RRB JE ECE (CBT I) Mock Test- 6 - Electronics and Communication Engineering (ECE) MCQ

= 2025 - 2380 - 58 + 438

= 2463 - 2438

= 25

= 5²

Let AB be the tower and C and D the two points.

Now AB/BC = tan⁡45∘=1

AB = BC = 90

Also AB/BD = tan⁡60^∘ = √3

BD = 90/√3 = 30√3

Hence CD = CB + BD = 90 + 30√3 = 90 + 51.96 = 141.96 ≈ 142m

16x² - Ax + 25 has real and equal roots

(-A)2 = 4 * 16 * 25

A = 40

Bx² + Ax + 4 = 0 has real and equal roots

(A)2 = 4 * B * 4

(40)² = 4 * B * 4

B = 100

√B = √100

√B = 10

Amount after two years = 17500 x (1+8/100) ²

= 17500 x 1.08 x 1.08 = 20412

Interest = 20412 - 17500 = Rs 2912

Let length = l

And breadth = b

Area = lb

After increment, length = l x (100 + 10)/100 = l x 110/100 = l x 11/10

After decrement, breadth = b x (100 - 10)/100 = b x 90/100 = b x 9/10

Area = l x 11/10 x b x 9/10

= 99lb/100 lb

% decrease = (lb - 99lb/100)/lb x 100

= (100lb - 99lb)/100 x 1/lb x 100

= lb/100 x 1/lb x 100

= 1%

Let the adjacent angles of the parallelogram be 14x and 31x

Therefore, 14x + 31x = 180o

45x = 180o

X = 4

Money donated to charity = Rs 10x and Money given to sister = Rs 15x

Money left with Aman = 100x - 10x - 15x = Rs 75x

Money left with him after giving to son = (40/100)*75x = Rs 30x

Money left with him after giving to daughter = (20/100)*30x = Rs 6x

Given, 15x + 6x = 84000

=> 21x = 84000

=> x = 4000

His Savings = Rs 4,00,000

Given, (a + 3d)/(a + d) = 5/3

=> 3a + 9d = 5a + 5d

=> 2a = 4d

=> a = 2d

Also, a(a + 2d) = 72

=> 2d(2d + 2d) = 72

=> 8d² = 72

=> d2 = 9

=> d = 3

∴ a = 2*3 = 6

d ≠ −3 as the 1st term will become a = 2(−3) = − 6 but all terms are positive.

5th term = a + 4d = 6 + 4*3 = 18

6th term = 18 + 3 = 21

Required product = 18*21 = 378

A, B and C can fill in 4 hour= 4/10 =2/5 of cistern

Remaining part = 1 - 2/5 =3/5 of cistern

3/5 of cistern is filled by A+B in 9 hours

Therefore, A and B can fill the cistern in 9*5/3 = 15 hrs

Hence in one hour C filled the cistern = 1/10 - 1/15 = 1/30 of cistern

Hence C can fill the cistern in 30 hrs.

According to question,

x + (x+2) + (x+4) + ...... + (x+22) = 113*12

12x + 132 = 1356

12x = 1224

x = 102

Therefore 3rd number = 102 + 4 = 106

8th number = 102 + 14 = 116

Hence the required answer = 106 + 116 = 222

? = (72)2 ÷ ∛(36x36x36) = (72)2 ÷ 36

? = (72 X 72)/36 = 144

D) Cost price of the article is Rs.660 and marked price = 125% of 660 = Rs.825

B) Selling price of the item after discount of Rs.99 = 825 - 99 = Rs.726

C) Profit amount earned on the item = 726 - 660 = Rs.66

A) Percent profit = (66/660) * 100 = 10%

In January = 18 + 22 + 25 = 65

In February = 20 + 12 + 32 = 64

In March = 40 + 10 + 13 = 63

In April = 21 + 22 + 24 = 67

In May = 25 + 21 + 16 = 62

Percentage increase/decrease:

In February = ((65 - 64)/65) x 100 = 1.54%

In March = ((64 - 63)/64) x 100 = 1.56%

In April = ((67 - 63)/63) x 100 = 6.35%

In May = ((67 - 62)/67) x 100 = 7.46%

time = Distance/Velocity

Distance = 140+160 = 300m = 0.3km

Relative velocity = 60+40 = 100kmph (opp. direction) Time =0.3/100h

or 0.3/100 × 3600 = 10.8sec

Time =10.8 sec.

Let (a+b) = c

c² = (a+b)² = a²+b² + 2ab = 5 + 4 = 9

=> a + b = 3

Now, (a+b)(a³+b³) = a⁴+b⁴+ab(a²+b²)

=> 3 x 9 = a⁴+b⁴ + 2 x 5

=> a⁴+b⁴ = 17

Hence, the answer is option (2).

Let the price at which T.V was purchased by shopkeeper = Rs 100a

Hence the price at which T.V was sold by shopkeeper = Rs 120a

If shopkeeper paid 15% less than the previous amount hence new cost price of the T.V = Rs (100a X 0.85) = Rs 85a

New selling price of the T.V = Rs (120a X 1.1) = Rs 132a

Profit % = (132a-85a)/85a X 100 = 55.3%

= (13/8) of (15/32) of 45% of 3072

= (13/8) * (15/32) * (45/100) * 3072

= (13/8) * (3/32) * (9/4) * 307

= 13 * 3 * 9 * 3

= 1053

total number of Males of age 20 to 60 = 210 + 120 = 330

total number of Females of age 20 to 60 = 150 + 40 = 190

Required difference = 330 - 190 = 140

Given, 100x + 100y = 6000

=> x + y = 60..(i)

And, 110x + 120y = 6840

=> 11x + 12y = 684..(ii)

12*(i) - (ii), gives

x = 36

Initial population of Males = 3600

Let 7x and x be their respective ages, then, 8x = 32 and x = 4

So, Sheela's age = 7x = 7 X 4 = 28 years . Hence, option 1.

x = 2y

x:y = 2:1

The denominator divides the numerator, so the answer is 0.

Simple Interest for 1 year = 1920/2 = Rs. 960

Compound Interest - Simple Interest = 2112 - 1920 = Rs. 912

Interest on Rs. 960 for 1 year = Rs. 912

= Rs. 4800

New rate = 24% per annum

S.I. = (4800×2×24)/100

= Rs. 2304

Compound Interest = 4800[(1+ 24/100)² - 1)

= 4800[(1.24)² - 1]4800

= Rs. 2580.48

Total interest = Rs. 4884.48

Let the number of liters of solution added be: x

The initial ratio of milk (m) to water (w) is:

=> m/w = 2/3

=> m = 2/5 of the solution

=> m = 40% of the solution

Acc. to the question, after adding x liters of 40% milk solution to 30 liters of 70% milk solution, we get 60% of (x+30) liters milk solution.

Hence, the equation becomes:

=> 40x + 30 * 70 = (x+30) * 60

=> 40x + 2100= 60x + 1800

=> 20x = 300

=> x = 15

=> a/b = 15/12

=> a/b = 5/4

=> a:b = 5:4

Downstream speed of boat A = (6/5) x downstream speed of boat B

Upstream speed of boat A - upstream speed of boat B = downstream speed of boat A - downstream speed of boat B = 6

(6/5) x downstream speed of boat B - downstream speed of boat B = 6

Downstream speed of boat B = 30 km/hr

Downstream speed of boat A = 30 + 6 = 36 km/hr

Speed of boat A in still water = 36 - 10 = 26 km/hr

Savings = a - b = a - 3a/4 = a/4

When income and expenditure are increased by 20%. Then,

New income = 120% of a = 1.2a

New expenditure = 140% of b = 1.4 x 3a/4 = 2.1a/2

New savings = 1.2a - 2.1a/2 = 3a/20

Decrement in savings = (a/4) - (3a/20) = a/10

Percentage = a/10)/(a/4 x 100 = 40%

1/A + 1/B = 1/2 (1)

1/B + 1/C = 1/3 (2)

1/A + 1/C = 1/4 (3)

(1)+(2)+(3) => 2(1/A+1/B+1/C) = 13/12

=> 1/A + 1/B + 1/C = 13/24 (4)

(4) - (2) => 1/A = 5/24

Thus A takes 24/5 = 4.8 days.

(4) - (1) => 1/C = 1/24

Hence C takes 24 days.

Required ratio = 4.8: 24 = 1:5

= (3 - 3√3)(3 + 3√3)

= - 18 (which is not irrational)

Option (2):

= Sum of (5 - 4√2) and 4(6 + √2)

= (5 - 4√2) + 4(6 + √2)

= 5 - 4√2 + 24 + 4√2

= 29 (which is not irrational)

Option (3):

= Sum of √4761 and √5175

= 69 + 15√23 (which is irrational)

Option (4):

= Product of √16875 and √27

= 75√3 x 3√3

= 675 (which is not irrational)