JUPEB 2019 – MATHEMATICS: SCI-J154 – Multiple Choice Questions

Let Q, N, Z, C and Q denote the set of Rational, Natural, Integer, Complex and Irrational numbers respectively. Which of the following set contains the whole set of real numbers?

Determine the solution set of the inequality: 2x² – 3x – 2 < 0

Evaluate the conjugate of the complex number:

$\mathrm{Z}=\frac{1}{–1+\mathrm{i}}$

$$\begin{gathered} \mathrm{Compete} \mathrm{the} \mathrm{value} \mathrm{of} \mathrm{x} \mathrm{if} \frac{4^{–\mathrm{x}}\times {32}^{\mathrm{x}+1}+5\mathrm{x}}{5}= \\ \frac{{16}^{2\mathrm{x}+1}}{5}+\mathrm{x} \end{gathered}$$

Find tan 75⁰ in surd form

Given that log₁₀2 = 0.3010, log₁₀3 = 0.4771 and log₁₀7= 0.8451, compute log₁₄72.

If U₁ = 3, U₂ = 4 and U_u = a + bn, computer U₆

$$\begin{gathered} \mathrm{Let} \mathrm{\alpha } \mathrm{and} \mathrm{\beta } \mathrm{be} \mathrm{the} \mathrm{roots} \mathrm{of} \mathrm{the} \mathrm{equation}: \\ {\mathrm{x}}^{\mathrm{x}}+5\mathrm{x}+6=0. \mathrm{Deduce} \mathrm{the} \mathrm{equation} \mathrm{whose} \\ \mathrm{roots} \mathrm{are} {\mathrm{\alpha }}^2 \mathrm{and} {\mathrm{\beta }}^2. \end{gathered}$$

Which form of the partial fraction is equivalent to the algebraic fraction:

$\frac{\mathrm{f}\left(\mathrm{x}\right)}{\left({\mathrm{x}}^2+1\right){\left(\mathrm{x}–\mathrm{b}\right)}^2}$

Determine the center and the radius of the circle x² + y² – 2ax + 2yb + a² = 0 in term of a and b

Express 1 + I in the conjugate of its polar

$$\begin{gathered} \mathrm{A} \mathrm{binary} \mathrm{equation}, ‘*‘ \mathrm{is} \mathrm{defined} \mathrm{on} \mathrm{the} \mathrm{set} \mathrm{of} \mathrm{real} \mathrm{numbers}. \\ \mathrm{R} \mathrm{by}: \mathrm{x}*\mathrm{y}=\frac{1}{5}\left(5\mathrm{x}+5\mathrm{y}–4\right) \mathrm{for} \mathrm{any} \mathrm{two} \mathrm{real} \mathrm{numbers} \\ \mathrm{x}, \mathrm{y}, \mathrm{\epsilon } \mathrm{R}. \mathrm{Calculate} \mathrm{the} \mathrm{identity} \mathrm{element}. \end{gathered}$$

$$\begin{gathered} \mathrm{If} \mathrm{P}=\left[\begin{array}{ccc}\mathrm{y}& 3& 0\\ 2& 1& \mathrm{y}\\ 2& 1& 2\end{array}\right], \mathrm{what} \mathrm{is} \mathrm{the} \mathrm{range} \mathrm{of} \\ \mathrm{values} \mathrm{of} \mathrm{y} \mathrm{for} \mathrm{which} \left|\mathrm{P}\right| >0? \end{gathered}$$

Calculate the sum to infinity of 1 + tan30⁰ + tan²30⁰ + tan³30⁰ + …

Estimate the value of the product log₂3 log₃4 log₄5 log₅6 log₆7 log₇8

Let the expression ax² + bx + c = 8 at x = 1, if the derivative is 4x+2, determine the values of a, b and c respectively

The distance, S in metres moved by a particle in time, t in second is given by S(t) = 3.5t³ – 2t^. Evaluate its speed after 1 second.

Calculate the gradient of the curve y = x³ – 3x² + 7x + 23 at the point (2, 1)

Find the derivative of the line joining the points A(3,5), to b(6,-8)

$\mathrm{Evaluate}: \underset{\mathrm{x}\to 0}{\lim }\left(\frac{\mathrm{x}+\mathrm{sinx}}{\mathrm{x}\left(\mathrm{x}+1\right)}\right)$

Give that x = Sin (t) and y = cos(t), then the letter t simply called that _______

Given that y = Cos 2θ, x = Sin θ. Express ^dy/_dx in term of θ.

Let the given curve of a parabola be y² = x. Estimate the area of the curve in terms of x.

Find the derivative of the function y = log_e tan 2x.

The radius of a sphere is increasing at the rate of 0.1cm/s. Determine the rate at which the surface area is increasing when the radius is 5cm

Evaluate y in terms of x if = 3x² – 6x + 2, given that y = 7 when x = 0

$$\begin{gathered} \mathrm{Obtain} \frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} \mathrm{for} \mathrm{the} \mathrm{function} \\ \mathrm{y}=2{\mathrm{x}}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}–5\mathrm{x}\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \end{gathered}$$

$$\begin{gathered} \mathrm{Evaluate} {\int }_0^{\mathrm{z}}12{\mathrm{x}}^{2}d\mathrm{x}= 1372 \mathrm{to} \mathrm{get} \mathrm{the} \\ \mathrm{value} \mathrm{of} \mathrm{z}. \end{gathered}$$

$\mathrm{The} \mathrm{expression} \mathrm{for} {\mathrm{e}}^{–\mathrm{x}} \mathrm{is} \mathrm{given} \mathrm{as} \mathrm{\_\_\_\_\_\_\_\_\_\_}$

Describe the unit vector in the direction of 2i + j – 2k

Compute the modules of the vector

$2\mathrm{i}+3\mathrm{j}–\sqrt{3\mathrm{k}}$

An object of mass 2.5kg moving at a constant velocity or 12ms^-1 comes in contact with a resistance of 10N. How long does it take the body to come to rest?

With what velocity should a stone be thrown vertically upwards to reach the top of a hill 50m high?

A truck travelling on level ground is subject to a resisting force (from the brakes and air resistance) of 250KN for a distance of 5km. How much kinetic energy does the train lose?

A body starts from rest and moves with a uniform acceleration of 100m^s-1. Calculate the distance it covers in the 4^th second.

A stone is dropped from the top of a building and reaches the ground after 2 seconds. Determine the height of the building (Take g = 9.8ms^-2)

A load of mass 70kg is placed in a lift. Calculate the reaction between the floor of the lift and the load when the lift moves upwards with an acceleration of 2ms^-2.

(Take g = 9.8ms^-2)

A block of mass 3kg rests on a rough horizontal table. If the coefficient of friction between the block and the table is 0.43, determine the minimum horizontal forces that will make the

(Take g = 9.8ms^-2)

$$\begin{gathered} \mathrm{Three} \mathrm{point} \mathrm{A}, \mathrm{B} \mathrm{and} \mathrm{C} \mathrm{have} \mathrm{spatial} \mathrm{coordinates} \\ \left(–5, –2, 3\right), \left(–2, 5, 3\right) \mathrm{and} \left(4, 5, 2\right) \mathrm{respectively}. \\ \mathrm{Find} \mathrm{the} \mathrm{scalar} \mathrm{product} \mathrm{of} \mathrm{displacement} \mathrm{vectors} \\ \overrightarrow{\mathrm{AB} } \mathrm{and} \overrightarrow{\mathrm{BC}} \end{gathered}$$

The mean score of 100 students in a class that took a statistics test is 72. IF the mean of score of the 70 boys in the class is 75, calculate the mean score of the girls in the class.

In how many ways can be first, second and third position be won by six athletes in a race of 100 metres?

A bag contains 5 white, 2 black and 3 green balls. IF three (3) balls are drawn at random without replacement, what is the probability that two (2) balls are white and one (1) ball is black?

When a distribution is moderately skewed wit one mode, which of the following relation is correct?

Which of the measures of central tendency is often affected by extreme values?

The heights, xcm of a sample of 80 female students are summarized by the equation Ʃ(x-160) = 24.0. Compute the mean height of a female student.

A fair coin is tossed 5 times, Find the probability of obtaining at least 4 heads.

Deduce the mode of 6, 8, 2, 1, 1, 2, 4, 2, 3.

$$\begin{gathered} \mathrm{A} \mathrm{population} \mathrm{with} \mathrm{variance} 16 \mathrm{has} \mathrm{unknown} \\ \mathrm{mean} \mathrm{\mu }. \mathrm{Let} \overline{\mathrm{X}} \mathrm{be} \mathrm{the} \mathrm{mean} \mathrm{of} \mathrm{a} \mathrm{random} \\ \mathrm{sample} \mathrm{of} \mathrm{size} 100 \mathrm{from} \mathrm{this} \mathrm{population}. \mathrm{If} \\ \overline{\mathrm{X}} \mathrm{is} \mathrm{used} \mathrm{to} \mathrm{estimate} \mathrm{\mu }, \mathrm{determine} \mathrm{the} \mathrm{standard} \mathrm{error} \mathrm{of} \overline{\mathrm{X}}. \end{gathered}$$

What is the mean value of a binominal variate whose number of repeated trials (n) equal to 8 and probability of success (p) equals 0.4?

The probability that a patient will die while undergoing a delicate heart operation is 0.175. What is the probability of the patient surviving from the operation?