JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech I Year BASIC MATHEMATICS Previous Question Paper (September - 2023 - R22)
Note: This question paper contains two parts A and B. i) Part- A for 10 marks, ii) Part - B for 50 marks. Part-A is a compulsory question which consists of ten sub-questions from all units carrying equal marks. Part-B consists of ten questions (numbered from 2 to 11) carrying 10 marks each. From each unit, there are two questions and the student should answer one of them. Hence, the student should answer five questions from Part-B.
PART - A
Compute 𝐴2 for the matrix 𝐴 =
Answer
Matrix multiplication A2 = [[2, -1, 1], [2, 3, 0], [4, 3, 2]] * [[2, -1, 1], [2, 3, 0], [4, 3, 2]] results in [[6, -2, 4], [10, 7, 2], [22, 11, 8]].
Find the sum of all the non-real roots of the equation
Answer
Let y = x2 + x. The equation becomes (y - 3)(y - 4) = 20, which simplifies to y2 - 7y - 8 = 0. Factoring gives (y - 8)(y + 1) = 0, so y = 8 or y = -1. For x2 + x - 8 = 0, roots are real. For x2 + x + 1 = 0, the discriminant is 1 - 4 = -3, so roots are non-real. By Vieta's formulas, the sum of these roots is -1.
Find the real numbers α and β such that
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Find the distances of the point 𝑃(-3, 5, 7) from the coordinate axes.
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Let 𝑥 lies in the second quadrant. If sin 𝑥 = 12/13, find the value of sec 𝑥 + tan 𝑥.
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Find the partial fraction decompose of the function
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Evaluate the integral
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Find
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Determine the order and degree of the differential equation
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In a single throw of two dice, find the probability of getting a total of 10.
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PART - B
Consider the matrix 𝐴 =
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Let 𝐴 =
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Solve the equation
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Find the square root of the complex number -8 - 6i.
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Let
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Prove or disprove that the points 𝑃(3,3,3), 𝑄(0,6,3), 𝑅(1,7,7) and 𝑆(4,4,7) are the vertices of a square.
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Find the equation of the locus of a point which moves such that the ratio of its distance from (0, 2) and (0, -2) is 6.
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Prove that
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Consider the triangle Δ ABC. If the sides of the triangle are a = 18, b = 24, and c = 30 and the ∠C = 90°, find sin A, sin B, and sin C.
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Find the partial fraction decompose of the fraction
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Find the partial fraction decompose of the fraction
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Find the derivative of the function
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Discuss the continuity and differentiability of the function 𝑓(𝑥) at 𝑥=2.
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Evaluate the integral
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Evaluate the integral
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Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.
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Find the general solution of the differential equation
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If A and B are two events associated with a random experiment such that P(A) = 0.6, P(B) = 0.3 and P(A ∩ B) = 0.2, find P(A ∪ B).
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One number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6.
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