ABOUT 53 MATHEMATICS TRUE OR FALSE NSMQ PAST QUESTIONS

ABOUT 53 MATHEMATICS TRUE OR FALSE NSMQ PAST QUESTIONS

1. Every triangle has a center of symmetry.

ANSWER: FALSE

2. An isosceles triangle has a center of symmetry.

ANSWER: FALSE

3. An equilateral triangle has a center of symmetry.

ANSWER: FALSE

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

ANSWER: FALSE

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

ANSWER: FALSE

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

ANSWER: FALSE

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NSMQ PAST QUESTION; CHEMISTRY (02)

NSMQ Past Question; Chemistry (03)

NSMQ Past Question; Chemistry (01)

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1. 3 > √8

ANSWER: TRUE

2. 2√7 > 3√3

ANSWER: TRUE

3. 3√5 >  4√3

ANSWER: FALSE

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

ANSWER: TRUE

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

ANSWER: TRUE

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

ANSWER: TRUE

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1. 4a² + 6ab + 9b² = (2a + 3b)²

ANSWER: FALSE

2. (5a – 2b)² = 25a² – 20ab + 4b²

ANSWER: TRUE

3. 9a² + 24ab + 16b² = (3a + 4b)²

ANSWER: TRUE 

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1. A triangle fits its outline in three positions.

ANSWER: FALSE

2. A parallelogram fits its outline in two positions.

ANSWER: TRUE

3. A square fits its outline in 4 positions.

ANSWER: FALSE

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1.  The point A(3, 4) is in the solution set of the inequality x² + y² > 25.

ANSWER: FALSE

2. The point B(-6, 7) is in the solution set of the inequality x² + y² < 81

ANSWER: FALSE

3. The point C(3, – 5) is in the solution set of the inequality x² + y² > 33

ANSWER: TRUE

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

ANSWER: FALSE

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

ANSWER: FALSE (only when it is equiangular)

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

ANSWER: TRUE

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The given equation has no real solution.

1. cosx = secx

ANSWER: FALSE   (cos²x = 1 has real solutions)

2. sinx = – cosecx

ANSWER: TRUE    (sin²x = -1 has no real solution)

3. tanx = – cotx

ANSWER: TRUE    (tan²x = -1 has no real solution)

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The pair of equations represent parallel lines.

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

ANSWER: TRUE

2. y = -5x + 3 and 5x – y = 3

ANSWER: FALSE

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

ANSWER: FALSE

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1. A rectangle can be circumscribed by a circle.

ANSWER: TRUE

2. A circle can be inscribed in a rectangle.

ANSWER: FALSE

3. A circle can be inscribed in a rhombus.

ANSWER: TRUE

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1. √(56) is an irrational number

ANSWER: FALSE           

[ √(2.56) = 1.6 a rational number]

2. π is a rational number.

ANSWER: FALSE

3. √(18/8) is a rational number.

ANSWER: TRUE          

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

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In linear programming,

1. the objective function is of the form Ax + By,

ANSWER: TRUE

2. the constraints can be quadratic inequalities,

ANSWER: FALSE

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

ANSWER: TRUE

---

The following quadrilateral has two pairs of adjacent congruent sides.

1. Parallelogram

ANSWER: FALSE

2. Rhombus

ANSWER: FALSE

3. Kite

ANSWER: TRUE

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1. the inequality x²/4 + y²/6 < 1 describes a region inside a circle.

ANSWER: FALSE

2. The inequality x² + y² > 16 describes a region outside a circle.

ANSWER: TRUE

3. The inequality y² > x² describes a region above the line y = x.

ANSWER: FALSE

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Determine if the converse of the statement is true or false

1. A cube is a hexahedron.

ANSWER: FALSE

2. A polygon is a pentagon.

ANSWER: TRUE

3. A tetrahedron is a pyramid.

ANSWER: FALSE

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

ANSWER: TRUE

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

ANSWER: FALSE

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

ANSWER: FALSE

---

Two triangles are congruent if

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

ANSWER: FALSE

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

ANSWER: TRUE

3. 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

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1. 234 is a rational number.

ANSWER: TRUE

2. √(9)  is a rational number.

ANSWER: FALSE

3. √(18/100) is a rational number

ANSWER: FALSE

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The system of equations has a unique solution.

1. x + y = 1 and x – y = -1

ANSWER: TRUE

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

ANSWER: FALSE  (parallel lines no intersection)

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

ANSWER:  FALSE

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

ANSWER: FALSE

2. 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

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

ANSWER: TRUE

---

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

ANSWER: FALSE

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

ANSWER: TRUE

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

ANSWER: FALSE    

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1. 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]

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

ANSWER: FALSE

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

3. 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

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d₁ and d₂ are the lengths of the diagonals of the given quadrilateral.

1. The area of a rhombus is ½d₁d

ANSWER: TRUE

2. The area of a rectangle is ½d₁d₂.

ANSWER: FALSE

3. The area of a kite is ½d₁d₂.

ANSWER: TRUE

---

1. A triangle has three axes of symmetry.

ANSWER: FALSE

2. A square has four axes of symmetry.

ANSWER: TRUE

3. A pentagon has five axes of symmetry.

ANSWER: FALSE

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

1. {x: 3 < x < 4}

ANSWER: FALSE

2. {x: x < -4, or x > – 3}

ANSWER: FALSE

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

ANSWER: TRUE

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1. x² – x + 1 is a factor of x³ – 1

ANSWER: FALSE

2. x² + x – 1 is a factor of x³ – 1

ANSWER: FALSE

3. x² – x – 1 is a factor of x³ – 1

ANSWER: FALSE

---

1. The equation y² = x² represents 2 perpendicular lines.

ANSWER: TRUE      

[ y = ± x, which are perpendicular]

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

ANSWER: FALSE

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

ANSWER: TRUE

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1. 3x⁴ + 5x² + 7 is a trinomial.

ANSWER: TRUE

2. 2x² – 3/x² + 7 is a trinomial.

ANSWER: FALSE

3. 3x²y³z is a monomial.

ANSWER: TRUE

---

1. For a reflex angle the cosine is negative.

ANSWER: FALSE

2. For a reflex angle the cosine is positive.

ANSWER: FALSE

3. For a reflex angle, the sine is negative.

ANSWER: TRUE

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NSMQ PAST QUESTION; MATHEMATICS pdf.

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In a triangle,

1. the point of intersection of the altitudes is the centroid,

ANSWER: FALSE

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

ANSWER: FALSE

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

ANSWER: FALSE

---

Consider the exponential function y = 2^x.

1. The domain is the set of all real numbers.

ANSWER: TRUE

2. The range is the set of all real numbers.

ANSWER: FALSE

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

ANSWER: TRUE

---

Consider 2 simultaneous linear equations in x and y

1. The equations have at most one solution.

ANSWER: FALSE

2. The equations have at least one solution.

ANSWER: FALSE

3. The equations may have an infinite number of solutions.

ANSWER: TRUE

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

ANSWER: TRUE

2. If 2 × 3 = 8, then 8 ÷ 3 = 5

ANSWER: TRUE

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

ANSWER: FALSE

---

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

1. the null set,

ANSWER: FALSE

2. the set {x: x = 0},

ANSWER: FALSE

3. the set {x: x < 0}.

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

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1. sin^-1(1/2) = 150

ANSWER: FALSE

2. cos^-1(-1/2) = 120

ANSWER: TRUE

3. tan^-1(-1) = 135

ANSWER: FALSE

---

1. 5⁴ < 4⁵

ANSWER: TRUE

(625 < 256 x 4 is true)

2. 5^-2 < 2^-5

ANSWER: FALSE

(1/25 < 1/32 is false)

3. (-3)³  < 3^-3

ANSWER: TRUE    

( -27 < 1/27 is true)

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

ANSWER: FALSE

2. The exterior angle of a regular polygon is an acute angle

ANSWER: FALSE

3. 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

1. P is true,

ANSWER: FALSE

2. exactly one of  P,  Q  is true,

ANSWER: FALSE

3. P is false.

ANSWER: TRUE

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1. The converse of a definition is true.

ANSWER: TRUE

2. The converse of a true statement is always true.

ANSWER: FALSE

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

ANSWER: FALSE

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

ANSWER: FALSE

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

ANSWER: FALSE

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

ANSWER: FALSE

---

1. The sequence 1, 2², 3³, 4⁴, . . . is an exponential sequence.

ANSWER: FALSE

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

ANSWER: FALSE

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

ANSWER: FALSE

---

1. The domain of the function f(x) = √(4 – x²) is {x: x > 2 or x < – 2}

ANSWER: FALSE

2. The domain of the function f(x) = (x – 1)/(x² + 1) is {x: x ≠ ± 1}

ANSWER: FALSE

3. the domain of the function f(x) = √(x² – 9) is {x: x ≥ 3, or x ≤ -3}.

ANSWER: TRUE

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

ANSWER: FALSE

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

ANSWER: FALSE

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

ANSWER: TRUE

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The pair of equations represent perpendicular lines.

1. 2x + 3y = 1 and x/2 – y/3 = 5

ANSWER: TRUE

2. y = 3x – 5 and x/3 + y/-1 = 9

ANSWER: FALSE

3. 2y = 7x + 5 and x/7 – y/2 = 5

ANSWER: FALSE

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1. (a – 2)(a² + 2a + 4) = a³ – 8

ANSWER: TRUE

2. (x + y)(x² + xy + y²) = x³ + y³

ANSWER: FALSE

3. (2a – 3)(4a² – 6a + 9) = 8a³ – 27

ANSWER: FALSE

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1. log₄ √8 = 3/2

ANSWER: FALSE

2. log_3­ ∛81 = 3/4

ANSWER: FALSE

3. log₅ ∜125 = 3/4

ANSWER: TRUE

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

ANSWER: FALSE

[-1 + 2 = 1 < 1 false]

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

ANSWER: FALSE    

[2(2) – 3 = 1 < 1 false]

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

ANSWER: TRUE

[3 – 1 = 2 < 3 true]

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

ANSWER: FALSE

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

ANSWER: TRUE

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

ANSWER: TRUE

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

1. 2y = 3x + 7

ANSWER: FALSE

2. x/3 + y/5 = 2

ANSWER: FALSE

3. y = -2x + 7

ANSWER: TRUE

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Consider the function f(x) = log x

1. The domain is the set of all real numbers.

ANSWER: FALSE

2. The range is the set of all real numbers.

ANSWER: TRUE

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

ANSWER: TRUE

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

ANSWER: TRUE

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

ANSWER: TRUE

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

ANSWER: FALSE

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For a natural number n to be divisible by 18,

1. it is necessary that n is divisible by 6,

ANSWER: TRUE

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

ANSWER: TRUE

3. it is necessary that n is divisible by 12.

ANSWER: FALSE

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