# Mathematics Skills Test

**In how many different ways can the letters of the word ‘DETAIN’ be arranged so that the vowels occupy only the even positions?**

a. 6

b. 12

c. 18

d. 36

**This question is based upon the figure shown below**

**What will be the output after simplifying the given equation?**

a. i +1

b. 4i/5 + 2/5

c. 4i/3

d. 2i/3 + 1/3

e. 2i

**Complete the following series: 4, 12, __, 108, 324**

a. 24

b. 36

c. 64

d. 48

**The two vertices of an equilateral triangle are (3,2) and (4,-1). Find the third vertex and choose the correct option.**

a. ((4 ± 3√ 3) / 2, (2 ± √ 3) / 2)

b. ((7 ± √ 3) / 2, (1 ± √ 3) / 2)

c. ((7 ± 3√ 3) / 2, (1 ± √ 3) / 2)

d. ((1 ± 3√ 3) / 2, (7 ± √ 3) / 2)

**Which of the following is the correct polar form of the equation:**

**z = 4√3 – 4i**

a. z=4√3(cos60° + isin60°)

b. z=4(cos45° – isin45°)

c. z=√8(cos60° + isin60°)

d. z=16(cos30° + isin30°)

e. z=8(cos30° – isin30°)

f. z=8√3(cos45° + isin45°)

**Find the equation of tangent to hyperbola 3x ^{2}-2y^{2} = 5 such that it is parallel to line y = 3x+5.**

a. y=3x ± √(75/6)

b. y=3x ± √(5)

c. y=3x ± √(89/8)

d. y=3x ± √(61/3)

e. y=3x ± √(23/12)

**Mark bought a laptop priced at $3260 at a discount of 20%. He also paid a sales tax of 8% after the discount. Which of the following is the amount paid by Mark?**

a. $3124.50

b. $2650.78

c. $2980.40

d. $2816.64

**Which of the following is the equation of a locus of a point, which moves in such a way that its distance from point A (0,ab) is b times its distance from point B (0,a/b) where b > 0 and b ≠ 1?**

a. x^{2} + y^{2} = a^{2}

b. x^{2} + y^{2} = a^{2} – 4aby

c. x^{2} + y^{2} = b^{2}

d. 2x^{2} + 2y^{2} = a^{2}

e. x^{2} – y^{2} = b^{2}