NIMCET 2011 Previous Year Questions (PYQs) – Page 9 of 12
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Showing 120 questions
Assume that the following three statements are true:
I. All freshmen are human
II. All students are human
III. Some students think
Given the following four statements:
(1) All freshmen are students
(2) Some humans think
(3) No freshmen think
(4) Some humans who think are not students
Those which are logical consequences of I, II and III are:
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Solution
From I: All freshmen are human
From II: All students are human
From III: Some students think ⇒ therefore those students are humans who think.
Check each statement:
(1) All freshmen are students
→ NOT necessarily true. We only know freshmen ⊆ humans, students ⊆ humans. No link freshmen ⊆ students.
⇒ NOT a consequence.
(2) Some humans think
Since some students think and all students are humans ⇒ some humans think is TRUE.
⇒ CONSEQUENCE.
(3) No freshmen think
Nothing in the statements says freshmen do not think.
⇒ NOT a consequence.
(4) Some humans who think are not students
We only know some students think. We do NOT know that any thinker is outside students.
⇒ NOT a consequence.
Directions for questions 83–85:
Mrs. Thomes received a large order for stitching school uniforms from Mayflower school and Little flower school. She has two cutters who will cut the fabric, five tailors who will do the stitching and two assistants to stitch the buttons and button holes. Each of these nine persons will work for exactly 10 hours a day. Each of the Mayflower uniforms requires 20 min for cutting the fabric, one hour for stitching, and 15 min for stitching buttons and button holes, whereas the Little flower uniform requires 30 min, 1 hour and 30 min respectively for these activities.
What is the number of Little flower uniforms that Mrs. Thomes can complete in a day?
What is the number of Little flower uniforms that Mrs. Thomes can complete in a day?
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Solution
Little flower uniform requires:
• Cutting = 30 min
• Stitching = 60 min
• Buttons = 30 min
Available daily working time:
• 2 cutters → 2 × 600 min = 1200 min
• 5 tailors → 5 × 600 min = 3000 min
• 2 assistants → 2 × 600 min = 1200 min
Calculate max number by each stage:
Cutting capacity = 1200 / 30 = 40
Stitching capacity = 3000 / 60 = 50
Button work capacity = 1200 / 30 = 40
Minimum of these = 40 uniforms
On a particular day, Mrs. Thomes decided to complete 20 Little flower uniforms. How many Mayflower uniforms can she complete on that day?
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Solution
Little flower uniform uses per piece:
Cutting 30 min → 20 uniforms = 600 min
Stitching 60 min → 20 uniforms = 1200 min
Buttons 30 min → 20 uniforms = 600 min
Remaining capacity:
Cutters: 1200 – 600 = 600 min
Tailors: 3000 – 1200 = 1800 min
Assistants: 1200 – 600 = 600 min
Mayflower uniform time:
Cutting = 20 min → capacity = 600 / 20 = 30
Stitching = 60 min → capacity = 1800 / 60 = 30
Buttons = 15 min → capacity = 600 / 15 = 40
Minimum = 30 uniforms
If she hires one more assistant, what is the maximum number of Mayflower uniforms that she can complete in a day?
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Solution
Mayflower uniform requires:
Cutting = 20 min
Stitching = 60 min
Buttons = 15 min
Daily capacity:
Cutters: 1200 min → 1200 / 20 = 60
Tailors: 3000 min → 3000 / 60 = 50
Assistants: previously 2 (1200 min), now 3 assistants → 3 × 600 = 1800 min
Buttons capacity = 1800 / 15 = 120
Minimum of 60, 50, 120 = 50 uniforms
Consider x and y be some Boolean variables, + denotes the OR operation and "." denotes the AND operation. What will be the simplified form of the Boolean expression: x.(x + y)?
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Solution
x(x + y) = xx + xy = x + xy = x(1 + y) = x
Which one of the following is not a valid rule of Boolean algebra?
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Solution
A = A' is false (a variable cannot equal its complement).
When two binary numbers are added, then an overflow will never occur if
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Solution
Overflow never occurs when carry into sign bit = carry out of sign bit.
Which protocol needs to be installed for Internet access on a network?
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Solution
TCP/IP is required for Internet access.
A petabyte represents approximately
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Solution
1 petabyte ≈ 1000 terabytes.
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