Answer

One of the roots is 5.

Answer

The common root is 29.

Answer

The smallest among the roots is 1.

Answer

Product of the roots of the other equation is 5.

Answer

All of the above are possible, but none are definitely correct.

Question 16

X and Y are the digits at the unit's place of the numbers (408X) and (789Y) where X ≠ Y. However, the digits at the unit's place of the numbers $\log_5(x - 2) = 2 \log_{25}(2x - 4)$ and $(789Y)^{85}$ are the same. What will be the possible value(s) of (X + Y)?

Accepted Answer

10

Answer

9

Answer

11

Answer

12

Answer

None of the above

Question 17

If $\log_5(x - 2) = 2 \log_{25}(2x - 4)$ and both $x$ and $2A + B \leq 2$ are negative integers, find the number of possible combinations of $x$ and $y$ .

Accepted Answer

10

Answer

4

Answer

5

Answer

6

Answer

8

Question 18

If $\log_5(x - 2) = 2 \log_{25}(2x - 4)$ and $y$ are real numbers, the least possible value of the expression $4(x - 2)^{2} + 4(y - 3)^{2} - 2(x - 3)^{2}$ is :

Accepted Answer

- 4

Answer

- 8

Answer

- 2

Answer

0

Answer

2

Question 19

If f(x) = ax + b, a and b are positive real numbers and if f(f(x)) = 9x + 8, then the value of a + b is:

Accepted Answer

5

Answer

3

Answer

4

Answer

6

Answer

None of the above

Question 20

If 5° $\log_5(x - 2) = 2 \log_{25}(2x - 4)$ x° $y$ 15°, then the value of sin 30° + cos x° - sin x° will be :

Accepted Answer

None of the above

Answer

Between -1 and -0.5 inclusive

Answer

Between -0.5 and 0 inclusive

Answer

Between 0 and 0.5 exclusive

Answer

between 0.5 and 1 inclusive

XAT Functions Practice Questions With Solutions

XAT Quantitative Ability & Data Interpretation Functions Practice Questions

Question 1.

Consider the equation log⁡5(x−2)=2log⁡25(2x−4)\log_5(x - 2) = 2 \log_{25}(2x - 4)log5​(x−2)=2log25​(2x−4), where x is a real number.For how many different values of x does the given equation hold?

Question 2.

The roots of the polynomial P(x)=2x3−11x2+17x−6P(x) = 2x^3 - 11x^2 + 17x - 6P(x)=2x3−11x2+17x−6 are the radii of three concentric circles.The ratio of their area, when arranged from the largest to the smallest, is:

Question 3.

Given A=∣x+3∣+∣x−2∣−∣2x−8∣A = |x + 3| + | x - 2 | - | 2x -8|A=∣x+3∣+∣x−2∣−∣2x−8∣. The maximum value of ∣A∣|A|∣A∣ is:

Question 4.

ABC is a triangle and the coordinates of A, B and C are (a, b-2c), (a, b+4c) and (-2a,3c) respectively where a, b and c are positive numbers. The area of the triangle ABC is:

Question 5.

Question 6.

Question 7.

The sum of the cubes of two numbers is 128, while the sum of the reciprocals of their cubes is 2.What is the product of the squares of the numbers?

Question 8.

Consider the real-valued function f(x)=log⁡(3x−7)2x2−7x+6f(x)=\frac{\log{(3x-7)}}{\sqrt{2x^{2}-7x+6}}f(x)=2x2−7x+6​log(3x−7)​ Find the domain of f(x).

Question 9.

Question 10.

Question 1.

Question 2.

Consider the function f(x) = (x + 4)(x + 6)(x + 8) ⋯ (x + 98). The number of integers x for which f(x) < 0 is:

Question 3.

If x2+x+1=0x^2 + x + 1 = 0x2+x+1=0, then x2018+x2019x^{2018} + x^{2019}x2018+x2019 equals which of the following:

Question 4.

Question 5.

Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B and C - all of them are positive integers. If (A + B + C) = 41 and the product of the roots of one of the equations is 35, which of the following options is definitely correct?

Question 6.

X and Y are the digits at the unit's place of the numbers (408X) and (789Y) where X ≠ Y. However, the digits at the unit's place of the numbers (408X)63(408X)^{63}(408X)63 and (789Y)85(789Y)^{85}(789Y)85 are the same. What will be the possible value(s) of (X + Y)?

Question 7.

If 2≤∣x−1∣×∣y+3∣≤52 \leq |x - 1| \times |y + 3| \leq 52≤∣x−1∣×∣y+3∣≤5 and both xxx and yyy are negative integers, find the number of possible combinations of xxx and yyy.

Question 8.

If xxx and yyy are real numbers, the least possible value of the expression 4(x−2)2+4(y−3)2−2(x−3)24(x - 2)^{2} + 4(y - 3)^{2} - 2(x - 3)^{2}4(x−2)2+4(y−3)2−2(x−3)2 is :

Question 9.

If f(x) = ax + b, a and b are positive real numbers and if f(f(x)) = 9x + 8, then the value of a + b is:

Question 10.

If 5° ≤\leq≤ x° ≤\leq≤ 15°, then the value of sin 30° + cos x° - sin x° will be :

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