# BITSAT Past Exam Paper Mathematics – 2015

/in BITSAT /by Krushna Chandra Satapathy#### Quiz-summary

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- Question 1 of 45
##### 1. Question

equals

CorrectIncorrect - Question 2 of 45
##### 2. Question

If ω is the complex cube root of unity, then the value of is

CorrectIncorrect - Question 3 of 45
##### 3. Question

Let α = a + a

^{2}+ a^{4}and β = a^{3}+ a^{5}= a. Then, the equation whose roots are α and β, isCorrectIncorrect - Question 4 of 45
##### 4. Question

The value of upto n term is

CorrectIncorrect - Question 5 of 45
##### 5. Question

The period of the function f(x) = cos x + {x} is

CorrectIncorrect - Question 6 of 45
##### 6. Question

If a function f(x) is given by then at x = 0, f(x)

CorrectIncorrect - Question 7 of 45
##### 7. Question

If g is the inverse of function f and f ′(x) = sin x, then g′(x) is equal to

CorrectIncorrect - Question 8 of 45
##### 8. Question

A bag contains (2n + 1) coins. It is know that n of these coins have a head on both sides, whereas the remaining (n + 1) coins are fair. A coin is picked up at random from the bag and tossed. if the probability that the toss results in a head is 31/42, then n is equal to

CorrectIncorrect - Question 9 of 45
##### 9. Question

If ϕ(x) is a differentiable function, then the solution of the differential equation dy + {yϕ′(x) – ϕ(x) ϕ′(x)}dx = 0 is

CorrectIncorrect - Question 10 of 45
##### 10. Question

The area of the region R = {(x, y) : |x| ≤ |y| and x

^{2}+ y^{2}≤ 1}isCorrectIncorrect - Question 11 of 45
##### 11. Question

A and B are any two non-empty sets and A is proper subset of B. If n(A) = 5, then find the minimum possible value of n(A ∆ B).

CorrectIncorrect - Question 12 of 45
##### 12. Question

If α = 2 tan

^{−1}(√2 – 1), and , thenCorrectIncorrect - Question 13 of 45
##### 13. Question

If then the value of 2a

_{1}+ 2^{3}a_{3}+ 2^{5}a_{5}+ … isCorrectIncorrect - Question 14 of 45
##### 14. Question

Let

**a**,**b**and**c**be three vectors satisfying**a**×**b**= (**a**×**c**), |**a**| = |**c**|=1, |**b**| = 4 and |**b**×**c**| = √15. If**b**– 2**c**=λ**a**, then λ equalsCorrectIncorrect - Question 15 of 45
##### 15. Question

The total number of 4-digit numbers in which the digits are in descending order, is

CorrectIncorrect - Question 16 of 45
##### 16. Question

The line which is parallel to X-axis and crosses the curve y = √x at an angle of 45°, is

CorrectIncorrect - Question 17 of 45
##### 17. Question

In a ∆ ABC, the lengths of the two larger sides are 10 and 9 units, respectively. If the angles are in AP, then the length of the third side can be

CorrectIncorrect - Question 18 of 45
##### 18. Question

The arithmetic mean of the data 0, 1, 2, …, n with frequencies 1,

^{n}C_{1},^{n}C_{2}, ….^{n}C_{n}isCorrectIncorrect - Question 19 of 45
##### 19. Question

The mean square deviation of a set of n observations x

_{1}, x_{2}, …., x_{n}about a point c is defined asThe mean square deviation about −2, and 2 are 18 and 10 respectively, the standard deviation of this et of observations is

CorrectIncorrect - Question 20 of 45
##### 20. Question

Let S be the focus of the parabola y

^{2}= 8x and PQ be the common chord of the circle x^{2}+ y^{2}– 2x – 4y = 0 and the given parabola. The area of ∆PQS isCorrectIncorrect - Question 21 of 45
##### 21. Question

The number of real roots of the equation e

^{x−1}+ x – 2 = 0 isCorrectIncorrect - Question 22 of 45
##### 22. Question

Minimise

Subject to is a LPP with number of constraints

CorrectIncorrect - Question 23 of 45
##### 23. Question

India plays two matches each with West Indies and Australia. In any match, the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50, respectively. Assuming that the outcomes are independent, the probability of India getting atleast 7 points is

CorrectIncorrect - Question 24 of 45
##### 24. Question

Let M be a 3 × 3 non-singular matrix with det(M) = α. If M

^{−1}adj adj A) = KI, then the value of K isCorrectIncorrect - Question 25 of 45
##### 25. Question

Tangents are drawn from the origin to the curve y = cos x. Their points of contact lie on

CorrectIncorrect - Question 26 of 45
##### 26. Question

The slope of the tangent to the curve y = e

^{x}cos x is minimum at x = a, 0 ≤ a ≤ 2π, then the value of a isCorrectIncorrect - Question 27 of 45
##### 27. Question

Two lines are coplanar. Then, α can take value (s)

CorrectIncorrect - Question 28 of 45
##### 28. Question

Let P be a point on the ellipse of eccentricity e. If A, A′ are the vertices and S, S′ are the foci of the ellipse, then area of ∆PSS′ : area of ∆APA′ is equal to

CorrectIncorrect - Question 29 of 45
##### 29. Question

The largest interval for which x

^{12}– x^{9}+ x^{4}– x + 1 > 0 isCorrectIncorrect - Question 30 of 45
##### 30. Question

If where Then, the value of is

CorrectIncorrect - Question 31 of 45
##### 31. Question

If (1 + 3 + 5 + … + p) + (1 + 3 + 5 + … + q) = (1 + 3 + 5 + … + r), then the least possible value of p + q + r, given p > 6, is

CorrectIncorrect - Question 32 of 45
##### 32. Question

For x > 0, is equal to

CorrectIncorrect - Question 33 of 45
##### 33. Question

If then

CorrectIncorrect - Question 34 of 45
##### 34. Question

The degree of the differential equation satisfying the relation is

CorrectIncorrect - Question 35 of 45
##### 35. Question

Let f(x) be a polynomial of degree three satisfying f(0) = –1 and f(1) = 0. Also, 0 is a stationary point of f(x). If f(x) does not have and extremum at x = 0, then the value of is

CorrectIncorrect - Question 36 of 45
##### 36. Question

If e

^{x}+ e^{f(x)}= e, then the domain of f(x) isCorrectIncorrect - Question 37 of 45
##### 37. Question

The equation of the line with gradient –3/2, which is concurrent with the lines 4x + 3y – 7 = 0 and 8x + 5y – 1 = 0, is

CorrectIncorrect - Question 38 of 45
##### 38. Question

Area of the circle in which a chord of length √2 makes an angle π/2 at the centre, is

CorrectIncorrect - Question 39 of 45
##### 39. Question

The ratio of the greatest value of 2 – cos x + sin

^{2 }x is to its least value, isCorrectIncorrect - Question 40 of 45
##### 40. Question

If z

_{1}, z_{2}, z_{3}and z_{4}represent the vertices of a rhombus taken in the anti-clockwise order, thenCorrectIncorrect - Question 41 of 45
##### 41. Question

If ρ = {(x, y) |x

^{2}+ y^{2}= 1; x, y ∈ R}. Then, ρ isCorrectIncorrect - Question 42 of 45
##### 42. Question

A line makes the same angle θ with each of the X and Z-axes. If the angle β, which is makes with Y-axis, is such that sin

^{2}β = 3sin^{2}θ, then cos^{2}θ equalsCorrectIncorrect - Question 43 of 45
##### 43. Question

If in a binomial distribution n = 4,then P(X = 4) equals

CorrectIncorrect - Question 44 of 45
##### 44. Question

Let f : R → R be a function such that f(x + y) = f(x) + f(y), ∀ x, y ∈ R

If f(x) is differentiable at x = 0, then which one of the following is incorrect?

CorrectIncorrect - Question 45 of 45
##### 45. Question

If binomial coefficients of three consecutive terms of (1 + x)

^{n}are in HP, then the maximum value of n isCorrectIncorrect