NSMQ 2024 Mathematics True/False
Review past NSMQ 2024 Mathematics True/False round questions with detailed answers and comprehensive explanations
A triangle has sides of length A, B, and C.
P, Q, and R are simple statements. If P is false, Q is true, and R is false, then the given compound statement is true.
If α and β are the roots of the equation x² + bx + c = 0, the value of α² + β² is
The following is an identity.
An arc subtends an angle of 30° at the center of a circle of radius 1 centimeter. The length of the arc is...
If the equation AX² + BY² + 2FX + 2GY + C = 0 represents a circle, then
sin(210°) = sin(30°)
The inequality 2/(x + 1) > 0 is equivalent to
15 ≡ −13 (mod 14)
sin(2π − x) = sin x
If √(2x² − 64) = x, then
π can represent
The function f(x) has no finite stationary point.
The center of the circle
f(θ) = sin 2θ has a maximum value of 1 in the interval 0 < θ < π/3.
If the sum of the first n terms of a series S_n is given by
If cos x = −1/2, then sin x = ±√3/2.
In the binomial expansion of (1 + x)ⁿ, the expansion is finite if…
The following is an identity.
The greatest value of the expression 6 cos θ + 8 sin θ is…
The expression (5 + 3√2) / (5 − 3√2)…
If the diagonals of a quadrilateral bisect each other, then it is a…
The given infinite series has a finite sum.
P, Q, and R are simple statements such that P is true, Q is false, and R is false.
N is a natural number. If N² is divisible by 12, then …
If the sum of the angles of a triangle is 300°, then it is a pentagon.
The given expression is an exact square.
If y² = x⁴ / z⁻³, then 2 log y = 4 log x − 3 log z.
An angle θ is such that tanθ is negative and cosθ is negative. Then, θ is in…
If x² + y² = 10, then dy/dx is …
The pair of vectors A and B where …
If x² − 2bx + c = 0 has equal roots, then …
If f(x) = x² and g(x) = sin x, then…
{3, 5, 7, 9, …} is a linear series.
The given quadratic expression is always positive for real x.
The given linear transformation has an inverse.
The given equation is the equation of a circle.
The gradient to the given curve is always non-negative.
The domain of the function f(x) = 2 / (x² − 1) is…
If a function f has an inverse, then…
A sector of a circle of radius r cm and sectoral angle θ° has…
If α and β are the roots of 2x² − 5x + 3 = 0, then…
In the following, P and Q are natural numbers.
The function g(x) is the reciprocal of the function f(x).
The function f(x) = x² − 3x − 4 is…
The interior angle of a regular…
In the first quadrant, cos θ and sin θ are both positive.
A and B are vectors. If their scalar product A·B equals zero, then…
The given statement is always true.
The given pair of equations represent perpendicular lines.
The two lines with given equations are either parallel or perpendicular.
The inequality (x + 2)/(x − 3) > 5 is equivalent to x + 2 > 5(x − 3).
The given line segments intersect inside a triangle.
In the coordinate XY plane, under a reflection in the…
The product of a rational number and an irrational number is an irrational number.
If sin θ > 0, then cos θ > 0.
If sin θ > 0, then θ lies in either the first or second quadrants.
∫(x³ − 1/x³) dx = x⁴/4 − 1/x⁴ + c
sin⁻¹(−1/2) = 5π/6
If f(x) = x + 1 and g(x) = sin x, then f(g(x)) = sin(x + 1).
The function f(x) = (x + 2)(x − 2) is negative and increasing on the interval −2 < x < 2.
cos(A + B) + cos(A − B) = 2cos A cos B.
In the expansion of (1 + Ax)ⁿ, the coefficient of x² is n(n−1)A²/2.
The gradient of f(x) = (x⁶ − 1)/x³ is 3x² + 1/(2x²).
If f(x) = v/u, the quotient rule gives df/dx = (u dv/dx − v du/dx)/u².
If X is a real number and non-negative, then X is greater than zero.
If f(x) is differentiable on the interval, 0 ≤ x ≤ A, then...
Expressed as a difference of two squares.
In the Cartesian xy plane,…
For a function y = f(x),…
The given expression is an exact cube.
A cubic polynomial function f(x) has…
