**1. If the length of the portion of the straight line 3x+4y =12 intercepted between the axes is:**

**a) 3**

**b) 4**

**c) 7**

**d) 5**

**Ans:d**

__Solution__To solve x-intercept, Let y=0.

3x+0 = 12

x=4

To solve y-intercept,let x=0.

0+4y=12

y=3

The line passes through (4,0) in x axis , and (0,3) in y axis.

Use equation:

x2=4, x1=0 ,y2 =3,y1=0

Ans: 5

**2.What is the sum of first 'n' natural numbers?**

**Ans: n(n+1)/2**

**3. The perimeter of one face of a cube is 20 cm. Its volume will be :**

**a) 100 cm**

^{3}**b) 125**

**cm**

^{3}**c) 400**

**cm**

^{3}**d) 625**

**cm**

^{3}**Ans:b**

__Solution:__**Let side of cube = a**

Perimeter of one face = 4a =20cm

So , a=5 cm

Volume = a

^{3}= 5

^{3}=125 cm

^{3}

**4. If 10% discount and then 20 % discount in succession is equiavalent to total of:**

**a) 15%**

**b) 30%**

**c) 24%**

**d) 28%**

**Ans: d**

__Solution:__If the first discount is x% and 2nd discount is y% then ,

Total discount = ( x + y - xy / 100 ) %

x = 10% and y = 20%

Total discount = [ 10 + 20 – ( 10 x 20) / 100] %

= ( 30 – 200 /100 ) %

Total discount = 28%

**5.**

**Allowing 20% and 15% successive discounts,the selling price of an article becomes**

**₹3060; then the marked price will be:**

**a) ₹4400 b) ₹5000**

**c) ₹4500 d) ₹4000**

**Ans: c**

__Solution:__Total discount = [ 20 + 15 – ( 20 x 15) / 100] % .

= ( 35 – 3 ) % = 32%

Selling price = Marked Price - Discount

Rs 3060 = MP - MP(32/100)

3060 = MP(68/100

MP= Rs. 4500

**6. Eighteen years ago,the ratio of A's age to B's age was 8:13. Their Present ratio's are 5:7. What is the present age of A?**

**a) 70 years b) 50 years**

**c) 40 years d) 60 years**

**Ans: b**

__Solution:__Eight years ago, let age of A = 8x

Then age of B will be 13x

After 8 years(present); (8x+18)/(13x+18) = 5/7

7(8x+18) = 5/(13x+18)

56x+126 = 65x+90

36x = 9 ; x=4

Present age of A = (8x+18) =50

7.

**If m= -4 ,n =-2, then the value of m**

^{3 }- 3**m**

^{2}+ 3m + 3n + 3n^{2}+ n^{3}is

**Ans: -126 (Direct substitution)**

**8. In a parellogram PQRS, angle P is four times of angle Q,then the measure of ∠**

**R**?

a) 36 degree b) 72 degree

c) 130 degree d) 144 degree

**Ans: d**

**Solution:**

**For a parallelogram , c**

**onsecutive angles are supplementary (P + Q = 180°).**

**∠P +**

**∠Q =**

**180°**

**4**

**∠Q**

**+**

**∠Q**

**=**

**180° (Since angle P is four times angle Q)**

**5(**

**∠Q**

**) = 180 degree**

**∠Q**

**= 180/5 =36 degree**

**Therefore**

**∠P =144 degree**

**For paralleogram opposite angles are equal. So**

**∠R =144 degree**

**9. The population of a town increases by 5% every year .If the present population is 9261, the population 3 years ago was:**

**Ans: 8000**

__Solution:__This can be solved by Compound interest equation.

CI= 9261

R=5%

n=3

CI= P(1+ R/100)

^{n}

**10. The average weight of 15 oarsmen in a boat is increased by 1.6kg when one of the crew,who weighs 42kg is replaced by a new man. Find the weight of new man.(in kg).**

Ans: 66 kg.

__Solution:__It is clear that new man has more weight than earlier one.

Total increase in weight= 1.6kg x 15 = 24kg

Weight of new man = 42+24= 66kg.

**11. the sides of a triangle having area 7776 sq.cm are in the ratio 3:4:5. the perimeter of the traingle is :**

**Ans: 432cm.**

__Solution:__Let the length of sides be 3x , 4x, 5x

Side 5x is the hypotenuse.

Area = 1/2bh

= 1/2 (3x)(4x) = 6x

^{2}

So, 6x

^{2}=7776

Solving x=36.

Length of Sides are 108cm, 144cm , 180cm.

Perimeter = 108+144+180 = 432sm.

12. The measure of an angle whose supplement is three times as large as its complement, is

a)30 degree b) 45 degree

c) 60 degree d) 75 degree

Ans: 45 degree

**12. FInd the value of tan4**

^{0 }tan43

^{0 }tan47

^{0 }tan86

^{0 }**Ans: 1**

__Solution__tan(86) = tan(90-86) =cot(4)

tan(47) = tan(90-47) = cot (43)

so, tan4 tan 43 cot 43 cot 4 = (tan4 cot 4 )( tan 43 cot 43) =1

**13. A ship after sailing 12 km towards south from a particular place covered 5km more towards east. Then the straight way distance of the ship from the place is :**

**Ans: 13km**

__Solution:__The distance will be the length of line joining initial points.

It can be found out by pythagoras theorem.

Distance = √(12

^{2}+ 5

^{2})

= 13.

**14. Two poles of height 7m and 12m stand on plane ground. If the distance between the feet is 12m, the distance between their top will be:**

**Ans: 13m**

__Solution:__BC = 12-7 =5m

AC= Distance between tops

Distance between tops,AC = √(12

^{2}+ 5

^{2})

= 13m

**15. The marked price of a watch was Rs.720. A man bought the same for Rs 550.80 after getting two discounts, the first being 10%. The second discount rate is:**

**Ans: 15%**

__Solution:__Total Discount = (720-550.8)/720 = .235

= 23.5 %

Total discount = ( x + y - xy / 100 ) %

23.5 = ( 10 + y - 10y / 100 )

9y/10 = 13.5

y=15

**16. If x+1/x =2.then the value of x**

^{12}- 1/ x^{12}is :**Ans: 0**

__Solution:__x+1/x =2

x

^{2}- 2x + 1 =0

x=1

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