# Important Mathematics Questions for RRB JE CBT-1 2019 Exam – Jagran Josh

RRB JE 1st Stage CBT 2019 Exam will be held from 22nd May 2019 onwards. The Mathematics section of CBT 1 Exam is of 30 Marks. You can start practicing these questions and understand the problems in detail with the help of explanations given alongwith the answers in the below Quiz:

1. The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number?
a) 270
b) 240
c) 284
d) 320

2. The profit percentage of M and N is same on selling the articles at Rs. 3600 each but M calculates his profit on the selling price while N calculates it correctly on the cost price which is equal to 20%. What is the difference in their profits?
a) Rs.260
b) Rs.160
c) Rs.140
d) Rs.120

3. A trader mixes 25% Vanaspati Ghee to Desi ghee and then he sells the whole mixture at the price of Desi ghee. If the cost price of Vanaspati Ghee be 50% of the cost price of Desi ghee, what is the net profit percentage?
a) 150/9 %
b) 111/9 %
c) 20%
d) 25%

4. What will be the simple interest on an amount of Rs. 2000 in 3 years at interest 4% per annum?
a) Rs. 280
b) Rs.240
c) Rs.250
d) Rs. 220

5. If x-1 / x = 3, then value of x3 – 1/x3  is:
a) 32
b) 36
c) 40
d) 49

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6. If a + b + c = 6, a2 + b2 + c2 = 14 and a3 + b3 + c3 = 36, then value of abc is:
a) 3
b) 5
c) 6
d) 12

7. Aayush walks from his home to his office at a rate of 8 km/hr and returned home in the evening at a rate of 6 km/hr. What is his average speed?
a) 6.52
b) 6.76
c) 6.85
d) 6.5

8. Walking at 8/9 th of his usual speed, a man reached his destination 20 minutes later than the time he usually takes to reach his destination. Find the usual time taken by him to reach his destination.
a) 12 hour, 44 minutes
b) 2 hour, 52 minutes
c) 2 hour, 36 minutes
d) 2 hour, 40 minutes

9. A work is done by three people A, B and C. A alone takes 20 hours to complete a single product but B and C working together takes 8 hours, for the completion of the same product. If all of them worked together and completed 28 products, then how many hours have they worked?
a) 160 hrs
b) 128 hrs
c) 120 hrs
d) 154 hrs

10. The average weight of 20 students in a class is 44 kg and that of the remaining 10 student is 38. Find the average weights of all the students the class:
a) 39 kg
b) 43 kg
c) 41 kg
d) 42 kg

11. If Ratio of weights of A and B are in the ratio of 5:9 respectively and weights of A and C are in the ratio 1: 3. If after 2 months all of them gain 5 Kgs, then sum of their weights are 189 kgs. Then find the present weight of A.
a) 29 Kg
b) 32 Kg
c) 30 kg
d) 27 Kg

12. The total salary of X, Y and Z is Rs. 1812. If they spend 80%, 85%, 75% of their salaries respectively, their savings are as 7:6:19. Then salary of Y is:
a) Rs 440
b) Rs 480
c) Rs 544
d) Rs 445

13. One root of the quadratic equation x2 – 12x + a = 0, is thrice the other. Find the value of a.
a) 29
b) 7
c) 28
d) None of these

14. In a right angled ∆ABC, ∠C = 90° and CD is the perpendicular on hypotenuse AB if BC = 15 cm and AC = 20 cm then CD is equal to:
a) 18 cm
b) 12 cm
c) 17.5 cm
d) Can’t be determined

15. In the adjoining figure m ∠CAB = 62° , m ∠CBA = 76° m ∠ADE = 58° and ∠DFG = 66°,Find measure of ∠FGE:
a) 44°
b) 32°
c) 36°
d) 34°

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16. C and D are points on the semi-circle subscribed on BA as diameter. If ∠BAD = 70° and ∠DBC = 30°. Calculate ∠ABD.
a) 40°
b) 35°
c) 20°
d) 65°

17. PQ and RS are parallel straight lines of lengths 9 cm and 6 cm respectively. PS and QR intersect at a point O such that PO=15 cm, then OS equals:
a) 7 cm
b) 8 cm
c) 10cm
d) 9 cm

18. The maximum value of 24 sin θ + 7 cos θ is:
a) 25
b) 20
c) 22
d) 21

19. If tan2θ.tan4θ =1 then value of tan3θ is:
a) -1
b) -2
c) 3
d) 1

20. If (a2 – b2) sinθ + 2ab cosθ = a2 + b2, then value of tanθ is:
a) (a2+b2) / 4ab
b) (a2-b2) / 2ab
c) (a2+b2) / 3ab
d) (a2-b2) / ab

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Directions (21 -25): The following pie-chart shows the hourly distribution (in degrees) of all the major activities of a student:

21. What per cent does he spend in school comparison to sleeping?
a) 817/11 %
b) 877/9 %
c) 1222/9  %
d) 762/11 %

22. What is the difference between the time he spent in Games and in others?
a) 3 hrs 20 min
b) 3 hrs 33 min
c) 3 hrs
d) 3 hrs 55 min

23. The percentage of time which he spends in homework is:
a) 11 2/9%
b) 13 2/7 %
c) 90%
d) 11 1/9%

24. If he spends the time in sleeping equal to the school and others and home work remains constant, then percentage decrease in time of games is:
a) 75%
b) 57 1/7%
c) 61 2/7%
d) 72%

25. If he spends 1/4 th time of homework in Physics, then the number of hours he spends in rest of the subject in homework is:
a) 3
b) 4
c) 1
d) None of these

Explanation: Let the smaller number be x. Then larger number = (x + 1365)
∴ X + 1365 = 6x + 15
5x = 1350
X = 270
∴  Smaller number = 270

Explanation: When profit calculate on S.P
Then Profit = 20% of 3600 = 720
When Profit calculate on CP = (x)
x + x/5 = 3600
x = 3000
Profit = 600
Required difference = Rs. 120

Explanation: Let quantity of Desi ghee = 100 litre
Then quantity of Vanaspati Ghee mixed = 25 litre
Let cost price of one litre Desi ghee = Rs.10
Let cost price of one litre Vanaspati Ghee = Rs.5
Total cost price = 100 × 10 + 25 × 5 = 1125
Total selling price = (100 + 25)×10 = 1250
Profit = 1250 – 1125 = 125
Net profit percentage
(125×100)/1125 = 100/9 = 11 1/9%

Explanation: Simple Interest = P×R× T/100
(2000×4×3)/100 = Rs.240

Explanation:

Explanation: a + b + c = 6
a2+b2+c2 = 14
a3+b3+c3 = 36
Put value as
a=1, b=2,c=3
1+2+3 = 6
1+4+9 = 14
1+8+27 = 36
∴ abc= 1×2×3 = 6

Explanation:

Explanation: Ratio of Speed  9 : 8 and Time  8 : 9
1 = 20
7 = 8 X 20 = 160 min
= 2 hour 40 minutes

Explanation: 1/A = 1/20 and
1/B + 1/C = 1/8 (Given)
1/A + 1/B + 1/C = 1/8 + 1/20 = 7/40
In 40 hours, working together they will complete 7 products.
Thus in 160 hours they will complete 28 products

Explanation: Total weight of 20 student = 20 × 44 = 880
Total weight of 10 student = 10 × 38 = 380
Average weights of all the students = (880 + 380)/30 = 1260/30 = 42 kg

Explanation: Ratio of weights of B : A : C = 9×1 : 5×1 : 5×3 = 9 : 5 : 15
∴ 9x + 5x + 15x + 15 = 189 ∴ x = 6, Present weight of A = 5 × 6= 30kgs

Explanation: Ratio of their incomes is X : Y : Z = 7/20 : 6/15 : 19/25 = 35 : 40 : 76
Income of Y = 40/151 × 1812 = Rs.480

Explanation: Let the roots of the quadratic equation be x and 3x.
Sum of roots = – (-12) = 12
=a + 3a = 4a = 12 => a = 3
Product of the roots= 3a2 = 3(3)2 = 27

Explanation:

Explanation:

Explanation: Since ABCD is a cyclic quadrilateral
∴    ∠BCD + ∠BAD = 180°
∠BCD + 70° = 180°
∠BCD = 110°
∴ In ∆ABCD we have
∠CBD + ∠BCD+∠BDC = 180°
30°+110°+∠BDC = 180°
∠BDC = 40°
In ∆ABD, ∠ ABD = 180° – (90° + 70°)
∠ABD = 20°

Explanation:

Explanation: Maximum value of sinθ + cosθ = √a2+b2
So, maximum value = √242+72
=√625 = 25

Explanation: tan2θ.tan4θ = 1
tan2θ = 1/tan4θ
tan2θ = cot4 θ
tan2θ = tan(90 – 4θ)
2θ = 90 – 4θ
6θ = 90
3θ = 45
tan3θ.tan45 = 1

Explanation:

Explanation: 110/90 × 100 = 122 2/9

Explanation: (85 – 35)/360 × 24 = 3hours 20min

Explanation: 40/360 × 100 = 11 1/9%