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A man undertakes to do a work in 150 days. He employs 200 men. He finds that only a quarter of the work is done in 50 days. How many additional men should he employ so that the whole work is finished in time?
A train moving with a speed of 60 km per hour crosses an electric pole in 30 seconds. What is the length of train in meters?
Rs. 120 is distributed among A, B and C so that A’s share is Rs. 20 more than B’s and Rs. 20 less than C’s. What is the B’s share?
In the following table of inverse variations, what are the values of A, B and C respectively?
A person borrows Rs. 5000 at 5% rate of interest per annum and immediately lent it at 5.5%. After two years he collected the amount and settled his loan. What is the amount gained by him this transaction?
At present the average of the ages of a father and a son is 25 years. After seven years, the son will be 17 years old. What will be the age of father after 10 years?
If 5 tractors can plough 5 hectares of land in 5 days, then what is the number of tractor required to plough 100 hectares in 50 days?
A merchant commences with a certain capital and gains annually at the rate of 25%. At the end of 3 years he has Rs. 10,000. What is the original amount that the merchant invested?
Which of the following decimal number is a rational number with denominator 37?
The annual income of a person decreases by Rs. 64 if the rate of interest decreases from 4% to 3.75%. What is his original annual income?
For 0 < m < 1, which one the following is correct?
A gentleman left a sum of Rs. 39000 to be distributed among his widow, 5 sons and 4 daughters. If each son receives three times as much as a daughter receives, and each daughter receives twice as much as their mother receives, then what is the widow’s share?
Three numbers which are coprime to each other, are such that the product of the first two 286 and that of the last two is 770. What is the sum of three terms?
The age of a woman is twodigit integer. On reversing this integer, the new integer is the age of her husband who is elder to her. The difference between their ages is one eleventh of their sum. What is the difference between their ages?
A passenger train and a goods train are running in the same direction on parallel railway tracks. If the passenger train now takes three times as long to pass the goods train, as when they are running in the opposite directions, then what is the ratio of the speed of the passenger train to that of the goods train?
All odd prime numbers up to 110 are multiplied together. What is the unit digit in this product?
An alloy A contains two elements, copper and tin in the ratio of 2 : 3, whereas an alloy B contains the same elements in the ratio of 3 : 4. If 20 kg of alloy A, 28 kg of alloy B and some more pure copper are mixed to form a third alloy C which now contains copper and tin in the ratio of 6 : 7, then what is the quantity of the pure copper mixed in the alloy C?
A quadratic polynomial ax^{2} + bx + c = 0 is such that when it is divided by x, (x  1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)?
If the average of 9 consecutive positive integers is 55, then what is the largest integer?
The average of the ages of 15 students in a class is 19 years. When 5 new students are admitted to the class, the average age of the class becomes 18.5 years. What is the average age of the 5 newly admitted students?
A water tank has been fitted with two taps P and Q and a drain pipe R. Taps P and Q fill at the rate of 12 litres per minute and 10 litres per minute respectively.
Consider the following statements S1, S2 and S3:
S1: Pipe R drains out at the rate of 6 litres per minute
S2: If both the taps and the drain pipe are opened simultaneously, then the tank is filled in 5 hours 45 minutes
S3: Pipe R drains out (fully) the filled tank in 15 hours 20 minutes.
To know what is the capacity of the tank, which one the following is correct?
A man can row at a speed of x km/h in still water. If in a stream which is flowing at a speed of y km/h it takes him z hours to row to a place and back, then what is the distance between the two places?
A car has an average speed of 60 km per hour while going from Delhi to Agra and has an average speed of y km per hour while returning to Delhi from Agra (by travelling the same distance). If the average speed of the car for the whole journey is 48 km per hour, what is the value of y?
An article is sold at a profit of 32%. If the cost price is increased by 20% and the sale price remains the same, then the profit percentage becomes
A, B, C, D and E start a partnership firm. Capital contributed by A is three times that contributed by D. E contributes half of A’s contribution, B contributes one third of E’s contribution and C contributes two third of A’s contribution. If the difference between the combined shares of A, D and E and the combined shares of B and C in the total profit of the firm is Rs. 13500, what is the combined share of B, C and E? (The shares are supposed to be proportional to the contributions)
5^{17} + 5^{18} + 5^{19} + 5^{20} is divisible by
If a + b = 2c, then what is the value of a/(a  c) + c/(b  c)?
If x = y^{1/a}, y = z^{1/b} and z = x^{1/c} where x ≠ 1, y ≠ 1 and z ≠ 1, then what is the value of abc?
If 2b = a + c and y^{2} = xz, then what is x^{b  c} y^{c  a} z^{a  b‑} equal to?
Which one of the following is correct?
If the roots of the equation px^{2} + x + r = 0 are reciprocal to each other, then which one of the following is correct?
If 65x  33y = 97 and 33x  65y = 1, then what is xy equal to?
If b/y + z/c = 1 and c/z + x/a = 1, then what is (ab + xy)/bx equal to?
If (a^{2}  1)/a = 5, then what is the value of (a^{6}  1)/a^{3}?
If x + y + z = 0, then what is (y + z  x)^{3} + (z + x  y)^{3} + (x + y z)^{3} equal to?
If (x + 3) is a factor of x^{3} + 3x^{2} + 4x + k, then what is the value of k?
The smallest integer with 4 digits which is a perfect square is
Which one the following is a zero of the polynomial 3x^{3} + 4x^{2}  7 = 0
There are two numbers which are greater than 21 and their LCM and HCF are 3003 and 21 respectively. What is the sum of these numbers?
If α and β are the roots of the equation ax^{2} + bx + c = 0, then what is the value of the expression (α + 1) (β + 1)?
The remainder when 3x^{3} + kx^{2} + 5x  6 is divided by (x + 1) is 7. What is the value of k?
If f(x) and g(x) are polynomials of degree p and q respectively, then the degree of [f(x) ± g(x)] (if it is non zero) is
What is the value of [(√5  √3) / (√5 + √3)]  [(√5 + √3) / (√5  √3)]?
What is the value of [1/(1 + x^{b  a }+ x^{c  a}) + 1/(1 + x^{a  b }+ x^{c  b}) + 1/(1 + x^{a  c }+ x^{b  c})] where x ≠ 0?
The sum of the number and its square is 20. Then the number is
If the price of wheat rises by 25%, then by how much percentage must a man reduce his consumption in order to keep his budget the same as before?
1/25 of the students who registered did not appear for the examination, 11/20 of those who appeared passed. If number of registered students is 2000, the number who passed is
What is the difference between
If A ∶ B = 1 ∶ 2, B ∶ C = 3 ∶ 4, C ∶ D = 2 ∶ 3 and D ∶ E = 3 ∶ 4, then what is B ∶ E equal to?
A work when done by 10 women is completed in 12 days. The same work can be completed in 8 days by 5 men. How many days will it take to complete when 6 women and 3 men are employed to perform the same job?
The locus of the midpoints of the radii of length 16 cm of a circle is
The curved surface area of a right circular cone is 1.76 m^{2} and its base diameter is 140 cm. What is the height of the cone?
Consider the following statements:
1. The orthocenter of a triangle always lie inside the triangle
2. The centroid of a triangle always lie inside the triangle
3. The orthocenter of the right angled triangle lies on the triangle
4. The centroid of a right angled triangle lies on the triangle
Q. Which of the above statements are correct?
The locus of a point equidistant from two intersecting lines is
Consider the following statements:
Two triangles are said to be congruent, if
1. Three angles of one triangle are equal to corresponding three angles of the other triangle
2. Three sides of one triangle are equal to the corresponding three sides of the triangle
3. Two sides and the included angle of one triangle are equal to the corresponding two sides and the included of the other triangle
4. Two angles and the included side of one triangle are equal to the corresponding two angles and the included sides of other triangle
Q. Which of the above statements are correct?
Given that the angles of a polygon are all equal and each angle is a right angle.
Statement 1: The polygon has exactly four sides
Statement 2: The sum of the angles of a polygon having n sides is (3n  8) right angles.
Q. Which one of the following is correct in respect of the above statements?
If the length of a side of a square increased by 8 cm, its area increased by 120 square cm. What is the length of a side of the square?
What is the largest power of 10 that divides the product 1 × 2 × 3 × 4⋯ × 23 × 24 × 25?
Walls (excluding their roofs and floors) of 5 identical rooms having length, breadth and height 6m, 4 m and 2.5 m respectively are to be painted. Paints are available only in cans of 1 L and one litre of paint can be used for painting 20 square metres. What is the number of cans required for painting?
A rectangular pathway having width 4.5 m and length 10 m will have to be tiled using square tiles of side 50 cm. Each packet of such tiles contains 20 pieces and costs Rs. 100. What will be the total cost of tiles for the pathway?
A cube of maximum value (each corner touching the surface from inside) is cut from a sphere. What is the ratio of volume of the cube to that of the sphere?
If the ratio of the circumference of the base of a right circular cone of radius r to its height is 3 : 1, then what is the area of the curved surface of the cone?
A wire is in the form of a circle of radius 98 cm. A square is formed out of the wire. What is the length of a side of the square? (Use π = 22/7)
Directions: Consider the following:
In a triangle ABC, a, b and c are the lengths of the sides and p, q and r are the lengths of its medians.
Q. Which one of the following is correct?
In a triangle ABC, a, b and c are the lengths of the sides and p, q and r are the lengths of its medians.
Q. Which of the following is correct?
What is the area of the largest circular disc cut from a square of side 2/√π units?
The product of the lengths of the diagonals of a square is 50 square units. What is the length of a side of the square?
The surface area of a closed cylindrical box is 352 square cm. If its height is 10cm, then what is its diameter? (Use π = 22/7)
A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?
What is the area of the region bounded internally by a square of side of length ‘a’ and externally by a circle passing through the four corners of the square?
In the figure given below, XA and XB are two tangents to a circle. If ∠AXB = 50° and AC is parallel to XB, then what is ∠ ACB equal to?
In the figure given below, p, q, r are parallel lines; l and m are two transversals.
Consider the following:
1. AB : AC = DE : DF
2. AB × EF = BC × DE
Q. Which of the above is/are correct?
In the equilateral triangle ABC given below, AD = DB and AD = EC. If l is the length of a side of the triangle, then what is the area of the shaded region?
In the figure given below, SPT is a tangent to the circle at P and O is the centre of the circle. If ∠QPT = α, then what is ∠ POQ equal to?
In the figure given below, two equal chords cut at point P. If AB = CD = 10 cm, OC = 13 cm (O is the centre of the circle) and PB = 3 cm, then what is the length of OP?
A pie chart is drawn for the following data:
Q. What is the angle (approximately) subtended by the social services sector at the centre of the circle?
The arithmetic mean of two numbers is 10 and their geometric mean is 8. What are the two numbers?
The arithmetic mean of 11 observations is 11. The arithmetic mean of the first 6 observations is 10.5 and the arithmetic mean of the last 6 observations is 11.5. What is the sixth observation?
What is sin^{4}θ  cos^{4}θ equal to for any real number θ?
What is cot 1° cot 23° cot 45° cot 67° cot 89° equal to?
What angle does the hour hand of a clock describe in 10 minutes of time?
Consider the following statements:
1. (sec^{2} θ  1) (1  cosec^{2} θ) = 1
2. sin θ (1 + cos θ)^{1} + (1 + cos θ) (sin θ)^{1} = 2 cosec θ
Q. Which of the above is/are correct?
Each side of a square subtends an angle of 60° at the tip of a tower of height h meters standing at the centre of the square. If l is the length of each side of the square, then what is h^{2} equal to?
From a height of h units, a man observes the angle of elevation as α and angle of depression as β of the top and bottom respectively of a tower of height H (> 4h). To what further height should be climb so that the values of angle of elevation and angle of depression get interchanged for the top and bottom of the tower?
If sec x cosec x = 2, then what is the tan^{n}x + cot^{n}x equal to?
If cos x + cos^{2} x = 1, then what is sin^{2} x + sin^{4} x equal to?
If sin A + cos A = p and sin^{3}A + cos^{3}A = q, then which one of the following is correct?
If x = (sec^{2} θ – tan θ) / (sec^{2} θ + tan θ), then which one of the following is correct?
ABC is a right angles triangle with base BC and height AB. The hypotenuse AC is four times the length of the perpendicular drawn to it from opposite vertex. What is tan C equal to?
ABC is a triangle right angled at C with BC = a and AC = b. If p is the length of the perpendicular from C on AB, then which one of the following is correct?
The radius and slant height of a right circular cone are 5 cm and 13 cm respectively. What is the volume of the cone?
Two equal circular region of greatest possible area are cut off from a given circular sheet of area A. What is the remaining area of the sheet?
If the ratio of the radius of the base of a right circular cone to its slant height is 1∶ 3, what is the ratio of the total surface area to the curved surface area?
A right circular cone is sliced into a smaller cone and a frustum of a cone by a plane perpendicular to its axis. The volume of the smaller cone and the frustum of the cone are in the ratio 64 ∶ 61. Then their curved surface areas are in the ratio
There are as many square centimeters in the surface area of a sphere as there are cube centimeters in its volume. What is the radius of the sphere?
The radii of two circles are 4.5cm and 3.5 cm respectively. The distance between the centres of the circles is 10 cm. What is the length of the transverse common tangent?
What is the volume of a cone of maximum volume cut out from a cube of edge 2a such that their bases are on the same plane?
A region of area A bounded by a circle C is divided into n regions, each of area A/n, by drawing circles of radii r_{1}, r_{2}, r_{3}, ⋯ , r_{n1} such that r < r_{2} < r_{3} < ⋯ r_{n1} concentric with the circle C. If p_{m} = r_{m+1} /r_{m}, then which one of the following is correct?
In a room whose floor is a square of side 10 m, an equilateral triangular table of side 2 m is placed. Four book shelves of size 4 m × 1 m × 9 m are also placed in the room. If the half of the rest of the area in the room is to be carpeted at the rate of Rs 100 per square meter, what is the cost of carpeting (approximately)?
The length of a line segment AB is 2 cm. It is divided into two parts at a point C such that AC^{2} = AB × CB. What is the length of CB?
23 docs33 tests

23 docs33 tests
