2015 JUPEB MATHEMATICS – Multiple Choice Questions

Find the non-zero negative value of x which satisfies the equation

$\left|\begin{array}{ccc}x& 1& 0\\ 1& x& 1\\ 0& 1& x\end{array}\right| = 0$

$\text{If Z = }\left[\begin{array}{ccc}2& 3& 3\\ 4& 1& 0\\ 1& 4& 0\end{array}\right]\text{ , find the determinant of Z}$

$\mathrm{Compute} {\left(1 + \frac{3}{1 + \mathrm{i}}\right)}^2$

Find the centre and radius of the circle 8x² + 8y² – 24x – 40y + 18 = 0

Find the equation of the tangent to the circle 2x² + 2y² = 30 at the point (-3,6).

Given the equations of the ellipse x²/2+y²=1. Find the equation of the directrices.

Find the gradient of the curve y = x³ – 6² + 11x – 6 at the point (1,0)

$$\begin{gathered} \text{Given sets A = }\left\{\mathrm{a},\mathrm{b},1,3\right\} \\ \mathrm{and} \mathrm{B} =\left\{\mathrm{a},2,4\right\}, \\ \mathrm{find} \mathrm{A}\cup \mathrm{B}. \end{gathered}$$

Let P be the set of prime factors of 42 and Q be the set of prime factors of 45. Find P n Q

A polynomial 2x³ + ax² + bx – 1 has a factor ( x −1) and the remainder when it is divided by  (x−2) is −4. Find a + b.

Solve the equation log₃ + log_x 3 = ¹⁰/₃

$\text{Solve the equation }\sqrt{2x+3}–\sqrt{\left(x–2\right)}=2$

If y  =  x (x⁶ – 1), find the range for which  y  = 0.

$\mathrm{Evaluate} \underset{\mathrm{x} \to –3}{\lim }\left\{\frac{3{\mathrm{x}}^{2 }– 27}{\mathrm{x} + 35}\right\}$

${\text{Evaluate ∫ }}_1^e\frac{1}{x}\text{dx}$

${\text{Evaluate ∫}}_0^{\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\cos \text{x }d\mathrm{x}$

$\text{Evaluate }\underset{\mathrm{x}\to \infty }{\lim }\left\{\frac{2{\mathrm{x}}^2+{\mathrm{x}}^2–5}{{\mathrm{x}}^3+2\mathrm{x}+1}\right\}$

The expression px² + qx + r equals 4 at x = 1. If the derivatives is 2x + 1, what are the values of p,q and r respectively

The gradient of a curve at any point (x, y) is given by 2x + 3. If the curve passes through the origin, find the equation of the curve.

The position of an object in motion at any time (t) is given by s = 3t³ – 5t – 2. Obtain the velocity of the object after 2 seconds

Find the derivatives of y = 2x³ – 5x² +2

Find the derivatives of y = (3x + 2x)(1 – x)

Differentiate (x + y)² = 5.

$\mathrm{Evaluate} \underset{\mathrm{x}\to 5}{\lim }\frac{{\mathrm{x}}^2–25}{\mathrm{x}–5}$

If y = (x – 1) e^-x, find ^dy/_dx

Find the modulus of 2i + 3j – 4k

Find the scalar products of a = 2i + 3j and b = – i + 4j

Find the value of n for which the vector si +nj -3k and ni – j + 5k are perpendicular

Obtain the projection of vector a = (3,-1.5) on the vector b = (2.1,-3)

Find the volume of the tetrahedron OABC with point A (2,1,1) ,B(0,-1,1) and C(-1,3,0).

The distance S in meters (m) moved by a particle in t time in seconds (s) given by S = 1.5t². find its speed after t seconds

A car starts from and travels 10km due West, 20km North-West and 30km due North. Find the displacement from A

The brakes of a train are able to produce retardation of 1.2m/s. if the train is traveling at 90km/h, at what distance from a station should the brakes be applied.

A particle is projected with a velocity of 20m/s up a smooth inclined plane of inclination 30°. Find the distance described up the plane.

A block of mass 20kg rests on a horizontal plane whose coefficient of friction is 0.4. Find the least force required to move the block if it acts horizontally.

A mass of 8kg hangs in equilibrium, suspended by two light inelastic strings making angles 30° and 45° with the horizontal, calculate the tensions in the two strings.

If = a = 2i + 3j   + 5k , b = 3i – 5j + 2k, c= i = j. calculate A such that 2d – 5b + AC is perpendicular to the x – axis.

The probabilities that John and Joanna will passed an examination are ²/₃ and ⁴/₅. Find the probability that only one of them will pass.

In how many ways can a committee of 2 men and 2 women be formed from 3 men and 5 women?

The formular for Spearman’s rank correlation is:

The following are continuous random variables except

The following are features of a standard normal curve except

An experiment in which the outcomes are two possibilities: “Success” or “failure” is said to be

The range of values of rank correlation (r_rank) is

Find the geometric mean of the data: 5, 15, 10, 8, 12.

One can easily determine the _________ of a distribution from histogram.

Find the mean of the following scores.

What is the mode of the following numbers 1,8,8,10,9,2,7,8,2,2,4,1,1,8,7,1

The ________ level of a test is the maximum probability of committing Type I error when the null hypothesis holds.

The standard deviation of a statistic describes