If N = 82^3 - 62^3 - 203 then N is divisible by:
1.31 and 41
2.13 and 67
3.17 and 7
4.None
Centre of a circle is (2, 3). If the line x + y = 1 touches, its equation is
1.x2 + y2 - 4x - 6y + 4 = 0
2. x2 + y2 - 4x - 6y + 5 = 0
3.x2 + y2 - 4x - 6y - 5 = 0
4.None of these
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
1.9
2.10
3.11
4.12
If a1 = 1 and an+1 = 2an + 5, n=1, 2....... then a100 is equal to
1.5 x 2^99 - 6
2. 5 x 2^99 + 6
3.6 x 2^99 + 5
4.6 x 2^99 - 5
If v,w,x,y, and z are non negative integers, each less than 11, then how many distinct combinations of (v,w,x,y,z) satisfy v(11^4) + w(11^3) +x(11^2) + y(11) + z =151001 ?
1.0
2.1
3.2
4.3
Let f : R ? R be a function defined by f(x) = max. {x, x3}. The set of all points where f(x) is not differentiable is
1.{-1, 1}
2. {-1, 0}
3. {0, 1}
4.{-1, 0, 1}
PT Usha and Shelly John decide to run a marathon between Ramnagar and Jamnagar. Both start from Ramnagar at 1 pm. On the way are two towns Ramgarh and Rampur, separated by a distance of 15 km. PT Usha reaches Ramgarh in 90 minutes running at a constant speed of 40 kmph. She takes additional 30 minutes to reach Rampur. Between Rampur and Jamnagar she maintains an average speed of V kmph (where V is a whole number),Shelly John being a professional marathon runner, maintains a constant speed of 18 kmph. They both reach Jamnagar together after 'n' hours, 'n' being a whole number. What could be total time taken by PT Usha?
1.5 hours
2.15 hours
3.41 hours
4.All of the above
-------------- is equal to
1.cos isin - ?
2.. cos9 isin9 ? - ?
3.sin icos ?- ?
4.sin 9 icos9 ? - ?
2.42n + 1 + 33n+1 is divisible by
1.2
2.9
3.11
4.27
A biker notices a certain number(2 digits number) on the milestone before starting the journey. After riding for an hour he notices a milestone with reversed digits of the previous number. Now after riding for another hour he notices that the number on a new milestone had same digits as the first one (in the same order) but with a "0" between the 2 digits. If the rider maintains a constant speed throughout, Calculate his speed.
1.45 kmph
2.50 kmph
3.35 kmph
4.None of these
A boat M leaves shore A and at the same time boat B leaves shore B. They move across the river. They met at 500 yards away from A and after that they met 300 yards away from shore B without halting at shores. Find the distance between the shore A & B.
1.1100 yards
2.1200 yards
3.1300 yards
4.1400 yards
A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two-thirds the time needed by the second pair to complete the work. Which is the first pair?
1.A and B
2. A and C
3.B and C
4.A and D
A common tangent to the circle x2 + y2 = 16 and an ellipse x2 / 49 + y2 / 4 = 1 is
1. y = x + 4v5
2.y = x + v53
3. y= x + z
4.None of These
A hexagon of side a cm is folded along its edges to obtain another hexagon What is the % decrease in the area aof orignal hexagon ?
1.70%
2.75%
3.80%
4. 60%
A lady gives a dinner party to six quests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is
1.112
2.140
3.164
4.None of these
A man can hit the target once in four shots. If he fires four shots in succession, what is the probability that he will hit the target?
1.1
2.1/256
3.81/256
4.175/256
A man from the top of a 100 metre high tower sees a car moving towards the tower at an angle of depression of 300. After sometimes, the angle of depression becomes 600. The distance (in metres) traveled by the car during this time is
1.100 v3
2.200 v3 / 3
3.100 v3 / 3
4.200 v3
A real number x satisfying 1- (1/n) ≤ 3 + (1/n), for every positive integer n, is best described by ≤
1.1 < x < 4
2.1 < x ≤ 3
3. 0 < x ≤4
4.1 ≤ x ≤ 3
A rectangular sheet of paper, when halved by folding it at the midpoint of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?
1.4√2
2.2√2
3.√2
4.None of the above
A tank has two compartments I and II. Two taps X and Y, whose filling rates are in ratio of 2:1, are used to fill the tank. The ration fo time taken by tap X to fill compartment I and tap Y to fill compartment II is 16:25. Find the ratio of the times taken by tap X to fill compartment II and tap Y to fill compartment I.
1.25:64
2.16:25
3.64:25
4. 4:5
Angle between the pair of straight lines x2 “ xy “ 6y2 “ 2x + 11y “ 3 = 0 is
1.450 , 1350
2. tan-1 2, p = tan-1 2
3. tan-1 3, p = tan-1 3
4.None of these
At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > 0. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?
1.p = q
2.p < q
3.p > q
4.p = q/2
Centre of circle whose normals are x2 - 2xy - 3x + 6y = 0 is
1.(3 , 3 / 2)
2.(3 / 2 , 3)
3.(-3 , 3 / 2)
4.(-3 , -3 / 2)
Find the number of ways you can fill a 3 x 3 grid (with 4 corners defined as a, b, c, d), if you have 3 white marbles and 6 black marbles.
1.75
2.84
3.80
4.None of These
Find the values of n for which n+18 and n+90 is a perfect square ?
1.6
2.5
3.4
4.3
Given that -1 ≤ v ≤ 1, -2 ≤ u ≤ -0.5, and -2 ≤ z ≤ -0.5 and w = vz/u, then which of the following is necessarily true?
1.-0.5 ≤ w ≤ -2
2.-4 ≤ w ≤ 4
3.-4 ≤ w ≤ 2
4. -2 ≤ w ≤ -0.5
Harish and Peter working separately can paint a building in 18 days and 24 days respectively. If they work for a day alternately, Harish beginning, in how many days, the painting work will be completed ?
1.41/2 days
2. 21/2 days
3.63/4 days
4. 65/4 days
If 1/a + 1/b + 1/c = 1 / (a + b + c); where a + b + c 1 0; abc 1 0, then what is the value of ( a + b ) ( b + c ) ( c + a )?
1.Equal to 0
2.Greater than 0
3.Less than 0
4.Cannot be determined
If 2x+y = 10, 2y+z = 20 and 2x+z = 30. Where x, y,and z are real number. What is the value of 2x ?
1.3/2
2. sqrt(15)
3.sqrt(6)/2
4.15
If a = tan60 tan 420 and B = cot660 cot 780
1. A = 2B
2.1 / 3 B
3.A = B
4.3A = 2B
If a circle cuts rectangles hyperbola xy = 1 in the point (xi, yi), i = 1, 2, 3, 4 then
1.x1x2x3x4 = 0
2. y1y2y3y4 = 1
3. y1y2y3y4 = 0
4.x1x2x3x4 = -1
If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then locus of its centre is
1.2ax + 2by + (a2 + b2 + 4) = 0
2.2ax + 2by - (a2 + b2 + 4) = 0
3.2ax - 2by + (a2 + b2 + 4) = 0
4.2ax - 2by - (a2 + b2 + 4) = 0
If a, ß are the roots of ax2 - 2bx + c = 0 then a3 ß3 + a2ß3 + a3ß2 is
1.c2(c + 2b) / a3
2.bc3 / a3
3.c2 / a3
4.None of these
If cosec? + cot ? = 5 / 2 , then the value of tan? is
1.15 / 15
2. 21 / 20
3.15 / 21
4.20 / 21
If length of the sides AB, BC and CA of a triangle are 8cm, 15 cm and 17 cm respectively, then length of the angle bisector of ?ABC is
1.120 v2 / 23cm
2. 60 v2 / 23cm
3.30 v2 / 23cm
4.None of these
If sin? + cos? = v2sin?, then
1.v2 cos?
2.- v2 sin?
3.- v2 cos?
4.None of these
If sin? + cosec? = 2, then value of sin3? + cosec3? is
1.2
2.4
3.6
4.8
If the hyperbolas x2 - y2 = a2 and xy = c2 are of equal size, then
1.c2 = 2a2
2. c = 2a
3. 2c2 = a2
4.None of These
If the product of n positive numbers in 1, then their sum is
1.pa ositive integer
2.divisible by n
3.equal to n + (1 / n)
4.never less than n
If x is very large and n is a negative integer or a proper fraction, then an approximate value of ((1 + X) / x )n is
1.1 + x / n
2.1 + n / x
3.1 + 1 / x
4.n(1 + 1 / x)
If | r- 6 | = 11 and |2q - 12| = 8, what is the minimum possible value of q / r ?
1.-2/5
2.-2
3.10/17
4.None of these
In how many ways can 10 engineers and 4 doctors be seated at a round table if all the 4 doctors do not sit together?
1.13! - (10! × 4!)
2.13! × 4!
3.14!
4.10! × 4!
Incentre of the triangle whose vertices are (6, 0) (0, 6) and (7, 7) is
1.(9 / 2 , 9 / 2)
2.(7 / 2 , 7 / 2)
3.(11 / 2 , 11 / 2)
4.None of these
Let A be a natural number consisting only 1. B is another natural number which is equal to quotient when A is divided by 13. C is yet another natural number equal to the quotient when B is divided by 7. Find B-C.
1.7236
2.7362
3.7326
4.None of These
Let A be a natural number consisting only 1. B is another natural number which is equal to quotient when A is divided by 13. C is yet another natural number equal to the quotient when B is divided by 7. Find B-C.
1.7236
2.7362
3.7326
4.None of These
Let R1 and R2 respectively denote the maximum and minimum possible remainders when (276)n is divided by 91 for any natural number n,n>= 144. Find R1+R2.
1.90
2.82
3.84
4.64
Let Sn denote the sum of first n terms of an A.P..If S2n = 3Sn, then the ratio S3n / 5n is equal to
1.4
2. 6
3.8
4.10
Solution of |3 “ x| = x “ 3 is
1.x < 3
2. x > 3
3.x = 3
4.x = 3
The angle between the tangents drawn from the origin to the parabola y2 = 4a (x “ a) is
1.900
2.300
3. tan-1(½)
4.450
The area bounded by curve y = 4x “ x2 and x “ axis is
1.30 / 7 sq. units
2. 31 / 7sq. units
3.32 / 3 sq. units
4.34 / 3 sq. units
The area bounded by curve y = 4x “ x2 and x “ axis is
1.30 / 7 sq. units
2.31 / 7sq. units
3.32 / 3 sq. units
4.34 / 3 sq. units
The area bounded by the curves y = x4 - 2x3 + x2 - 3, the x-axis and the two ordinates corresponding to the points of minimum of this Function is
1.91 / 15
2.91 / 30
3.19 / 30
4.None of these
The area bounded by the curves y = |x| - 1 and y = - |x| + 1 is
1.1
2.2
3.2 v2
4.4
The area of the triangle formed by the tangent and the normal to the parabola y2 = 4ax, both drawn at the same end of the latus rectum and the axis of the parabola is
1.2 v2a2
2.2a2
3.4a2
4.None of these
The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2 = 9 is
1.(3 / 2 , 1 / 2)
2. (1 / 2 , 3 / 2)
3. (1 / 2 , 1 / 2)
4. (1 / 2 , -2½)
The coordinates of foot of the perpendicular drawn from the point (2, 4) on the line x + y = 1 are
1.(1 / 2 , 3 / 2)
2.(-1 / 2 , 3 / 2)
3.(3 / 2 , -1 / 2)
4. (-1 / 2 , -3 / 2)
The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is
1.7 / 2
2. 7 / 3
3.7 / 5
4.7 / 10
The eccentricity of the eclipse 16x2 + 7y2 = 112 is
1.4/3
2.7/16
3.3 / 17
4.3 / 4
The line y = mx + 1 is a tangent to the parabola y2 = 4x if
1. m = 1
2.m = 2
3.m = 3
4.m = 4
The Range of the function f(x) = (x - 2) / (2 - x) is
1.R
2.R "“ {1}
3.(-1)
4. R "“ {-1}
The roots of the quadratic equation ax2 + bx + c = 0. will be reciprocal to each other if
1.a = 1/b
2. a = c
3.b = ac
4.a = b
The set of all integers x such that |x “ 3| < 2 is equal to
1.{1, 2, 3, 4, 5}
2.{1, 2, 3, 4}
3.{2, 3, 4}
4.{-4, -3, -2}
The shadow of a tower of height (1 + v3) metre standing on the ground is found to be 2 metre longer when the sun's elevation is 300, then when the sun's elevation was
1.300
2.450
3.600
4.750
The sixth term of a HP is 1/61 and the 10th term is 1/105. The first term of the H.P. is
1.1/39
2.1/28
3.1/17
4.1/6
The straight lines x + y “ 4 = 0, 3x + y “ 4 = 0, x + 3y “ 4 = 0 form a traigle which is
1. isosceles
2.right angled
3.equilateral
4.None of these
The value of (i)i is
1.e
2.e^2
3.e-p/2
4.2v2
Three lines 3x + 4y + 6 = 0, 2x 3y 2 2 0 + + = and 4x 7y 8 0 + + = are
1.Parallel
2.Sides of a triangles
3.Concurrent
4.None of these
Two dices are thrown simultaneously. What is the probability that the sum of the two number is 10 or the product of two numbers is >= 25 or both?
1.5/27
2.4/27
3.5/36
4.None of these
Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial salary of Rs. 200 with a rise of Rs. 15 every 6 months. Assume that the arrangements remained unaltered till December 31, 1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period?
1. Rs. 93,300
2.Rs. 93,200
3. Rs. 93,100
4.None of these
Two squares are chosen on a chessboard at random. What is the probability that they have a side in common?
1.1/18
2.64/4032
3.63/64
4.1/9
Value of is
1.-1 / 2
2.1 / 2
3.v3 / 2
4.None of these
What is the approx. value of W, if W=(1.5)11, Given log2 = 0.301, log3 = 0.477.
1.85
2.86
3.84
4.89