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Questions and Answers
Given $A = {a, e, i, o, u}$ and $B = {a, b, c, d}$, what is $(A - B) \cap B$?
Given $A = {a, e, i, o, u}$ and $B = {a, b, c, d}$, what is $(A - B) \cap B$?
- $\phi$ (correct)
- $A - B$
- $B$
- $A$
Vectors $\vec{a} = 2\hat{i} - \hat{j} - 2\hat{k}$ and $\vec{b} = 3\hat{i} - A\hat{j}$ are perpendicular. What is the value of 'A'?
Vectors $\vec{a} = 2\hat{i} - \hat{j} - 2\hat{k}$ and $\vec{b} = 3\hat{i} - A\hat{j}$ are perpendicular. What is the value of 'A'?
- -6
- 3 (correct)
- -3
- 6
From a selection of 10 differently colored balls, how many ways can you choose 7 balls if black and white balls are excluded?
From a selection of 10 differently colored balls, how many ways can you choose 7 balls if black and white balls are excluded?
- 12 (correct)
- 60
- 10
- 8
Given $\cos{\theta}\sin{\theta} = 0.22$, what is $(\cos{\theta} - \sin{\theta})^2$?
Given $\cos{\theta}\sin{\theta} = 0.22$, what is $(\cos{\theta} - \sin{\theta})^2$?
Point C divides points A(1, 2) and B(7, -4) in the ratio 1:2. What are the coordinates of point C?
Point C divides points A(1, 2) and B(7, -4) in the ratio 1:2. What are the coordinates of point C?
If $a = 4$ and $r = \frac{1}{3}$, what is the geometric progression?
If $a = 4$ and $r = \frac{1}{3}$, what is the geometric progression?
What is the derivative of $f(x) = 7x^6 + 6x^5 + 5x^4$?
What is the derivative of $f(x) = 7x^6 + 6x^5 + 5x^4$?
What is the fifth derivative of $f(x) = e^{axb}$?
What is the fifth derivative of $f(x) = e^{axb}$?
For what value of 'x' is the matrix $\begin{bmatrix} 2 & 4 \ 4 & x \end{bmatrix}$ singular?
For what value of 'x' is the matrix $\begin{bmatrix} 2 & 4 \ 4 & x \end{bmatrix}$ singular?
The matrix $A = \begin{bmatrix} 2 & 4 \ \frac{1}{2} & 1 \end{bmatrix}$ is of what type?
The matrix $A = \begin{bmatrix} 2 & 4 \ \frac{1}{2} & 1 \end{bmatrix}$ is of what type?
What is the value of $2 \sin{45^\circ} \cos{45^\circ}$?
What is the value of $2 \sin{45^\circ} \cos{45^\circ}$?
The equation $r^2 = g^2 + f^2 - c$ represents what?
The equation $r^2 = g^2 + f^2 - c$ represents what?
If $a = x + y$ and $b = x - y$, what is the value of $ab$?
If $a = x + y$ and $b = x - y$, what is the value of $ab$?
What is the probability of drawing a red card from a standard deck of 52 cards?
What is the probability of drawing a red card from a standard deck of 52 cards?
For the curve $x^2 - \frac{y^2}{5} = 1$, what are the coordinates of the foci?
For the curve $x^2 - \frac{y^2}{5} = 1$, what are the coordinates of the foci?
What is $\int \frac{\cos{x}}{\sqrt{\sin{x}}} dx$?
What is $\int \frac{\cos{x}}{\sqrt{\sin{x}}} dx$?
What is $\frac{d}{dx} e^{x^3}$?
What is $\frac{d}{dx} e^{x^3}$?
What is the sum of the first 'n' odd integers?
What is the sum of the first 'n' odd integers?
Evaluate: $\begin{vmatrix} xyz^2 & x^2yz & xy^2z \ x & y & z \ y & z & x \end{vmatrix}$
Evaluate: $\begin{vmatrix} xyz^2 & x^2yz & xy^2z \ x & y & z \ y & z & x \end{vmatrix}$
How many tangents can be drawn to a circle from a point lying outside the circle?
How many tangents can be drawn to a circle from a point lying outside the circle?
What is the value of $\sin{15^\circ}$?
What is the value of $\sin{15^\circ}$?
What is $\int{x^2e^x dx}$?
What is $\int{x^2e^x dx}$?
If the focus of a parabola is (0, -3), which direction does it open?
If the focus of a parabola is (0, -3), which direction does it open?
What is $\frac{1}{1 - \sin^2{\theta}} + \frac{1}{1 + \sin^2{\theta}}$ equivalent to?
What is $\frac{1}{1 - \sin^2{\theta}} + \frac{1}{1 + \sin^2{\theta}}$ equivalent to?
What is $\frac{d}{dx} \tan^2{x}$?
What is $\frac{d}{dx} \tan^2{x}$?
Evaluate the integral: $\int{\ln{e^{2x}} x^2 e^{3x^3} dx}$
Evaluate the integral: $\int{\ln{e^{2x}} x^2 e^{3x^3} dx}$
What is the distance between points (2, -6) and (6, -3)?
What is the distance between points (2, -6) and (6, -3)?
The equation of the line is $\frac{5x}{2} + \frac{7y}{2} = \frac{49}{10}$, what is the slope?
The equation of the line is $\frac{5x}{2} + \frac{7y}{2} = \frac{49}{10}$, what is the slope?
The standard equation of a hyperbola with center at (0, 0) is which of the following?
The standard equation of a hyperbola with center at (0, 0) is which of the following?
Find the equation of the tangent to the curve $3x^2 - 4y^2 = 12$ at (4, -3).
Find the equation of the tangent to the curve $3x^2 - 4y^2 = 12$ at (4, -3).
What is $\frac{d}{dx} [f(x) \cdot g(x)]^2$?
What is $\frac{d}{dx} [f(x) \cdot g(x)]^2$?
If $z = -7 + \sqrt{3}i$, find $(z - \bar{z})^3$.
If $z = -7 + \sqrt{3}i$, find $(z - \bar{z})^3$.
If $f(x) = x^3 + \cos{x}$, then what type of function is it?
If $f(x) = x^3 + \cos{x}$, then what type of function is it?
Evaluate the limit: $\lim_{x \to 3} \frac{3x^2 - 7x - 6}{x^2 - 8x + 15}$
Evaluate the limit: $\lim_{x \to 3} \frac{3x^2 - 7x - 6}{x^2 - 8x + 15}$
If $f(x) = \sin^3{x}$, what is $f'(x)$?
If $f(x) = \sin^3{x}$, what is $f'(x)$?
If $\frac{dy}{dx} = \ln{x}$ and the slope at (x, y) is the same as when it is parallel to the x-axis, find x.
If $\frac{dy}{dx} = \ln{x}$ and the slope at (x, y) is the same as when it is parallel to the x-axis, find x.
What is the derivative of $\cos^2{3x}$?
What is the derivative of $\cos^2{3x}$?
The curve $y = x^2 - 8$ has which of the following?
The curve $y = x^2 - 8$ has which of the following?
Flashcards
(A - B) ∩ B
(A - B) ∩ B
Intersection of (A - B) and B, where A = {a, e, i, o, u} and B = {a, b, c, d}
Value of 'A' for perpendicular vectors
Value of 'A' for perpendicular vectors
Perpendicular vectors have a dot product of zero. Solve for 'A' in a · b = 0.
Choosing balls of different colors
Choosing balls of different colors
Calculate combinations of choosing 7 balls from 10, excluding black and white balls
Value of (cos θ – sin θ)^2
Value of (cos θ – sin θ)^2
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Point dividing a line segment
Point dividing a line segment
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Geometric progression for a = 4, r = 1/2
Geometric progression for a = 4, r = 1/2
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Derivative of 7x^6 + 6x^5 + 5x^4
Derivative of 7x^6 + 6x^5 + 5x^4
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Fifth derivative of e^(ab)
Fifth derivative of e^(ab)
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Value of 'x' for singular matrix
Value of 'x' for singular matrix
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What is a singleton matrix?
What is a singleton matrix?
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Value of 2sin45°cos45°
Value of 2sin45°cos45°
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What does r² = g² + f² – c represent?
What does r² = g² + f² – c represent?
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Finding value of ab
Finding value of ab
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Probability of a red card
Probability of a red card
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Coordinates of foci
Coordinates of foci
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∫ cosx / √(sinx) dx
∫ cosx / √(sinx) dx
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d/dx e^(x³)
d/dx e^(x³)
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Sum of first n odd integers
Sum of first n odd integers
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Value of the expression
Value of the expression
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Tangents from an external point
Tangents from an external point
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Value of sin 15°
Value of sin 15°
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∫ x²e^x dx =?
∫ x²e^x dx =?
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Value of expression
Value of expression
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Parabola with focus at (0,-3)
Parabola with focus at (0,-3)
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d/dx tan²x
d/dx tan²x
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∫e^x²x²e^x³
∫e^x²x²e^x³
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Distance between (2,-6) and (6, -3)
Distance between (2,-6) and (6, -3)
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Slope of line
Slope of line
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standard equation of hyperbola.
standard equation of hyperbola.
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equation tangent to curve
equation tangent to curve
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Study Notes
FAST Admission Test: Past Papers - Mathematics
- Find the intersection of set A minus set B with set B, given A = {a, e, i, o, u} and B = {a, b, c, d}. The result is the null set, denoted by Φ.
- Determine the value of 'λ' such that vectors a = 2i - j - 2k and b = 3i - λj are perpendicular. The value is 3.
- There are 10 differently colored balls; to find out the number of ways 7 balls can be chosen with exclusion of black and white, the answer is 12.
- Given cosθsinθ = 0.22, find (cosθ - sinθ)². The result is 0.56.
- Determine the point that divides the line segment joining (1, 2) and (7, -4) in the ratio 1:2. The point is (3, 0).
- If the first term a = 4 and common ratio r = 1/2, find the geometric progression. It's 4, 2, 1, 1/2,...
- The derivative of 7x⁶ + 6x⁵ + 5x⁴ is 42x⁵ + 30x⁴ + 20x³.
- The fifth derivative of f(x) = e^(ab) is (ab)⁵e^(ab).
- Find x if |[2, 4], [4, x]| is a singular matrix. The value of x is 8.
- A = |[2,4], [2,4]| is a Null
- Calculate 2sin45°cos45°. The answer is 1.
- r² = g² + f² - c represents a circle.
- If a = x + y and b = x - y, then the value of ab = x² - y².
- The probability of drawing a red card from a standard deck is ½.
- For the curve x² - y²/5 = 1, foci coordinates are (±√6, 0).
- The integral of cosx/√sinx dx = 2√sinx + c.
- The derivative of e^(x³) with respect to x is 3x²e^(x³).
- The sum of the first n odd integers is n².
- Evaluate the expression (xyz² / x) (x²yz / y) (xy²z / z). The expression equals 1.
- Two tangents can be drawn to a circle from any point lying outside the circle.
- sin15° = (√6 - √2) / 4.
FAST Admission Test: Past Papers - IQ
These questions evaluate pattern recognition, sequencing, and problem-solving skills using letters, numbers, and shapes.
FAST Admission Test: Past Papers - Basic Math
- Determine which number of rows is not possible if 180 students are seated with the same number of students in each row. The constraint eliminates 40 rows.
- Save $160 annually by paying the monthly parking rate rather than the weekly rate.
- Given y = 5x² - 2x and x = 3, the value of y is 39.
- √0.0026 approximates to 0.05.
FAST Admission Test: Past Papers - Analogies
- BANDAGE : LACERATION :: B. alcohol : antiseptic
- PEDAL : FOOT :: B. crutch: leg
FAST Admission Test: Past Papers - Synonyms
- Synonym of ANTIPATHY is indifference
- Synonym of ENGENDER is to produce
FAST Admission Test: Past Papers - Antonyms
- Antonym of NORM is anomaly
- Antonym of APPREHEND is release
FAST Admission Test: Past Papers - Sentence Completion
- After having investigated their current level of study, students are typically ready to move on to the next one.
- My friend generously offered to look after my children while I was out, but because we already had a babysitter, I took the offer.
FAST Admission Test: Past Papers - Prepositions
- He will appear before the magistrate.
- I would like to move into Marketing.
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