Commerce (English Medium)
Science (English Medium)
Arts (English Medium)
Academic Year: 2021-2022
Date & Time: 7th June 2022, 10:30 am
Duration: 2h
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General Instructions :
- This question paper contains three Sections - A, Band C.
- Each section is compulsory.
- Section - A has 6 short answer type-I questions of 2 marks each.
- Section - B has 4 short answer type-II questions of 3 marks each.
- Section - C has 4 long answer type questions of 4 marks each.
- There is an internal choice in some questions.
- Question 14 is a case study based question with two sub-parts of 2 marks each.
Find: `int (dx)/(x^2 - 6x + 13)`
Chapter: [0.07] Integrals
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
Chapter: [0.07] Integrals
Write the projection of the vector `(vecb + vecc)` on the vector `veca`, where `veca = 2hati - 2hatj + hatk, vecb = hati + 2hatj - 2hatk` and `vecc = 2hati - hatj + 4hatk`.
Chapter: [0.1] Vectors
If the distance of the point (1, 1, 1) from the plane x – y + z + λ = 0 is `5/sqrt(3)`, find the value(s) of λ.
Chapter: [0.11] Three - Dimensional Geometry [0.11] Three - Dimensional Geometry
Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distnbution of the number of spade cards.
Chapter: [0.13] Probability
A pair of dice is thrown and the sum of the numbers appearing on the dice is observed to be 7. Find the probability that the number 5 has appeared on atleast one die.
Chapter: [0.13] Probability
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The probability that A hits the target is `1/3` and the probability that B hits it, is `2/5`. If both try to hit the target independently, find the probability that the target is hit.
Chapter: [0.13] Probability
Evaluate: `int_0^(2π) (1)/(1 + e^(sin x)`dx
Chapter: [0.07] Integrals
Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.
Chapter: [0.09] Differential Equations
Find the general solution of the differential equation `x (dy)/(dx) = y(logy - logx + 1)`.
Chapter: [0.09] Differential Equations
The two adjacent sides of a parallelogram are represented by vectors `2hati - 4hatj + 5hatk` and `hati - 2hatj - 3hatk`. Find the unit vector parallel to one of its diagonals, Also, find the area of the parallelogram.
Chapter: [0.1] Vectors
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If `veca = 2hati + 2hatj + 3hatk, vecb = -veci + 2hatj + hatk and vecc = 3hati + hatj` are such that `veca + lambdavecb` is perpendicular to `vecc`, then find the value of λ.
Chapter: [0.1] Vectors
Show that the lines: `(1 - x)/2 = (y - 3)/4 = z/(-1)` and `(x - 4)/3 = (2y - 2)/(-4) = z - 1` are coplanar.
Chapter: [0.11] Three - Dimensional Geometry
Find the area of the region bounded by curve 4x2 = y and the line y = 8x + 12, using integration.
Chapter: [0.08] Applications of the Integrals
Find: `int x^2/((x^2 + 1)(3x^2 + 4))dx`
Chapter: [0.07] Integrals
Evaluate: `int_-2^1 sqrt(5 - 4x - x^2)dx`
Chapter: [0.07] Integrals
Find the distance of the point (1, –2, 0) from the point of the line `vecr = 4hati + 2hatj + 7hatk + λ(3hati + 4hatj + 2hatk)` and the point `vecr.(hati - hatj + hatk)` = 10.
Chapter: [0.11] Three - Dimensional Geometry [0.11] Three - Dimensional Geometry
Read the following passage and answer the questions given below.
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A shopkeeper sells three types of flower seeds A1, A2, A3. They are sold is the form of a mixture, where the proportions of these seeds are 4:4:2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively.
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Based on the above information:
- Calculate the probability that a randomly chosen seed will germinate.
- Calculate the probability that the seed is of type A2, given that a randomly chosen seed germinates.
Chapter: [0.13] Probability
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