Solution

Ans: (A, B, C, D)

Maximum number of points 4 lines can intersect are $^{4}C_{2}=\frac{4!}{2!\times 2!}$=6

Lines can intersect maximum of 6 points.

A coin is biased so that probability of getting head is more than tail. If coin is to be tossed 3 times, what is the probability that on at least one of the tosses, coin will turn up heads?

Solution

Ans: (A, E)

We should take negative approach.

Find out the probability of not getting head at all. i.e. getting only tails on all three coins.

¹⁄₂ × ¹⁄₂ × ¹⁄₂ = ¹⁄₈ is the max probability of getting t son tree coins.

∴ Probability 0 getting ea at least on one corns is greater t an 1 - ¹⁄₈ = ⁷⁄₈

Solution

Ans: (C, E)

n things can be given to r persons is rⁿ ways.

∴ 6 things can be given to 4 fingers in 4⁶ ways. Also 4⁶= 2¹²

Tom and Dick enter into a partnership by investing in some ratio. After one year, Dick invests another $ 3000. At the end of that year, profits are shared in the ratio 3:5. The initial investments of Tom and Dick could be

Solution

Ans: (B, C, D)

Let initial investment of Tom and Dick be $x and $y. Dick's investment for 2 years will be y + 3000.

∴ Ratio of capital of tom and Dick is $\frac{x}{y+3000}$ = ³⁄₅

5x = 3y + 3000. Hence check for options that satisfy this equation

A milk vendor receives 2 adulterated supplies S1 and S2 that contains 11% and 5% of water respectively. How much of each kind must be taken so as to form 66 liters of mixture containing 90% milk?

Mark two correct options

Solution

Ans: (C, D)

11% of water in S1

5% of water in S2

Mixture contains 90% milk i.e. 10% water.

By the principle of allegation

∴ The required ratio = 5 : 1

∴ Quantity of supply S1 = $\frac{5}{5+1}$ × 66 = 55 liters.

Quantity of supply S2 = $\frac{1}{5+1}$ × 66 = 11 liters.

8 carpenters working 6 hours a day can make some chairs in 30 days. If the same numbers of chairs are made by x carpenters working y hours a day for 30 days, then x and y can be

Solution

Ans: (A, B, E)

The man hours required for the chairs will be same. Since both jobs are for 30 days, the man hours will be: 8 × 6 = 48 = xy.

PRECISION SYSTEMS purchased 2 robots R1 and R2 to match their weekly production schedule. On Monday, robot R1 produces 900 units. On Tuesday, robot R2 produces 1300 units. Each day thereafter robot R1 produces 8 units for every 5 units R2 produces. By the end of the week, the two collectively manufactured more than 8700 units. The number of units delivered by robot R2 in week could be

Solution

Ans: (B, D, E)

Total production of units on Monday and Tuesday = 900 + 1300 = 2200

∴ Minimum Total production on the remaining 5 days

= 8700 - 2200 = 6500

R2 will produce $\frac{5}{13}$ of the remaining products

∴ R2 will produce 1300 + $\frac{5}{13}$ × 6500

= 1300 + 2500 = 3800 or more units

When a certain integer n is divided by 18, the remainder is 1. Which of the following could not be an integer?

Solution

The number n is not divisible by 18.

∴ The number n is also not divisible by any of the factors of 18. Since 2, 3, 6, 9 are factors of 18.

∴ (A),(B), (e), (D) will not give integral values.

∴ The answer has to be (A,B, C, D)

Given rectangular box of dimensions 8cm X 6 m X 2cm, the possible lengths of pencils than can be kept in it are?

A. 2 cm
B. 2$\sqrt{26}$ cm
C. 13 cm
D. 1√3 cm

Solution

Ans: (A, B, D)

For a rectangular cuboid, maximum length of a pencil is equal to the length of diagonal Diagonal = $\sqrt{L^{2}+B^{2}+H^{2}}$

= $\sqrt{64+36+4}$

= $\sqrt{104}$

= $\sqrt{26}$ cm

ABC is an equilateral triangle, AC = 2. What are the values of p and q? Select 2 correct options.

Solution

Ans: (B, C)

Draw a perpendicular from vertex B.

Then BD = altitude

Also AD = DC ∴ AD = ¹⁄₂AC

Co-ordinate p = AD (co-ordinate) = 1

Co-ordinate q = BD (co-ordinate) = √3

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