# CAT Model Paper 2 Questions and Answers with Explanation Part 1

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Q: 1. If number of digits in

(A) 83

(B) 84

(C) 85

(D) 86

Ans: C

Sol:

Taking logarithm for

Since the characteristic is 84, the number of digits in is **85**.

Q: 2. Consider the following cubic polynomial . It is known that the polynomial has zero value for more than three distinct values of x. Find the value of k.

(A) 3

(B)

(C) 5

(D) No such value of k exists

Ans: B

Sol:

Factorizing the coefficients of the various powers of x, we obtain that where is a different cubic polynomial expression which has the same roots as P (x) has. Since a cubic has exactly three roots, for to satisfy more than three distinct values of x, must take zero value.

This implies .

Q: 3. If the term of an A. P is n. If the term of the same is m, find the term.

(A)

(B)

(C)

(D)

Ans: B

Sol:

term of an AP:

term of an AP:

Subtracting the above two equations,

The 7^{th} term of the AP:

Note: It can be concluded that if term of an is n and if the term of an A. P is m, then the term of the AP is

ABC Private Limited owns and operates a multi-level-parking lot in T. Nagar, a busy commercial area in the city of Chennai. All types of vehicles are allowed to use the parking lot and the parking charge depends on the vehicle type (one among 2-wheelers, 3-wheelers, Cars, SUVs and Heavy vehicles) and the number of hours for which a vehicle is parked. The hourly parking charges for different types of vehicles is given in the bar graph below.

In case, the time for which a vehicle uses the parking lot is not in integral hours, the usage time is rounded off to the nearest higher hour. Hence, if a 2-wheeler uses the parking lot for three-and-a-half hours, the parking charge is ′ 80.

The following pie chart gives details about the vehicles that used the parking lot on January 1,2013.

The total number of vehicles that used the parking lot on January 1,2013 is 12,000.

Q: 4. On the given day, all the 2-wheelers, 3-wheelers, cars, SUVs and heavy vehicles used the parking lot for one-and-a-half hours, two hours, two hours and fifteen minutes, forty five minutes and three-and-a-half hours, respectively. Find the total parking charges received.

(A)

(B)

(C)

(D) None of these

Ans: D

Sol:

The data given in the question can be reduce to a simple table as below:

Vehicle type | No. of Vehicles using the parking lot | No. of hours of usage | No. of hours to be charged (rounded off to the nearest higher hour) | Total parking charges per vehicle | Parking charges for all the vehicles |

2-wheelers | 500 | 1.5 | 2 | ||

3-wheelers | 1200 | 2 | 2 | ||

Cars | 3000 | 2.25 | 3 | ||

SUVs | 1000 | . 75 | 4 | ||

Heavy Vehicles | 1000 | 3.5 | 4 |

Hence, total parking charges received

Hence, total parking charges received.

Q: 5. On 1^{st} January 2013, two – fifths of the 2-wheelers used the parking lot for two-and-a-half hours and the remaining two wheelers used the parking lot for more than three hours but less than four hours. None of the cars used the parking lot for more than two hours while one-third of them used the parking lot for less than or equal to one hour. Find the difference between the average parking charge per bike and the average parking charge per car.

(A)

(B)

(C)

(D)

Ans: C

Sol:

Vehicle Type | T = Hours of Usage | No. Of Vehicles | Parking Charge Per vehicle (₹) |

2-Wheeler | T = 2.5 | ||

3000 | ₹ 20 × 4 = ₹ 80 | ||

Car | 0 < T⩽1 | ||

2000 |

Average parking charge per 2- wheeler

Average parking charge per Car

Hence the required difference

Hence, the required difference is **₹ 11.33**.

Q: 6. On 2^{nd} January 2013, the number of 2-wheelers using the parking lot decreased by 25 % ; the number of 3-wheelers using the parking lot increased by 20 % ; the number of cars using the parking lot decreased by 33.33 % ; the number of SUVs using the parking lot increased by 50 % while the number of heavy vehicles using the parking lot remained the same. Find the number of 2-wheelers that used the parking lot on 2^{nd} January 2013 as a percentage of the total number of vehicles that used the parking lot on 2^{nd} January 2013.

(A)

(B)

(C)

(D)

Ans: C

Sol:

Vehicle type | No. of Vehicles using the parking lot on January 1,2013 | No. of vehicles using the parking lot on January 2,2013 |

2-wheelers | 5000 | |

3-wheelers | 1200 | |

Cars | 3000 | |

SUVs | 1000 | |

Heavy Vehicles | 1000 | 1000 |

Total | 112000 | 10890 |

Required percentage