# ABOUT 53 MATHEMATICS TRUE OR FALSE NSMQ PAST QUESTIONS

## ABOUT 53 MATHEMATICS TRUE OR FALSE NSMQ PAST QUESTIONS

- Every triangle has a center of symmetry.

**ANSWER: FALSE**

- An isosceles triangle has a center of symmetry.

**ANSWER: FALSE**

- An equilateral triangle has a center of symmetry.

**ANSWER: FALSE**

- y = 2sinx has a maximum value at x = π.

**ANSWER: FALSE**

- y = 3cosx has a maximum value at x = π.

**ANSWER: FALSE**

- y = tanx has a maximum value at x = π.

**ANSWER: FALSE**

### NSMQ PAST QUESTION; CHEMISTRY (02)

### NSMQ Past Question; Chemistry (03)

### NSMQ Past Question; Chemistry (01)

- 3 > √8

**ANSWER: TRUE**

- 2√7 > 3√3

**ANSWER: TRUE**

- 3√5 > 4√3

**ANSWER: FALSE**

- If the sum of the interior angles of a triangle is 300°, then it is a rectangle.

**ANSWER: TRUE**

- If 3 + 6 = 10, then 3 x 6 = 15.

**ANSWER: TRUE**

- If the interior angle of a rectangle measures 120°, then it is a pentagon.

**ANSWER: TRUE**

- 4a
^{2}+ 6ab + 9b^{2}= (2a + 3b)^{2}

**ANSWER: FALSE**

- (5a – 2b)
^{2}= 25a^{2}– 20ab + 4b^{2}

**ANSWER: TRUE**

- 9a
^{2}+ 24ab + 16b^{2}= (3a + 4b)^{2}

**ANSWER: TRUE**** **

- A triangle fits its outline in three positions.

**ANSWER: FALSE**

- A parallelogram fits its outline in two positions.

**ANSWER: TRUE**

- A square fits its outline in 4 positions.

**ANSWER: FALSE**

- The point A(3, 4) is in the solution set of the inequality x
^{2}+ y^{2}> 25.

**ANSWER: FALSE**

- The point B(-6, 7) is in the solution set of the inequality x
^{2}+ y^{2}< 81

**ANSWER: FALSE**

- The point C(3, – 5) is in the solution set of the inequality x
^{2}+ y^{2}> 33

**ANSWER: TRUE**

- Sum of the interior angles of a polygon of n sides is (n + 2)π radians

**ANSWER: FALSE**

- The interior angle of a polygon of n sides has measure (n – 2)π/n.

**ANSWER: FALSE** (only when it is equiangular)

- The sum of the exterior angles of any polygon is 2 straight angles.

**ANSWER: TRUE**

#### The given equation has no real solution.

- cosx = secx

**ANSWER: FALSE (cos ^{2}x = 1 has real solutions)**

- sinx = – cosecx

**ANSWER: TRUE (sin ^{2}x = -1 has no real solution)**

- tanx = – cotx

**ANSWER: TRUE (tan ^{2}x = -1 has no real solution)**

#### The pair of equations represent parallel lines.

- y = 3x + 5 and x/(1/3) + y/(-1) = 12

**ANSWER: TRUE**

- y = -5x + 3 and 5x – y = 3

**ANSWER: FALSE**

- x/2 + y/3 = 1 and y = 3x/2 + 7

**ANSWER: FALSE**

- A rectangle can be circumscribed by a circle.

**ANSWER: TRUE**

- A circle can be inscribed in a rectangle.

**ANSWER: FALSE**

- A circle can be inscribed in a rhombus.

**ANSWER: TRUE**

- √(56) is an irrational number

**ANSWER: FALSE **

[ √(2.56) = 1.6 a rational number]

- π is a rational number.

**ANSWER: FALSE**

- √(18/8) is a rational number.

**ANSWER: TRUE **

** **[18/8) = 9/4) = 3/2 a rational number]

#### In linear programming,

- the objective function is of the form Ax + By,

**ANSWER: TRUE**

- the constraints can be quadratic inequalities,

**ANSWER: FALSE**

- the solution occurs at a corner point of the graphed region.

**ANSWER: TRUE**

#### The following quadrilateral has two pairs of adjacent congruent sides.

- Parallelogram

**ANSWER**: **FALSE**

- Rhombus

**ANSWER**: **FALSE**

- Kite

**ANSWER: TRUE**

- the inequality x
^{2}/4 + y^{2}/6 < 1 describes a region inside a circle.

**ANSWER: FALSE**

- The inequality x
^{2}+ y^{2}> 16 describes a region outside a circle.

**ANSWER: TRUE**

- The inequality y
^{2}> x^{2 }describes a region above the line y = x.

**ANSWER: FALSE**

#### Determine if the converse of the statement is true or false

- A cube is a hexahedron.

**ANSWER: FALSE**

- A polygon is a pentagon.

**ANSWER: TRUE**

- A tetrahedron is a pyramid.

**ANSWER: FALSE**

- The point A(5, 2) is in the solution set of the inequality 3x – 5y < 8.

**ANSWER: TRUE**

- The point B(3, -2) is in the solution set of the inequality 5x + 7y > 1.

**ANSWER: FALSE**

- The point C(-4, -2) is in the solution set of the inequality 3x – 6y < -1.

**ANSWER: FALSE **

#### Two triangles are congruent if

- two sides and an angle of one are congruent to any two sides and an angle of the other.

**ANSWER: FALSE**

- two angles and an included side of one are congruent to the corresponding parts of the other triangle.

**ANSWER: TRUE**

- two angles and a side opposite to one of the angles are congruent to two angles and a side opposite to the corresponding other angle.

**ANSWER: TRUE**

- 234 is a rational number.

**ANSWER: TRUE**

- √(9) is a rational number.

**ANSWER: FALSE**

- √(18/100) is a rational number

**ANSWER: FALSE**

#### The system of equations has a unique solution.

- x + y = 1 and x – y = -1

**ANSWER: TRUE**

- x + 2y = 1 and x/2 + y/1 = 4

**ANSWER: FALSE** (parallel lines no intersection)

- x/2 + y/3 = 1 and y = -3x/2 + 3 (same line infinite solutions)

**ANSWER: FALSE**

- A sequence is exponential if the ratio of successive differences of consecutive terms are the same.

**ANSWER: FALSE**

- An exponential series has a finite sum to infinity provided the common ratio r is such that | r | < 1. (Read as absolute value of r is less than 1)

**ANSWER: TRUE**

- An exponential sequence with common ratio r = 1 is also a linear sequence.

**ANSWER: TRUE**

- In a parallelogram, the diagonals bisect each other and bisect the vertex angles.

**ANSWER: FALSE**

- In a kite one diagonal bisects its vertex angles and bisects the other diagonal.

**ANSWER: TRUE**

- In a rhombus, the diagonals bisect each other perpendicularly and are congruent.

**ANSWER: FALSE **

- The ordered pair (2, 3) is a solution of the inequality 3x – 2y < 1

**ANSWER: TRUE **

[3(2) – 2(3) = 6 – 6 = 0 < 1, true]

- The ordered pair (3, – 2) is a solution of the inequality 2x + 4y > -2

**ANSWER: FALSE**

[2(3) + 4(-2) = -2 > -2 false]

- The ordered pair (-2, 2) is a solution of the inequality 2x + 3y < 3

**ANSWER: TRUE**

[2(-2) + 3(2) = -4 + 6 = 2 < 3, true

#### d_{1} and d_{2} are the lengths of the diagonals of the given quadrilateral.

- The area of a rhombus is ½d
_{1}d

**ANSWER: TRUE**

- The area of a rectangle is ½d
_{1}d_{2}.

**ANSWER: FALSE**

- The area of a kite is ½d
_{1}d_{2}.

**ANSWER: TRUE**

- A triangle has three axes of symmetry.

**ANSWER: FALSE**

- A square has four axes of symmetry.

**ANSWER: TRUE**

- A pentagon has five axes of symmetry.

**ANSWER: FALSE**

#### The solution set of the inequality (x – 3)(4 – x) < 0 is

- {x: 3 < x < 4}

**ANSWER: FALSE**

- {x: x < -4, or x > – 3}

**ANSWER: FALSE**

- {x: x < 3, or x > 4}

**ANSWER: TRUE**

- x
^{2}– x + 1 is a factor of x^{3}– 1

**ANSWER: FALSE**

- x
^{2}+ x – 1 is a factor of x^{3}– 1

**ANSWER: FALSE**

- x
^{2}– x – 1 is a factor of x^{3}– 1

**ANSWER: FALSE**

- The equation y
^{2}= x^{2}represents 2 perpendicular lines.

**ANSWER: TRUE **

[ y = ± x, which are perpendicular]

- The equations x + 2y = 5 and 2x + y = 5 represent 2 perpendicular lines.

**ANSWER: FALSE**

- The equations x/3 + y/4 = 1 and y = 3x/4 + 1 represent 2 perpendicular lines.

**ANSWER: TRUE**

- 3x
^{4}+ 5x^{2}+ 7 is a trinomial.

**ANSWER: TRUE**

- 2x
^{2}– 3/x^{2}+ 7 is a trinomial.

**ANSWER: FALSE**

- 3x
^{2}y^{3}z is a monomial.

**ANSWER: TRUE**

- For a reflex angle the cosine is negative.

**ANSWER: FALSE**

- For a reflex angle the cosine is positive.

**ANSWER: FALSE**

- For a reflex angle, the sine is negative.

**ANSWER: TRUE**

NSMQ PAST QUESTION; MATHEMATICS pdf.

#### In a triangle,

- the point of intersection of the altitudes is the centroid,

**ANSWER: FALSE**

- the point of intersection of the angle bisectors is the ortho-center,

**ANSWER: FALSE**

- the point of intersection of the perpendicular bisectors of the sides is in the center.

**ANSWER: FALSE**

#### Consider the exponential function y = 2^{x}.

- The domain is the set of all real numbers.

**ANSWER: TRUE**

- The range is the set of all real numbers.

**ANSWER: FALSE**

- The point (0, 1) is a member of the function.

**ANSWER: TRUE**

#### Consider 2 simultaneous linear equations in x and y

- The equations have at most one solution.

**ANSWER: FALSE **

- The equations have at least one solution.

**ANSWER: FALSE**

- The equations may have an infinite number of solutions.

**ANSWER: TRUE**

- If a triangle has four sides, then the sum of its interior angles is 400°

**ANSWER: TRUE**

- If 2 × 3 = 8, then 8 ÷ 3 = 5

**ANSWER: TRUE**

- If the sum of 2 integers is odd, then both integers are odd.

**ANSWER: FALSE**

#### The truth set of the equation | x | = – x is

- the null set,

**ANSWER: FALSE**

- the set {x: x = 0},

**ANSWER: FALSE**

- the set {x: x < 0}.

**ANSWER: FALSE [the truth set is {x: x}]**

- sin
^{-1}(1/2) = 150

**ANSWER: FALSE**

- cos
^{-1}(-1/2) = 120

**ANSWER: TRUE**

- tan
^{-1}(-1) = 135

**ANSWER: FALSE**

- 5
^{4}< 4^{5}

**ANSWER: TRUE**

(625 < 256 x 4 is true)

- 5
^{-2}< 2^{-5}

**ANSWER: FALSE**

(1/25 < 1/32 is false)

- (-3)
^{3 }< 3^{-3}

**ANSWER: TRUE **

( -27 < 1/27 is true)

- The interior angle of a regular polygon is an obtuse angle.

**ANSWER: FALSE**

- The exterior angle of a regular polygon is an acute angle

**ANSWER: FALSE**

- The sums of the interior angles and the exterior angles of a polygon of n sides is n

**ANSWER: TRUE**

#### The implication ‘P implies Q’ is true whenever

- P is true,

**ANSWER: FALSE**

- exactly one of P, Q is true,

**ANSWER: FALSE**

- P is false.

**ANSWER: TRUE**

- The converse of a definition is true.

**ANSWER: TRUE**

- The converse of a true statement is always true.

**ANSWER: FALSE**

- The inverse of a true statement is also a true statement.

**ANSWER: FALSE**

- Multiplying a positive number by a non-negative number gives a positive number.

**ANSWER: FALSE**

- Multiplying a negative number by a non-negative number gives a negative number.

**ANSWER: FALSE**

- Multiplying a non-negative number by a non-negative number gives a positive number.

**ANSWER: FALSE**

- The sequence 1, 2
^{2}, 3^{3}, 4^{4}, . . . is an exponential sequence.

**ANSWER: FALSE**

- The sequence 1, 3, 6, 10, 15, . . . is a linear sequence.

**ANSWER: FALSE**

- The sequence 1, ½, ¼, 1/6, 1/8, . . . is an exponential sequence.

**ANSWER: FALSE**

- The domain of the function f(x) = √(4 – x
^{2}) is {x: x > 2 or x < – 2}

**ANSWER: FALSE**

- The domain of the function f(x) = (x – 1)/(x
^{2}+ 1) is {x: x ≠ ± 1}

**ANSWER: FALSE**

- the domain of the function f(x) = √(x
^{2}– 9) is {x: x ≥ 3, or x ≤ -3}.

**ANSWER: TRUE**

- The range of y = tan
^{-1}x is {y: -∞ < y < ∞} (tan inverse of x)

**ANSWER: FALSE**

- The domain of the function y = cos
^{-1}x is {x: 0 < x < 1} (cosine inverse of x)

**ANSWER: FALSE**

- The range of y = sin
^{-1}x is {y: – π/2 ≤ y ≤ π/2} (sine inverse of x)

**ANSWER: TRUE**

#### The pair of equations represent perpendicular lines.

- 2x + 3y = 1 and x/2 – y/3 = 5

**ANSWER: TRUE**

- y = 3x – 5 and x/3 + y/-1 = 9

**ANSWER: FALSE**

- 2y = 7x + 5 and x/7 – y/2 = 5

**ANSWER: FALSE**

- (a – 2)(a
^{2}+ 2a + 4) = a^{3}– 8

**ANSWER: TRUE**

- (x + y)(x
^{2}+ xy + y^{2}) = x^{3}+ y^{3}

**ANSWER: FALSE**

- (2a – 3)(4a
^{2}– 6a + 9) = 8a^{3}– 27

**ANSWER: FALSE**

- log
_{4 }√8 = 3/2

**ANSWER: FALSE**

- log
_{3 }∛81 = 3/4

**ANSWER: FALSE**

- log
_{5 }∜125 = 3/4

**ANSWER: TRUE**

- The ordered pair (-1, 2) satisfies the inequality x + y < 1.

**ANSWER: FALSE**

[-1 + 2 = 1 < 1 false]

- The ordered pair (2, – 3) satisfies the inequality 2x + y < 1

**ANSWER: FALSE **

[2(2) – 3 = 1 < 1 false]

- The ordered pair (3, – 1) satisfies the inequality x + y < 3.

**ANSWER: TRUE**

[3 – 1 = 2 < 3 true]

- The sum of the interior angles of a decagon is 1400°.

**ANSWER: FALSE**

- The sum of the interior angles of a septagon is 900°.

**ANSWER: TRUE**

- The sum of the interior angles of a duo-decagon is 1800°.

**ANSWER: TRUE**

#### The given equation of a line is in the slope-intercept form

- 2y = 3x + 7

**ANSWER: FALSE**

- x/3 + y/5 = 2

**ANSWER: FALSE**

- y = -2x + 7

**ANSWER: TRUE**

#### Consider the function f(x) = log x

- The domain is the set of all real numbers.

**ANSWER: FALSE**

- The range is the set of all real numbers.

**ANSWER: TRUE**

- The point (1, 0) lies on the graph of f(x).

**ANSWER: TRUE**

- The rational number 5/8 is less than the rational number 7/11.

**ANSWER: TRUE**

- The rational number 7/15 is less than the rational number 8/17.

**ANSWER: TRUE**

- The rational number 4/7 is less than the rational number 7/13.

**ANSWER: FALSE **

#### For a natural number n to be divisible by 18,

- it is necessary that n is divisible by 6,

**ANSWER: TRUE**

- it is sufficient that n is even and divisible by 9.

**ANSWER: TRUE**

- it is necessary that n is divisible by 12.

**ANSWER: FALSE**

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