### Counting - Linear Equations

3x + 4|y| = 33. How many integer values of (x, y) are possible?

- 6
- 3
- 4
- More than 6

**Correct Answer**Choice (D).

More than 6. Correct answer- Explanatory Answer
- Integer Values; Modulus
- Medium

### Counting - Linear Equations

(|x| - 3) (|y| + 4) = 12. How many pairs of integers (x, y) satisfy this equation?

- 4
- 6
- 10
- 8

**Correct Answer**Choice (C).

10 Correct answer- Explanatory Answer
- Integer Values; Modulus
- Medium

### Counting - Linear Equations

x + |y| = 8, |x| + y = 6. How many pairs of x, y satisfy these two equations?

- 2
- 4
- 0
- 1

**Correct Answer**Choice (D).

1 Correct answer- Explanatory Answer
- Integer Values; Modulus
- Hard

### Counting - Quadratic Equations

What is the number of real solutions of the equation x

^{2}- 7|x| - 18 = 0?- 2
- 4
- 3
- 1

**Correct Answer**Choice (A).

2 Correct answer- Explanatory Answer
- Quadratic Discriminant
- Medium

### Counting - Quadratic Equations

x

^{2}- 9x + |k| = 0 has real roots. How many integer values can 'k' take?- 40
- 21
- 20
- 41

**Correct Answer**Choice (D).

41 Correct answer- Explanatory Answer
- Quadratic Discriminant
- Medium

### Integer Roots

x

^{2}- 11x + |p| = 0 has integer roots. How many integer values can 'p' take?- 6
- 4
- 8
- More than 8

**Correct Answer**Choice (D).

More than 8. Correct answer- Explanatory Answer
- Quadratics - Counting
- Medium

### Linear Equations - Integer Solutions

2x + 5y = 103. Find the number of pairs of positive integers x and y that satisfy this equation.

- 9
- 10
- 12
- 20

**Correct Answer**Choice (B).

10 Correct answer- Explanatory Answer
- Integer Solutions
- Medium

### Maximum, Minimum

Consider three numbers a, b and c. Max (a,b,c) + Min (a,b,c) = 13. Median (a,b,c) - Mean (a,b,c) = 2. Find the median of a, b, and c.

- 11.5
- 9
- 9.5
- 12

**Correct Answer**Choice (C).

9.5 Correct answer- Explanatory Answer
- Linear Equations - Median
- Medium

### Unique Solutions

a

_{1}x + b_{1}y + c_{1}z = d_{1}, a_{2}x + b_{2}y + c_{2}z = d_{2}, a_{3}x + b_{3}y + c_{3}z = d_{3}.

Which of the following statements if true would imply that the above system of equations does not have a unique solution?

i.

ii. ;

iii. a_{1}, a_{2}, a_{3}are integers; b_{1}, b_{2}, b_{3}are rational numbers, c_{1}, c_{2}, c_{3}are irrational numbers

**Correct Answer**Statement i.

Correct answer- Explanatory Answer
- Condition for Unique Soln.
- Hard

### Roots - Quadratic Equation

Equation x

^{2}+ 5x – 7 = 0 has roots a and b. Equation 2x^{2}+ px + q = 0 has roots a + 1 and b + 1. Find p + q.- 6
- 0
- -16
- 2

**Correct Answer**Choice (C).

Correct answer- Explanatory Answer
- Roots - Quadratic Equation
- Easy

### Sum and product of the roots

Sum of the roots of a quadratic equation is 5 less than the product of the roots. If one root is 1 more than the other root, find the product of the roots?

- 6 or 3
- 12 or 2
- 8 or 4
- 12 or 4

**Correct Answer**Choice (B).

12 or 2 Correct answer- Explanatory Answer
- Sum and product of the roots
- Easy

### Real and imaginary solutions for an equation

How many real solutions are there for the equation x

^{2}– 7|x| - 30 = 0?- 3
- 1
- 2
- none

**Correct Answer**Choice (C).

2 Correct answer- Explanatory Answer
- Real and imaginary solutions for an equation
- Easy

- 3
### Value of the variables - Quadratic Equation

If (3x+2y-22)

^{2}+ (4x-5y+9)^{2}= 0 and 5x-4y = 0. Find the value of x+y.- 7
- 9
- 11
- 13

**Correct Answer**Choice (B).

9 Correct answer- Explanatory Answer
- Sum of the variables
- Medium

### Progressions and Equations

Let x

^{3}- x^{2}+ bx + c = 0 has 3 real roots which are in A.P. which of the following could be true- b=2,c=2
- b=1,c=1
- b= -1,c = 1
- b= -1,c= -1

**Correct Answer**Choice (B).

9 Correct answer- Explanatory Answer
- AP and roots of an equation
- Hard

### Roots of an Equation

(3 + 2√2)

^{(x2 - 3)}+ (3 - 2√2)^{(x2 - 3)}= b which of the following can be one of the roots of the equation- 2
- √2
- -√2
- All of the above

**Correct Answer**Choice (D).

Correct answer- Explanatory Answer
- Roots of an Equation
- Medium

### Real roots

If f(y) = x

^{2}+ (2p + 1)x + p^{2}- 1 and x is a real number, for what values of ‘p' the function becomes 0?- p > 0
- p > -1
- p >= -5/4
- p <= 3/4

**Correct Answer**Choice (C).

Correct answer- Explanatory Answer
- Real roots
- Easy

### Linear and Quadratic Expressions

A merchant decides to sell off 100 articles a week at a selling price of Rs. 150 each. For each 4% rise in the selling price he sells 3 less articles a week. If the selling price of each article is Rs x, then which of the below expression represents the rupees a week the merchant will receive from the sales of the articles?

- 175 - x/2
- x/3 + 156
- 350 - x
^{2}/2 - x
^{2}- 2x + 75

**Correct Answer**Choice (A).

Correct answer- Explanatory Answer
- Linear and Quadratic Expressions
- Medium

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- Percents Profits & Interests
- DI - Bar Graphs
- Geometry
- VA - Sentence Rearrangement
- Speed Time Races
- DI - Pie Charts
- Coordinate Geometry
- VA - Sentence Elimination
- Ratio Mixtures, Averages
- DI - Multiple Graphs
- Trigonometry
- VA - Sentence Correction
- Logarithms and Exponents
- DI - Word Problems
- Mensuration
- VA - Para Completion
- Pipes Cisterns
- DI - Line Graphs
- Permutation; Probability
- VA - Text Completion