3
Q:

# In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?

 A) 160 B) 175 C) 180 D) 195

Explanation:

Suppose the man works overtime for x hours.

Now, working hours in 4 weeks = (5 x 8 x 4) = 160.

${\color{Blue}&space;\therefore&space;}$ 160 x 2.40 + x x 3.20 = 432

=> 3.20x = 432 - 384 = 48

=> x = 15.

Hence, total hours of work = (160 + 15) = 175.

Q:

$\inline \fn_jvn \small 5sinx+12cosx+r$ is always greater than or equal to zero. What is the smallest value satisfied by 'r' ?

 A) -13 B) 11 C) 13 D) -11

Explanation:

Given,

5sinx + 12cosx ≥ -r

$\small&space;\Rightarrow$13($\inline&space;\small&space;\frac{5}{13}$sinx+$\inline&space;\small&space;\frac{12}{13}$cosx) ≥ -r

$\small&space;\Rightarrow$$\inline&space;\small&space;\frac{5}{13}$= cosA => sinA =$\inline&space;\small&space;\frac{12}{13}$

$\small&space;\Rightarrow$13(sinx cosA + sinA cosx) ≥ -r

$\small&space;\Rightarrow$13(sin(x + A)) ≥ -r

we know that , -1 ≤ sin (angle) ≤ 1

$\inline&space;\small&space;\Rightarrow$13sin (x + A) ≥ -13 $\small&space;\Rightarrow$ $\inline&space;\small&space;r_{min}$ = 13

4 63
Q:

If a+b=5 and 3a+2b=20,then (3a+b)will be :

 A) 20 B) 15 C) 25 D) 30

Explanation:

a+b=5   ...(1)    and    3a+2b=20 ...(2)

Multiplying (1) by 2 and subtracting from (2), we get : a=10.

Putting a=10 in (1), we get : b=-5

$\therefore$   (3a+b) = 3 x 10+(-5)=30-5=25.

4 76
Q:

Simplify the following equation.

$\inline \frac{19}{43}+ \frac{1}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}$

 A) 43/19 B) 1 C) 38/19 D) None of these

Explanation:

$\inline \frac{19}{43}+ \frac{1}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}=\frac{19}{43}+ \frac{1}{2+\frac{5}{19}}=\frac{19}{43}+\frac{19}{43}=\frac{38}{43}$

20 1649
Q:

Simplify  $\inline \frac{(1.5)^{3}+(4.7)^{3}+(3.8)^{3}-3\times 1.5\times 4.7\times 3.8}{(1.5)^{2}+(4.7)^{2}+(3.8)^{2}-1.5\times 4.7\times -4.7\times 3.8-1.5\times 3.8}$

 A) 6 B) 8 C) 10 D) 12

Explanation:

Apply $\inline \frac{a^{3}+b^{3}+c^{3}-3abc}{a^{2}+b^{2}+c^{2}-ab-bc-ca}=a+b+c$

13 1054
Q:

$\inline 48\sqrt{?}+32\sqrt{?}=320$

 A) 4 B) 8 C) 16 D) 32

Explanation:

$\inline 48\sqrt{?}+32\sqrt{?}=320$

$\inline \Rightarrow 6\sqrt{?}+4\sqrt{?}=40$

$\inline \Rightarrow 36\times ?+16\times ?+48\times ?=1600$

$\inline \Rightarrow 100\times ? =1600$

$\inline \Rightarrow ? =16$