NAT IIP Physical Science Mathematics Preparation Online Test for Pakistani Students

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In the expansion of (a + b)ⁿin every term the sum of the exponents of a and b is

• n A
• n + 1 B
• 2n - 1 C
• 2n + 1 D

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  B
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  D

A farmer possesses 100 hectometers of land and wants to grow corn and wheat. Cultivation of corn requires 3 hours per hectometer while cultivation of wheat requires 2 hours pert hectometer. Working hours cannot exceed 240. If he gets a profit of Rs. 20 per hectometer for corn and Rs. 20 per hectometer for wheat. The profit function for the farmer is

• P(x,y) = 20x + 15y A
• P(x,y) = 2x + 3y B
• P(x,y) = x + y C
• P(x,y) = 3x + 2y D

• A < G < H A
• A > G > H B
• A < G > H C
• A > G < H D

A point of a solution region where two of its boundary lines intersect, is called

• Boundary A
• Inequality B
• Half Plane C
• Vertex D

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The number ways in which 5 distinct toys can be distributed among 3 children is

• 3⁵ A
• 5³ B
• C₃⁵ C
• P₃⁵ D

If any two rows (or any two columns) of a square matrix are inter changed, the determinant of the resultant matrix is

• Same as the original determinant A
• Additive inverse of the original determinant
  B
• Both A and B C
• Adj of the original matrix D

• n = 3 only A
• n > 5 B
• n > 3 C
• n < 5 D

If 1 + Cos x = 0, then x =

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  D

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The constant distance of all points of the cirlce from its centre is called the

• Radius of the circle A
• Secant of the circle B
• Chord of the circle C
• Diameter of the circle D

In a school, there are 150 students. Out of these 80 students enrolled for mathematics class, 50 enrolled for English class, and 60 enrolled for Physics class. The student enrolled for English cannot attend any other class, but the students of mathematics and Physics can take two courses at a time. Find the number of students who have taken both physics and mathematics

• 40 A
• 30 B
• 50 C
• 20 D