**Question 1 :**

The unit digit of 13^{17} + 17^{13} is

(A) 0 (B) 9 (C) 1

**Solution :**

Unit digit of 13 Unit digit of 13 Unit digit of 13 Unit digit of 13 |
Unit digit of 17 Unit digit of 17 Unit digit of 17 Unit digit of 17 |

(The order is repeated after every multiple of 4)

Hence the unit digit of 13^{17 }is 3

Units digit of 17^{13} = 7

Units digit of sum of both the numbers = 3+7 = 0

Answer = 10

(The order is repeated after every multiple of 4)

**Question 2 :**

If the diameter of a circle is 376216 inches, using the approximation π = 3:14, compute the ratio of the its area, in square inches, to its circumference in inch.

(A) 94054:5 (B) 94554:1 (C) 94054:1

**Solution :**

Radius of circle = 376216/2 = 188108

Area of circle : Circumference of circle

πr^{2} : 2 πr

r : 2

188108 : 2

Divide both terms by 2

188108/2 : 2/2

94054 : 1

**Question 3 :**

If 1/7 is written in decimal form, then the 100th digit after the decimal point is

(A) 8 (B) 3 (C) 7

**Solution :**

1/7 = 0.142857142857............

From the above decimal value, we come to know that this 6 digits is repeating.

Now let us calculate how many 6 are in 100.

16 (6) = 96

1 is the 97^{th} digit

4 is the 98^{th} digit

2 is the 99^{th} digit

8 is the 100^{th} digit

**Question 4 :**

The length of the two parallel sides of a trapezium are 15 cm and 10 cm. If its area is 100 sq. cm. Find the distance between the parallel sides.

(A) 12 cm (B) 16 cm (C) 8 cm

**Solution**

Given: a = 15 cm, b = 10 cm, Area = 100 sq. cm.

Area of the trapezium = 100

(1/2) h (a + b) = 100

(1/2) h (15 + 10) = 100

h = 200/25

h = 8

So, the distance between the parallel sides = 8 cm.

**Question 5 :**

.If a, b, and c are nonzero numbers satisfying 3a = 4b and 5b = 6c, what is c/(a + b) ?

(A) 5/14 (B) 3/10 (C) 2/19

**Solution :**

3a = 4b a = 4b/3 |
5b = 6c (5b/6) = c |

c/(a + b) = (5b/6)/((4b/3) + b)

= (5b/6)/(7b/3)

= (5b/6)**⋅**(3/7b)

= (5/2)**⋅**(1/7)

= 5/14

So, the answer is 5/14.

**Question 6 :**

The radii of two spheres are of 2 and 6, then the ratio of the volume of the larger sphere to the volume of the smaller sphere is

(A) 1 : 27 (B) 2 : 15 (C) 5 : 14

**Solution :**

Volume of sphere = (4/3) πr^{3}

(4/3) πR^{3 }: (4/3) πr^{3}

R^{3 }: r^{3}

2^{3 }: 6^{3 }==> (2 ⋅ 2 ⋅ 2)/(6 ⋅ 6 ⋅ 6)

1 / 27

1 : 27

So, the required ratio is 1 : 27

**Question 7 :**

If P be the product of the first nine multiples of 19 (i.e. P = 19x38x57……….152x171). What is the unit digit of P?

(A) 5 (B) 9 (C) 0

**Solution :**

= 19 x 38 x 57……….152 x 171

= (1 x 19) x (2 x 19) x (3 x 19)……….(9 x 19)

= 19 (1 + 2 + 3 + .......... + 9)

= 19 ( 9(9+1) / 2)

= 19 (9 ⋅ 10 / 2)

= 19 ⋅ 45

= 855

So, the unit digit is 5.

**Question 8 :**

Find the perimeter of the rectangle whose length is 5cm and breadth is 3 cm.

(A) 10 cm (B) 16 cm (C) 15 cm

**Solution :**

Perimeter of rectangle = length ⋅ breadth

= 5 (3)

= 15 cm

So, the perimeter of rectangle is 15 cm.

**Question 9 :**

What is the value of 1 + 3 + 5 +…………………… + 195 + 197 + 199?

(A) 10500 (B) 10001 (C) 10000

**Solution :**

Sum of odd numbers = [(l + 1)/2]^{2}

= [(199 + 1)/2]^{2}

= (200/2)^{2}

= 100^{2}

= 10000

So, the answer is 10000.

**Question 10 :**

The number of positive divisors of 120 are divisible by 4 are

(A) 7 (B) 3 (C) 8

**Solution :**

Divisors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

From the above numbers 4, 8, 12, 20, 24, 40, 60, 120 are divisible by 4.

So, the answer is 8.

If you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**