What is the value of $$3 \sin^2 30^\circ + \frac{3}{5} \cos^2 60^\circ - 2 \sec^2 45^\circ$$?
SSC CGL Tier-2 8th August 2022 Maths
For the following questions answer them individually
An article is sold at 25 percent loss. If its cost price is doubled and selling price is increased by ₹ 660, then there is a profit of 20 percent. What is the original cost price of the article?
Sum ₹ 20000 and ₹ 40000 are given on simple interest at the rate of 10 percent and 15 percent per annum respectively for three years. What will be the total simple interest?
The bar chart given below shows the discount percentage offered by a shopkeeper on seven articles. Selling price of these seven articles : A1, A2, A3, A4, A5, A6 and A7 is Rs. ₹ 420, ₹ 600, ₹ 816, ₹ 825, ₹ 425, ₹ 800 and ₹ 840.
Selling price - Marked price $$\left[1 - \frac{Discount \ percent}{100}\right]$$
What is the sum of the marked price of these seven articles?
How many composite numbers are there from 53 to 97?
What is the value of $$99\frac{11}{99}+99\frac{13}{99}+99\frac{15}{99}+......+99\frac{67}{99}$$?
Which fraction among the following is the least?
$$\frac{5}{11}, \frac{7}{12}, \frac{8}{13}, \frac{9}{17}$$
The graph of the equation $$x = a (a \neq 0)$$ is a ______________.
The radius of a solid sphere is 42 cm. It is melted to form identical small solid spheres whose radius is 7 cm. What is the number of small solid spheres obtained?
The pie chart given below shows the number of males in 6 departments. Number of males in a particular department are shown in the terms of degrees with respect to the total number of males in all the 6 departments. Number of males in department S are 1080.
J = Total number of males in T and P
K = Difference between the number of males in P and Q
What is the value of J + K?
What is the solution of the following equations ?
$$2x + 3y = 12$$ and $$3x - 2y = 5$$
If $$A = 0.3\overline{12}, B = 0.4\overline{15}$$ and $$C = 0.30\overline{9}$$, then what is the value of $$A + B + C$$?
If $$A = \frac{\sqrt{0.0004} \times \sqrt[3]{0.000008}}{\sqrt[4]{16000} \times \sqrt[3]{125000} \times \sqrt[4]{810}}$$ and $$B = \frac{\sqrt[3]{0.729} \times \sqrt[4]{0.0016}}{\sqrt{0.16}}$$, then what is $$A \times B$$?
If $$x + y = 1$$, then what is the value of $$x^3 + 3xy + y^3$$?
The height of a solid cylinder is 35 cm. The circumference of its base is 37 cm more than the radius. What will be the volume of this cylinder?
x, y and z are the sides of a triangle. If z is the largest side and $$x^2 + y^2 > z^2$$, then the triangle is a :
ABCDEF is a regular hexagon. Side of the hexagon is 36 cm. What is the area of the triangle ABC?
Two pie charts are given below. There are 6 departments in a office. Pie chart l shows the number of males in these 6 departments. Number of males in a particular department is shown as a percentage of total number of males in these 6 departments. Pie chart 2 shows the number of females in these 6 departments. umber of females in a particular department is shown as a percentage of total number of females in these 6 departments.
Difference between the number of males in B and C is 600 and difference between the number of females in D and E is 900. What is the sum of number of females in A, B, F and number of males in D, E, A?
Salary of Mohit is 60 percent more than Vijay. Salary of Vijay is how much percent less than Mohit?
The pie chart given below shows the number of tyres of 6 companies. Number of tyres of a particular company are shown as a percentage of total number of tyres of these 6 companies.
What is the sum of central angles formed by the sectors representing tyres of company F and A?
A sum of ₹ 1250 has to distributed among A, B, C and D. Total share of B and D is equal to (14/11) of total share of A and C. Share of D is half of share of A. Share of C is 1.2 of share of A. What are the shares of A, B, C and D respectively ?
A alone can do 2/5 of a work in 12 days. B is 25 percent more efficient than A. C alone can do the same work in 12 days less than B. D is 25 percent less efficient than C. If they all work together, then the work will be completed in how many days?
ABCD is a quadrilateral. The length of diagonal AC is 24 cm. The sum of perpendicular drawn from vertex B and D on the diagonal AC is 10 cm. What is the area of the quadrilateral?
Raju spends 10 percent and 20 percent of his income on transport and food respectively. He spends 30 percent of the remaining income on clothing . He saves rest of his income. If his saving is ₹ 26460, then what will be total expendinture on food and clothing together?
An article is sold for ₹ 54120 after two successive discounts of 12 percent and 18 percent. What is the marked price of the article?
Which of the following is equal to $$\left[\frac{\cos \theta}{\sin \theta} + \frac{\sin \theta}{\cos \theta}\right]$$?
A mixture of acid and water contains 20 percent acid. When 10 litres of water is added to the mixture, then the percentage of acid becomes 15 percent. What is the original quantity of mixture?
Average age of 7 students of a class is 28 years. Average age of first three students is 30 years. Age of fourth student is 4 years less than the age of fifth student. Ages of last two students is same and is 5 more than the average age of first three students. What is the average age of fourth and fifth student?
The base of a right prism is an equilateral triangle whose side is 10 cm. If height of this prism is $$10\sqrt{3}$$ cm, then what is the total surface area of prism?
If a + b = 6 and ab = 5, then what is the value of $$a^3 + b^3$$?
x, y and z are distinct prime numbers where x < y < z. If x + y + z = 70, then what is the value of z?
ABC is a right angle triangle and angle ABC = 90 degrees. BD is a perpendicular on the side AC. What is the value of $$BD^2$$?
A, B and C sianed a business with ihe investment on ₹ 100000, ₹ 140000 and ₹ 200000 respeciively. After 3 months, C left the business. 7 months after C left the business, B also left the business. B and C took their investments with them. At the end of the year, C received his share of profit as ₹ 1155. What is the total share of profits of A and B?
The cost of a diamond is directly proportional to the square of its weight.The cost of a 14 gm diamond is ₹ 2560. This diamond got broken down into two pieces in the raiio of 5 : 9. How much loss percent is incurred due to this breakage? (Correct to two decimal places)
Marked price of an a1iicle is ₹ 28000. It can be sold at one of the following ways:
Way A : A single discount of 24 percent.
Way B: Two successive discounts of 16 percent and 10 percent.
Which way , will have lowest selling price and what will be the value of it?
The bar chart given below shows the number of boys and girls in 5 schools.
If the number of boys in school S6 are 30 percent more than the number of girls in school S1, then number of girls in schools S3 and S4 is what percentage of number of boys in schools S6 and S1?(correct to two decimal places)
Which of the following is equal to $$\frac{1}{\tan \theta} + \tan \theta$$?
Price of rice is decreased by 25 percent and therefore a person can purchase 30 kg more rice in the same expenditure. If expenditure is ₹ 5400, then what was the original price of rice per kg?
If the digits of a two digit number is reversed, then the number is decreased by 36. Which of the following is correct regarding the number?
I. The difference of the digits is 4.
II. The value of number can be 84.
III. Number is always a composite number.
If xy = -6 and $$x^3 + y^3 = 19$$ (x and y are integers), then what is the value of $$\frac{1}{x^{-1}} + \frac{1}{y^{-1}}$$?
PQR is au equilateral triangle and the centroid of triangle PQR is point A. If the side of the triangle is 12 cm, then what is the length of PA?
Rohit's income is ₹ 32000. If his expenses is 30 percent of total income, then what will be the saving of Rohit?
A alone can do a work in 14 days. B alone can do the same work in 28 days. C alone can do the same work in 56 days. They start the work together and completed the work such that B was not working on last 2 days and A did not work in last 3 days. In how many days (total) was the work completed?
A can do 1/4 part of a work in 9 days. B can do 2/3 part of the same work in 28 days. Working together, in how many days can A and B complete the whole work?
What will be the simple interest on a sum of ₹ 12000 at the rate of 15 percent per annum for three years?
Two line charts are given below. Line chart shows the ratio of number of males to the number of females in two companies A and B for the 5 years. Line chart 2 shows the total number of males (both companies A and B) and total number of females (both companies A and B) for the 5 years.
What is the ratio of number of males of company B in Y1 to the total number of females of company A in Y3 and Y5?
How many numbers are there from 400 to 700 in which the digit 6 occurs exactly twice?
Which of the following is equal to $$\sec A - \cos A$$?
Vipul and Manish invested the sum of ₹ 15000 and ₹ 20000 at the rate of 20 percent p.a and 30 percent p.a. respectively on compound interest (compounding annually). If time period is 3 years for both, then what will be the total compound interest earned by Vipul and Manish?
Volume of a cuboid is 4800 cm$$^3$$. If the height of this cuboid is 20 cm, then what will be ihe area of the base of cuboid?
Ratio of monthly incomes of A and B is 4 : 5 respectively. Ratio of monthly savings of A and B is 14 : 19 respectively. If the monthly expenditure of A and B is ₹ 1200 each, then what is the difference between the monthly incomes of A and B?
An person 1.8 metre tall is $$30\sqrt{3}$$ metre away from a tower. If the angle of elevation from his eye to the top of the tower is 30 degree, then what is the height (in m)of the tower?
A, B and C staned a business with initial investments of ₹ 20000, ₹ 25000 and ₹ 10000, respectively. After 5 months from start, A invested ₹ 4000 more. After 6 months from sta1t, C invested ₹ 8000 more. After 4 months from start, B withdrew ₹ 8000. At the end of the year, they will receive a profit of ₹ 'x' . In what ratio they will shru·e the profits?
AB is the chord of a circle such that AB = 10 cm. If the diameter of the circle is 20 cm, then the angle subtended by the chord at the centre is __________
If $$\sqrt{3} \tan \theta = 3 \sin \theta$$, then what is the value of $$\sin^2 \theta - \cos^2 \theta$$?
Radius of a large solid sphere is 14 cm. If is melted to form 8 equal small solid sphere. What is the sum of total surface areas of all the 8 small solid spheres? (use $$\pi = \frac{22}{7}$$)
What is the value of $$5 \sin^2 60^\circ + 7 \sin^2 45^\circ + 8 \cos^2 45^\circ$$?
A bus covered a distance of 162 km. If speed of this bus is 15 m/s, then what will be the time taken?
Triangle BAC is similar to triangle PQR. The area of triangle BAC and triangle PQR is 25 cm$$^2$$ and 36 cm$$^2$$ respectively. If BA = 4 cm, then what is the length of PQ?
The ratio of milk to water in a 100 litres mixture is 2: 3. 10 litres of this mixture is withdrawn and replaced with milk. This process is repeated 2 more times. What is the percentage of milk in final mixture?
Two trains whose lengths are 450 metres and 300 metres are moving towards each other at the speed of 162 km/hr and 108 km/hr respectively. If distance between trains is 300 metres, then in how much time, these trains will cross each other?
What is the sum of first 20 terms of the following series?
$$1 \times 2 + 2 \times 3 + 3 \times 4 + 4 \times 5 + ...........$$
The compound interest (compounding annually) on a certain sum at the rate of 8 percent per annum for rwo years is ₹ 6656. What would be the simple interest on the same sum at the same rate of interest for two years?
The difference between the areas of two concentric circles is 264 cm$$^2$$. What is the difference between the square of their radius? (use $$\pi = \frac{22}{7}$$)
What is the difference between the average of first 148 even positive numbers and the average of first 129 odd positive numbers?
ABC is an equilateral triangle with side 12 cm. What is the length of the radius of the circle inscribed in it?
The height of a cylinder is 6 cm more ihan the radius of iis base. If its radius is 14 cm, then what will be volume of this
cylinder? (use $$\pi = \frac{22}{7}$$)
The following bar graph shows the amounts (in ₹ lakhs) invested by a company in purchasing raw materials and the values (in ₹ lakhs) of finished goods sold by the company, from 2012 to 2017.
The difference between the average amount invested in purchasing raw materials during 2012 to 2017 and the average value of sales of finished goods during the same period 2012 to 2017 is:
ABC and PQR are two triangles. AB = PQ = 6 cm, BC = QR = 10 cm and AC = PR = 8 cm. If angle ABC = x degree, then what is the value of angle PRQ?
Which of the following given value is greater than $$\sqrt[3]{12}$$.?
What is the value of $$\frac{\sqrt{29.13}}{\sqrt{1.1664}} + \frac{\sqrt{0.2916}}{\sqrt{116.64}} + \frac{\sqrt{0.0036}}{\sqrt{0.36}}$$?
If $$\left(x + \frac{1}{x}\right)^2 = 3$$, then what is the value of $$x^6 + x^{-6}$$?
What is the simplefied value of $$\frac{(x + y + z)(xy + yz + zx) - xyz}{(x + y)(y + z)(z + x)}$$?
A person sells an ru1icle for a loss of 18 percent. If he increases the selling price by ₹ 144 ru1d decreases the cost price by 30 percent, then there is profit of 20 percent. What is the original selling price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both an icles is ₹ 48640, then what is the cost price of A and B, respectively?
If $$\sin \theta = \left(\frac{9}{41}\right), 0^\circ < \theta < 90^\circ$$ then what is the value of $$\cos \theta$$?
The ratio of the three sides of the triangle are 5 : 13 : 12. What is the largest angle of the triangle?
The cost price of an anicle is ₹ 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in ₹)?
The curved surface area of a solid hemisphere is 22 cm$$^2$$. What is the total smface area of the hemisphere? (use $$\pi = \frac{22}{77}$$)
Salaries of B, C, D and E are in the ratio of 2 : 3 : 4 : 5 respectively. Their salaries are increased by 20 percent, 30 percent, 40 percent and 50 percent respectively. If the increased sala1y of D is ₹ 560, then what is the sum of the original salaries of B, C, D and E?
ABC is an isosceles right angle triangle. Angle ABC = 90 degree and AB = 12 cm. What is the ra tio of the radius of the circle inscribed in it to the radius of the circle circumscribing triangle ABC ?
A alone can do a work in 11 days. B alone can do the same work in 22 days. C alone can do the same work in 33 days.
They work in the following manner:
Day 1 : A and B work.
Day 2: B and C work.
Day 3: C and A work.
Day 4: A and B work. And so on.
In how many days will the work be completed?
What is the sum of all the common terms between the given series S1 and S2?
S1 = 2, 9, 16 ...... 632
S2 = 7, 11 15, ..... , 743
ABC is an equilateral triangle. If the area of the triangle is $$36\sqrt{3}$$ , then what is the radius of circle circumscribing the triangle ABC?
What is the value of $$\frac{3 \sin 58^\circ}{\cos 32^\circ} + \frac{3 \sin 42^\circ}{\cos 48^\circ}$$
What is the value of $$\frac{\cos 50^\circ}{\sin 40^\circ} + \frac{3 \cosec 80^\circ}{\sec 10^\circ} - 2 \cos 50^\circ.\cosec 40^\circ$$ ?
Which of the following is equal to $$\left[\frac{\tan \theta + \sec \theta - 1}{\tan \theta - \sec \theta + 1}\right]$$?
Two circles each of radius 36 cm are intersecting each other such that each circle is passing through the centre of the other circle. What is the length of common chord to the two circles?
The height of a cylinder is 45 cm. If circumference of its base is 132 cm, then what is the curved surface of this cylinder? ( use $$\pi = \frac{22}{7}$$)
The slant height ofa cone is 20 cm. If area of its base is 616 cm$$^2$$, then what is the cmv ed smface area of this cone? (use $$\pi = \frac{22}{7}$$)
The base of a prism is a right angle triangle whose sides are 9 cm, 12 cm and 15 cm. Volume of this prism is 648 cm$$^3$$. What will be the height of prism?
Three years ago, Raman's salary was ₹ 45000. His salruy is increased by 10 percent, A percent and 20 percem in first, second and third year respectively. Raman's presem salruy is ₹ 83160. What is the value of A?
What is the value of $$\frac{7}{2}+\frac{11}{3}+\frac{7}{6}+\frac{11}{15}+\frac{7}{12}+\frac{11}{35}+........+\frac{7}{156}+\frac{11}{575}$$?
Vinay and Mahesh are 250 metres aprut from each other. They are moving towrards each other with the speed of 36 km/hr and 54 km/hr respectively. In how much time will they meet each other?
Length of a train is 330 metres and it is moving at the speed of 72 km/hr. In how much time will it takes cross a platform of length 710 metres?
If $$\sqrt[3]{N}$$ lies between 6 and 7, where N is an integer then how many values N can take?
Volume of a cone whose radius of a base and height are r and h respectively, is 400 cm$$^3$$. What will be the volume of a cone whose radius of base and height are 2r cm and h cm respectively?
What is the value of $$\frac{\sqrt{7} + \sqrt{5}}{\sqrt{7} - \sqrt{5}} \div \frac{\sqrt{14} + \sqrt{10}}{\sqrt{14} - \sqrt{10}} + \frac{\sqrt{10}}{\sqrt{5}}$$?
The sum of the curved surface area and total surface area of a solid cylinder is 2068 cm$$^2$$. If radius of its base is 7 cm, then what is the volume of this cylinder? ( use $$\pi = \frac{22}{7}$$)
When an article is sold at 5 percent discount, then there is a profit of 14 percent. If the discount is 11 percent, then what will be the profit?
