NDA & NA (I & II) 2020 — Mathematics (Full Question Paper)

If matrix A = [[1-i, i],[-i, 1-i]] where i = sqrt(-1), then which one of the following is correct?

• (a)A is hermitian
• (b)A is skew-hermitian
• (c)(A-bar)^T + A is hermitian
• (d)(A-bar)^T + A is skew-hermitian

The term independent of x in the binomial expansion of (2/x^2 – sqrt(x))^10 is equal to

• (a)180
• (b)120
• (c)90
• (d)72

If (1 + 2x – x^2)^6 = a0 + a1*x + a2*x^2 + … + a12*x^12, then what is a0 – a1 + a2 – a3 + a4 – … + a12 equal to?

• (a)32
• (b)64
• (c)2048
• (d)4096

If C(20, n+2) = C(20, n-2), then what is n equal to?

• (a)18
• (b)25
• (c)10
• (d)12

For how many values of k, is the matrix [[0,k,4],[-k,0,-5],[-k,k,-1]] singular?

• (a)Only one
• (b)Only two
• (c)Only four
• (d)Infinite

The number (1101101 + 1011011) base 2 can be written in decimal system as

• (a)(198) base 10
• (b)(199) base 10
• (c)(200) base 10
• (d)(201) base 10

What is the value of (1/10)log5(1024) – log5(10) + (1/5)log5(3125)?

• (a)0
• (b)1
• (c)2
• (d)3

If x = log_c(ab), y = log_a(bc), z = log_b(ca), then which of the following is correct?

• (a)xyz = 1
• (b)x+y+z = 1
• (c)(1+x)^-1 + (1+y)^-1 + (1+z)^-1 = 1
• (d)(1+x)^-2 + (1+y)^-2 + (1+z)^-2 = 1

Let A = [[x+y, y],[2x, x-y]], B = [2, -1] (column) and C = [3, 2] (column). If AB = C, then what is the value of the determinant of the matrix A?

• (a)-10
• (b)-14
• (c)-24
• (d)-34

If 1.5 <= x <= 4.5, then which one of the following is correct?

• (a)(2x-3)(2x-9) > 0
• (b)(2x-3)(2x-9) < 0
• (c)(2x-3)(2x-9) >= 0
• (d)(2x-3)(2x-9) <= 0

Let S = {1, 2, 3, …}. A relation R on S x S is defined by xRy if log_a(x) > log_a(y) when a = 1/2. Then the relation is

• (a)reflexive only
• (b)symmetric only
• (c)transitive only
• (d)both symmetric and transitive

What is the value of the determinant |[i, i^2, i^3],[i^4, i^6, i^8],[i^9, i^12, i^15]| where i = sqrt(-1)?

• (a)0
• (b)-2
• (c)4i
• (d)-4i

Let A = [[a,h,g],[h,b,f],[g,f,c]] and B = [x,y,z] (column), then what is AB equal to?

• (a)[ax+hy+gz, y, z] (column)
• (b)[ax+hy+gz, hx+by+fz, z] (column)
• (c)[ax+hy+gz, hx+by+fz, gx+fy+cz] (column)
• (d)[ax+hy+gz hx+by+fz gx+fy+cz] (row)

What is the number of ways in which the letters of the word ‘ABLE’ can be arranged so that the vowels occupy even places?

• (a)2
• (b)4
• (c)6
• (d)8

What is the maximum number of points of intersection of 5 non-overlapping circles?

• (a)10
• (b)15
• (c)20
• (d)25

If the number of elements in Y and Z are in the ratio 4:5, then what is the value of b?

• (a)18
• (b)19
• (c)21
• (d)23

What is the value of n(X) + n(Y) + n(Z) – n(X∩Y) – n(Y∩Z) – n(X∩Z) + n(X∩Y∩Z)?

• (a)a+b+43
• (b)a+b+63
• (c)a+b+96
• (d)a+b+106

If the number of elements belonging to neither X, nor Y, nor Z is equal to p, then what is the number of elements in the complement of X?

• (a)p+b+60
• (b)p+b+40
• (c)p+a+60
• (d)p+a+40

What is tan^2(A) equal to?

• (a)(K+3)/(3K-1)
• (b)(K-3)/(3K-1)
• (c)(3K-3)/(K-3)
• (d)(K+3)/(3K+1)

For real values of tan A, K cannot lie between

• (a)1/3 and 3
• (b)1/2 and 2
• (c)1/5 and 5
• (d)1/7 and 7

Consider the following: 1. AD sin(theta) = AB sin(alpha) 2. BD sin(theta) = AB sin(theta + alpha). Which of the above is/are correct?

• (a)1 only
• (b)2 only
• (c)Both 1 and 2
• (d)Neither 1 nor 2

What is AB equal to?

• (a)(p^2+q^2)sin(theta) / (p cos(theta) + q sin(theta))
• (b)(p^2-q^2)cos(theta) / (p cos(theta) + q sin(theta))
• (c)(p^2+q^2)sin(theta) / (q cos(theta) + p sin(theta))
• (d)(p^2-q^2)cos(theta) / (q cos(theta) + p sin(theta))

If tan(theta) = (cos17 – sin17)/(cos17 + sin17), then what is the value of theta?

• (a)0 degrees
• (b)28 degrees
• (c)38 degrees
• (d)52 degrees

A and B are positive acute angles such that cos(2B) = 3 sin^2(A) and 3 sin(2A) = 2 sin(2B). What is the value of (A + 2B)?

• (a)pi/6
• (b)pi/4
• (c)pi/3
• (d)pi/2

What is sin(3x) + cos(3x) + 4sin^3(x) – 3sin(x) + 3cos(x) – 4cos^3(x) equal to?

• (a)0
• (b)1
• (c)2 sin(2x)
• (d)4 cos(4x)

The value of ordinate of the graph of y = 2 + cos(x) lies in the interval

• (a)[0,1]
• (b)[0,3]
• (c)[-1,1]
• (d)[1,3]

What is the value of 8 cos(10) . cos(20) . cos(40)?

• (a)tan(10)
• (b)cot(10)
• (c)cosec(10)
• (d)sec(10)

What is the value of cos(48) – cos(12)?

• (a)(sqrt5 – 1)/4
• (b)(1 – sqrt5)/4
• (c)(sqrt5 + 1)/2
• (d)(1 – sqrt5)/8

Consider the following statements: 1. If ABC is a right-angled triangle, right-angled at A and if sin B = 1/3, then cosec C = 3. 2. If b cos B = c cos C and if the triangle ABC is not right-angled, then ABC must be isosceles. Which of the above statements is/are correct?

• (a)1 only
• (b)2 only
• (c)Both 1 and 2
• (d)Neither 1 nor 2

Consider the following statements: 1. If in a triangle ABC, A = 2B and b = c, then it must be an obtuse-angled triangle. 2. There exists no triangle ABC with A = 40 degrees, B = 65 degrees and a/c = sin40.cosec15. Which of the above statements is/are correct?

• (a)1 only
• (b)2 only
• (c)Both 1 and 2
• (d)Neither 1 nor 2

What is tan^2(x) equal to?

• (a)(c-b)/(a-c)
• (b)(a-c)/(c-b)
• (c)(c-a)/(c-b)
• (d)(c-b)/(c-a)

What is (d-a)/(b-d) equal to?

• (a)sin^2(y)
• (b)cos^2(y)
• (c)tan^2(y)
• (d)cot^2(y)

What is p^2/q^2 equal to?

• (a)(b-c)(b-d) / (a-d)(a-c)
• (b)(a-d)(c-a) / (b-c)(d-b)
• (c)(d-a)(c-a) / (b-c)(d-b)
• (d)(b-c)(b-d) / (c-a)(a-d)

What is (t3-t5)/(t5-t7) equal to?

• (a)t1/t3
• (b)t3/t5
• (c)t5/t7
• (d)t1/t7

What is t1^2 – t2 equal to?

• (a)cos(2theta)
• (b)sin(2theta)
• (c)2cos(theta)
• (d)2sin(theta)

What is the value of t10 where theta = 45 degrees?

• (a)1
• (b)1/4
• (c)1/16
• (d)1/32

What is the value of sin(alpha) + cos(beta)?

• (a)1/sqrt2
• (b)1/(2sqrt2)
• (c)sqrt3/(2sqrt2)
• (d)sqrt3/sqrt2

What is the value of sin(7*alpha) – cos(7*beta)?

• (a)1/sqrt2
• (b)1/(2sqrt2)
• (c)sqrt3/(2sqrt2)
• (d)sqrt3/sqrt2

What is sin(alpha+1) + cos(beta+1) equal to?

• (a)sqrt3 cos1 + sin1
• (b)sqrt3 cos1 – (1/2)sin1
• (c)(1/sqrt2)(sqrt3 cos1 – sin1)
• (d)(1/2)(sqrt3 cos1 + sin1)

If sin(x) + sin(y) = cos(y) – cos(x), where 0 < y < x < pi/2, then what is tan((x-y)/2) equal to?

• (a)0
• (b)1/2
• (c)1
• (d)2

If A is a matrix of order 3×5 and B is a matrix of order 5×3, then the order of AB and BA will respectively be

• (a)3×3 and 3×3
• (b)3×5 and 5×3
• (c)3×3 and 5×5
• (d)5×3 and 3×5

If p^2, q^2 and r^2 (where p, q, r > 0) are in GP, then which of the following is/are correct? 1. p, q and r are in GP. 2. ln p, ln q and ln r are in AP. Select the correct answer using the code given below:

• (a)1 only
• (b)2 only
• (c)Both 1 and 2
• (d)Neither 1 nor 2

If cot(alpha) and cot(beta) are the roots of the equation x^2 – 3x + 2 = 0, then what is cot(alpha+beta) equal to?

• (a)1/2
• (b)1/3
• (c)2
• (d)3

The roots alpha and beta of a quadratic equation, satisfy the relations alpha+beta = alpha^2+beta^2 and alpha*beta = alpha^2*beta^2. What is the number of such quadratic equations?

• (a)0
• (b)2
• (c)3
• (d)4

What is the argument of the complex number (1 – i*sqrt3)/(1 + i*sqrt3), where i = sqrt(-1)?

• (a)240 degrees
• (b)210 degrees
• (c)120 degrees
• (d)60 degrees

What is the modulus of the complex number (cos(theta) + i sin(theta)) / (cos(theta) – i sin(theta)), where i = sqrt(-1)?

• (a)1/2
• (b)1
• (c)3/2
• (d)2

Consider the proper subsets of {1,2,3,4}. How many of these proper subsets are superset of the set {3}?

• (a)5
• (b)6
• (c)7
• (d)8

Let p, q and r be three distinct positive real numbers. If D = |[p,q,r],[q,r,p],[r,p,q]| (determinant), then which one of the following is correct?

• (a)D < 0
• (b)D <= 0
• (c)D > 0
• (d)D >= 0

What is the sum of the last five coefficients in the expansion of (1+x)^9 when it is expanded in ascending powers of x?

• (a)256
• (b)512
• (c)1024
• (d)2048

Consider the following in respect of a non-singular matrix of order 3: 1. A(adj A) = (adj A)A 2. |adj A| = |A|. Which of the above statements is/are correct?

• (a)1 only
• (b)2 only
• (c)Both 1 and 2
• (d)Neither 1 nor 2

The center of the circle (x-2a)(x-2b) + (y-2c)(y-2d) = 0 is

• (a)(2a, 2c)
• (b)(2b, 2d)
• (c)(a+b, c+d)
• (d)(a-b, c-d)

The point (1,-1) is one of the vertices of a square. If 3x + 2y = 5 is the equation of one diagonal of the square, then what is the equation of the other diagonal?

• (a)3x – 2y = 5
• (b)2x – 3y = 1
• (c)2x – 3y = 5
• (d)2x + 3y = -1

Let P(x,y) be any point on the ellipse 25x^2 + 16y^2 = 400. If Q(0,3) and R(0,-3) are two points, then what is (PQ+PR) equal to?

• (a)12
• (b)10
• (c)8
• (d)6

If the circumcentre of the triangle formed by the lines x+2=0, y+2=0 and kx+y+2=0 is (-1,-1), then what is the value of k?

• (a)-1
• (b)-2
• (c)1
• (d)2

In the parabola, y^2 = x, what is the length of the chord passing through the vertex and inclined to the x-axis at an angle theta?

• (a)sin(theta).sec^2(theta)
• (b)cos(theta).cosec^2(theta)
• (c)cot(theta).sec^2(theta)
• (d)2tan(theta).cosec^2(theta)

Under which condition, are the points (a,b), (c,d) and (a-c, b-d) collinear?

• (a)ab = cd
• (b)ac = bd
• (c)ad = bc
• (d)abc = d

Let ABC be a triangle. If D(2,5) and E(5,9) are the mid-points of the sides AB and AC respectively, then what is the length of the side BC?

• (a)8
• (b)10
• (c)12
• (d)14

If the foot of the perpendicular drawn from the point (0,k) to the line 3x-4y-5=0 is (3,1), then what is the value of k?

• (a)3
• (b)4
• (c)5
• (d)6

What is the obtuse angle between the lines whose slopes are 2-sqrt3 and 2+sqrt3?

• (a)105 degrees
• (b)120 degrees
• (c)135 degrees
• (d)150 degrees

If 3x-4y-5=0 and 3x-4y+15=0 are the equations of a pair of opposite sides of a square, then what is the area of the square?

• (a)4 square units
• (b)9 square units
• (c)16 square units
• (d)25 square units

What is the length of the diameter of the sphere whose centre is at (1,-2,3) and which touches the plane 6x-3y+2z-4=0?

• (a)1 unit
• (b)2 units
• (c)3 units
• (d)4 units

What is the perpendicular distance from the point (2,3,4) to the line (x-0)/1 = (y-0)/0 = (z-0)/0?

• (a)6 units
• (b)5 units
• (c)3 units
• (d)2 units

If a line has direction ratios <a+b, b+c, c+a>, then what is the sum of the squares of its direction cosines?

• (a)(a+b+c)^2
• (b)2(a+b+c)
• (c)3
• (d)1

Into how many compartments do the coordinate planes divide the space?

• (a)2
• (b)4
• (c)8
• (d)16

What is the equation of the plane which cuts an intercept 5 units on the z-axis and is parallel to xy-plane?

• (a)x+y=5
• (b)z=5
• (c)z=0
• (d)x+y+z=5

If a-hat is a unit vector in the xy-plane making an angle 30 degrees with the positive x-axis, then what is a-hat equal to?

• (a)(sqrt3 i-hat + j-hat)/2
• (b)(sqrt3 i-hat – j-hat)/2
• (c)(i-hat + sqrt3 j-hat)/2
• (d)(i-hat – sqrt3 j-hat)/2

Let A be a point in space such that |OA| = 12, where O is the origin. If OA is inclined at angles 45 degrees and 60 degrees with x-axis and y-axis respectively, then what is OA equal to?

• (a)6i-hat + 6j-hat +- sqrt2 k-hat
• (b)6i-hat + 6sqrt2 j-hat +- 6k-hat
• (c)6sqrt2 i-hat + 6j-hat +- 6k-hat
• (d)3sqrt2 i-hat + 3j-hat +- 6k-hat

Two adjacent sides of a parallelogram are 2i-hat-4j-hat+5k-hat and i-hat-2j-hat-3k-hat. What is the magnitude of dot product of vectors which represent its diagonals?

• (a)21
• (b)25
• (c)31
• (d)36

If |a x b|^2 + |a.b|^2 = 144 and |a| = 4, then what is |b| equal to?

• (a)3
• (b)4
• (c)6
• (d)8

If the vectors a = 2i-hat-3j-hat+k-hat, b = i-hat+2j-hat-3k-hat and c = j-hat+p k-hat are coplanar, then what is the value of p?

• (a)1
• (b)-1
• (c)5
• (d)-5

What is lim(x to 1) (x+x^2+x^3-3)/(x-1) equal to?

• (a)1
• (b)2
• (c)3
• (d)6

The radius of a circle is increasing at the rate of 0.7 cm/sec. What is the rate of increase of its circumference?

• (a)4.4 cm/sec
• (b)8.4 cm/sec
• (c)8.8 cm/sec
• (d)15.4 cm/sec

If lim(x to 1) (x^4-1)/(x-1) = lim(x to k) (x^3-k^3)/(x^2-k^2), where k not equal 0, then what is the value of k?

• (a)2/3
• (b)4/3
• (c)8/3
• (d)4

The order and degree of the differential equation k(dy/dx) = integral[1+(dy/dx)^2]^(2/3) dx are respectively

• (a)1 and 1
• (b)2 and 3
• (c)2 and 4
• (d)1 and 4

What is lim(x to 0) (sin x . log(1-x))/x^2 equal to?

• (a)-1
• (b)Zero
• (c)-e
• (d)-1/e

If f(x) = 3x^2-5x+p and f(0) and f(1) are opposite in sign, then which of the following is correct?

• (a)-2<p<0
• (b)-2<p<2
• (c)0<p<2
• (d)3<p<5

If e^(theta.phi) = c + 4(theta)(phi), where c is an arbitrary constant and phi is a function of theta, then what is phi d(theta) equal to?

• (a)theta d(phi)
• (b)-theta d(phi)
• (c)4theta d(phi)
• (d)-4theta d(phi)

If p(x) = (4e)^2x, then what is integral p(x) dx equal to?

• (a)p(x)/(1+2ln2) + c
• (b)p(x)/(2(1+2ln2)) + c
• (c)2p(x)/(1+ln4) + c
• (d)p(x)/(1+ln2) + c

What is the value of integral from 0 to pi/4 of (tan^3 x + tan x) dx?

• (a)1/4
• (b)1/2
• (c)1
• (d)2

Let y = 3x^2+2. If x changes from 10 to 10.1, then what is the total change in y?

• (a)4.71
• (b)5.23
• (c)6.03
• (d)8.01

If f(x) = sin x / x, where x is in R, is to be continuous at x=0, then the value of the function at x=0

• (a)should be 0
• (b)should be 1
• (c)should be 2
• (d)cannot be determined

The solution of the differential equation dy = (1+y^2) dx is

• (a)y = tan x + c
• (b)y = tan(x+c)
• (c)tan^-1(y+c) = x
• (d)tan^-1(y+c) = 2x

What is integral (e^(log x) + sin x) cos x dx equal to?

• (a)sin x + x cos x + (sin^2 x)/2 + c
• (b)sin x – x cos x + (sin^2 x)/2 + c
• (c)x sin x + cos x + (sin^2 x)/2 + c
• (d)x sin x – x cos x + (sin^2 x)/2 + c

What is the domain of the function f(x) = cos^-1(x-2)?

• (a)[-1,1]
• (b)[1,3]
• (c)[0,5]
• (d)[-2,1]

What is the area of the region enclosed between the curve y^2=2x and the straight line y=x?

• (a)1/2
• (b)1
• (c)2/3
• (d)2

If f(x) = 2x-x^2, then what is the value of f(x+2)+f(x-2) when x=0?

• (a)-8
• (b)-4
• (c)8
• (d)4

If x^m y^n = a^(m+n), then what is dy/dx equal to?

• (a)my/nx
• (b)-my/nx
• (c)mx/ny
• (d)-ny/mx

What is integral dx/(x(x^n+1)) equal to?

• (a)(1/n)ln(x^n/(x^n+1)) + c
• (b)ln((x^n+1)/x^n) + c
• (c)ln(x^n/(x^n+1)) + c
• (d)(1/n)ln((x^n+1)/x^n) + c

What is the minimum value of |x-1|, where x is in R?

• (a)0
• (b)1
• (c)2
• (d)-1

What is the value of k such that integration of (3x^2+8-4k)/x with respect to x, may be a rational function?

• (a)0
• (b)1
• (c)2
• (d)-2

Consider the following statements for f(x) = e^(-|x|): 1. The function is continuous at x=0. 2. The function is differentiable at x=0. Which of the above statements is/are correct?

• (a)1 only
• (b)2 only
• (c)Both 1 and 2
• (d)Neither 1 nor 2

What is the maximum value of sin x . cos x?

• (a)2
• (b)1
• (c)1/2
• (d)2sqrt2

What is lim(x to 0) (3^x + 3^-x – 2)/x equal to?

• (a)0
• (b)-1
• (c)1
• (d)Limit does not exist

What is the derivative of tan^-1 x with respect to cot^-1 x?

• (a)-1
• (b)1
• (c)1/(x^2+1)
• (d)x/(x^2+1)

The function u(x,y) = c which satisfies the differential equation x(dx-dy) + y(dy-dx) = 0, is

• (a)x^2+y^2 = xy+c
• (b)x^2+y^2 = 2xy+c
• (c)x^2-y^2 = xy+c
• (d)x^2-y^2 = 2xy+c

What is the minimum value of 3cos(A + pi/3) where A is in R?

• (a)-3
• (b)-1
• (c)0
• (d)3

Consider the following statements: 1. The function f(x) = ln x increases in the interval (0, infinity). 2. The function f(x) = tan x increases in the interval (-pi/2, pi/2). Which of the above statements is/are correct?

• (a)1 only
• (b)2 only
• (c)Both 1 and 2
• (d)Neither 1 nor 2

Which one of the following is correct in respect of the graph of y = 1/(x-1)?

• (a)The domain is {x in R | x not equal 1} and the range is the set of reals.
• (b)The domain is {x in R | x not equal 1}, the range is {y in R | y not equal 0} and the graph intersects y-axis at (0,-1).
• (c)The domain is the set of reals and the range is the singleton set {0}.
• (d)The domain is {x in R | x not equal 1} and the range is the set of points on the y-axis.

What is the solution of the differential equation ln(dy/dx) = x?

• (a)y = e^x + c
• (b)y = e^-x + c
• (c)y = ln x + c
• (d)y = 2 ln x + c

Let l be the length and b be the breadth of a rectangle such that l+b=k. What is the maximum area of the rectangle?

• (a)2k^2
• (b)k^2
• (c)k^2/2
• (d)k^2/4

The numbers 4 and 9 have frequencies x and (x-1) respectively. If their arithmetic mean is 6, then what is the value of x?

• (a)2
• (b)3
• (c)4
• (d)5

If three dice are rolled under the condition that no two dice show the same face, then what is the probability that one of the faces is having the number 6?

• (a)5/6
• (b)5/9
• (c)1/2
• (d)5/12

If P(AUB) = 5/6, P(A∩B) = 1/3 and P(not A) = 1/2, then which one of the following is not correct?

• (a)P(B) = 2/3
• (b)P(A∩B) = P(A)P(B)
• (c)P(AUB) > P(A)+P(B)
• (d)P(not A and not B) = P(not A) P(not B)

The sum of deviations of n number of observations measured from 2.5 is 50. The sum of deviations of the same set of observations measured from 3.5 is -50. What is the value of n?

• (a)50
• (b)60
• (c)80
• (d)100

A data set of n observations has mean 2M, while another data set of 2n observations has mean M. What is the mean of the combined data sets?

• (a)M
• (b)3M/2
• (c)2M/3
• (d)4M/3

Table (Q106–108): Marks vs. Number of students in Physics and Mathematics — 10–20: 8/10; 20–30: 11/21; 30–40: 30/38; 40–50: 26/15; 50–60: 15/10; 60–70: 10/6.

[Table: Marks vs Number of students in Physics and Mathematics – see table above] The difference between number of students under Physics and Mathematics is largest for the interval

• (a)20-30
• (b)30-40
• (c)40-50
• (d)50-60

[Same table] Consider the following statements: 1. Modal value of the marks in Physics lies in the interval 30-40. 2. Median of the marks in Physics is less than that of marks in Mathematics. Which of the above statements is/are correct?

• (a)1 only
• (b)2 only
• (c)Both 1 and 2
• (d)Neither 1 nor 2

[Same table] What is the mean of marks in Physics?

• (a)38.4
• (b)39.4
• (c)40.9
• (d)41.6

What is the standard deviation of the observations -sqrt6, -sqrt5, -sqrt4, -1, 1, sqrt4, sqrt5, sqrt6?

• (a)sqrt2
• (b)2
• (c)2sqrt2
• (d)4

If sum(xi) = 20, sum(xi^2) = 200 and n=10 for an observed variable x, then what is the coefficient of variation?

• (a)80
• (b)100
• (c)150
• (d)200

What is the probability that February of a leap year selected at random, will have five Sundays?

• (a)1/5
• (b)1/7
• (c)2/7
• (d)1

The arithmetic mean of 100 observations is 40. Later, it was found that an observation ’53’ was wrongly read as ’83’. What is the correct arithmetic mean?

• (a)39.8
• (b)39.7
• (c)39.6
• (d)39.5

A husband and wife appear in an interview for two vacancies for the same post. The probability of the husband’s selection is 1/7 and that of the wife’s selection is 1/5. If the events are independent, then the probability of which one of the following is 11/35?

• (a)At least one of them will be selected
• (b)Only one of them will be selected
• (c)None of them will be selected
• (d)Both of them will be selected

A dealer has a stock of 15 gold coins out of which 6 are counterfeits. A person randomly picks 4 of the 15 gold coins. What is the probability that all the coins picked will be counterfeits?

• (a)1/91
• (b)4/91
• (c)6/91
• (d)15/91

A committee of 3 is to be formed from a group of 2 boys and 2 girls. What is the probability that the committee consists of 2 boys and 1 girl?

• (a)2/3
• (b)1/4
• (c)3/4
• (d)1/2

In a lottery of 10 tickets numbered 1 to 10, two tickets are drawn simultaneously. What is the probability that both the tickets drawn have prime numbers?

• (a)1/15
• (b)1/2
• (c)2/15
• (d)1/5

Let X and Y represent prices (in Rs.) of a commodity in Kolkata and Mumbai respectively. It is given that X-bar=65, Y-bar=67, sigma_X=2.5, sigma_Y=3.5 and r(X,Y)=0.8. What is the equation of regression of Y on X?

• (a)Y = 0.175X – 5
• (b)Y = 1.12X – 5.8
• (c)Y = 1.12X – 5
• (d)Y = 0.17X + 5.8

Consider a random variable X which follows Binomial distribution with parameters n=10 and p=1/5. Then Y = 10-X follows Binomial distribution with parameters n and p respectively given by

• (a)5, 1/5
• (b)5, 2/5
• (c)10, 3/5
• (d)10, 4/5

If A and B are two events such that P(A)=0.6, P(B)=0.5 and P(A∩B)=0.4, then consider the following statements: 1. P(not-A U B) = 0.9. 2. P(not-B | not-A) = 0.6. Which of the above statements is/are correct?

• (a)1 only
• (b)2 only
• (c)Both 1 and 2
• (d)Neither 1 nor 2

Three cooks X, Y and Z bake a special kind of cake, and with respective probabilities 0.02, 0.03 and 0.05, it fails to rise. In the restaurant where they work, X bakes 50%, Y bakes 30% and Z bakes 20% of cakes. What is the proportion of failures caused by X?

• (a)9/29
• (b)10/29
• (c)19/29
• (d)28/29