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Study the given pie charts and answer the question that follows.
Total number of students appeared = 1200
Total number of students passed = 900
Which institute has the second highest percentage of students who passed to the students who appeared from that instinne?
The radius of a solid right circular cone is 36 cm and its height is 105 cm. The total surface area (in cm$$^2$$) of the cone is:
Study the given graph and answer the question that follows.
The total production of fertilisers by country Y in 2017 and 2019 and by country X in 2016 is what percentage of the total production of fertilisers by country Z in 2016. 2018 and 2020?
What is the difference (in ₹) between the interests on ₹50,000 for one year at 8% per annum
compounded half yearly and yearly?
In $$\triangle$$ABC , M is the midpoint of the side AB. N is a point in the iterior of $$\triangle$$ABC such that CN is the bisector of $$\angle$$C and CN $$\perp$$ NB . What is the length (in cm) of MN , if BC= 10 cm and AC= 15 cm?
If $$3\tan\theta=2\sqrt{3}\sin\theta$$, $$0^{\circ} <\theta <90^{\circ}$$, then the value of $$\frac{\csc^{2} 2\theta+\cot^{2} 2\theta}{\sin^{2}\theta+\tan^{2}2\theta}$$ is:
O is a point in the interior of $$\triangle$$ABC such that OA = 12 cm,OC = 9 cm,$$\angle$$AOB = $$\angle$$BOC = $$\angle$$COA and $$\angle$$ABC = 60°. What is the length (in cm) of OB?
An article is sold at a certain price. If it is sold at $$33\frac{1}{3} \%$$ of this price, there is a loss of $$33\frac{1}{3}\%$$. What is the percentage profit if the article is sold at 80% of its original selling price?
The value of $$\frac{3\left(\cot^{2}47^{\circ} - \sec^{2}43^{\circ}\right) - 2\left(\tan^{2}23^{\circ} - \cosec^{2}67^{\circ}\right)}{\cosec^{2}\left(68^{\circ} + \theta\right) - \tan\left(\theta + 61^{\circ}\right) - \tan^{2}\left(22^{\circ} - \theta\right) + \cot\left(29^{\circ} - \theta\right)}$$ is:
When the price of an item was reduced by 20%, its sale increased by $$x$$% . If there is an increase of 25% in receipt of the revenue, then the value of $$x$$ is:
What is the area (in unit squares) of the region enclosed by the graphs of the equations $$2x-3y+6=0$$, $$4x+y=16$$ and $$y=0$$
The slant height and radius of right circular cone are in the ratio 29 : 20. If its volume is 4838.4 $$\pi$$ $$cm^{3}$$, then its radius is:
If the selling price of 7 articles is equal to the cost price of 8 articles, then what is the profit percentage (correct to one decimal place)?
The value of $$0.4\overline{6}+0.7\overline{23}+0.3\overline{9}\times0.\overline{7}$$ is:
In an examination, average marks of a student per paper were 71. If he would have obtained 35 more marks in sciences; 11 more marks in history and 4 more marks in computer science, his average marks per paper would have been 76. How many papers were there in the examination?
In $$\triangle$$PQR , S is a point on the side QR such that $$\angle QPS = \frac{1}{2}\angle PSR$$, $$\angle QPR =78^{\circ}$$ and $$\angle PRS = 44^{\circ}$$. What is the measure of $$\angle$$PSQ?
The value of $$\left(1\frac{1}{3}\div2\frac{6}{7} of 5\frac{3}{5}\right)\times\left(6\frac{2}{5}\div4\frac{1}{2} of 5\frac{1}{3}\right)\div\left(\frac{3}{4}\times2\frac{2}{3}\div\frac{5}{9} of 1\frac{1}{5}\right)$$= k, where k lies between.
If $$2x-y = 2$$ and $$xy=\frac{3}{2}$$, then what is the value of $$x^{3}-\frac{y^{3}}{8}$$?
The income of A is $$\frac{2}{3}$$ of B's income and the expenditure of A is $$\frac{3}{4}$$ of B's expenditure. If $$\frac{1}{3}$$ of the income of B is equal to the expenditure of A, then the ratio of the savings of A to those of B is:
G is the centroid of a triangle ABC, whose sides AB= 35 cm. BC= 12 cm, and AC= 37 cm. The length of BG is (correct to one decimal place):
A covered a distance of 240 km at a certain speed. Had his speed been 8 km/h less, then the time taken would have been one hour more for covering the same distance. How much time (in hours) will he take to cover a distance of 480 km at his original speed?
If $$1 + 2\tan^{2}\theta+2\sin\theta\sec^{2}\theta=\frac{a}{b},0^\circ < \theta < 90^\circ$$, then $$\frac{a+b}{a-b}=$$?
A sum of money becomes ₹11,880 after 4 years and ₹17,820 after 6 years on compound interest, if the interest is compounded annually. What is the half of the sum (in ₹)?
The radius of a spherical balloon is inflated from 3.5 cm to 4.9 cm by pushing air into it. What is the percentage increase in the volume of the original balloon?
The numbers of students in section A and section B of a class are 50 and 62, respectively. The average score in mathematics of all the students is 75. If the average score of students in section A is 20% more than that of students in section B, then what is the average score of students in section A (correct to one decimal place)?
If the sum of 40% of a number and 30% of the same number is 70, then the number is:
A solid metallic cuboid of dimensions 12 cm $$\times$$ 54 cm $$\times$$ 72 cm is melted and converted into 8 cubes of the same size. What is the sum of the lateral surface areas (in $$cm^{2}$$) of 2 such cubes?
ABCD is a quadrilateral in which AB $$\parallel$$ DC. E and F are the midpoints of the diagonals AC and BD, respectively. If AB = 18 cm and CD = 6 cm, EF = ?
A sum of ₹46,800 is divided among A, B, C and D in such a way that the ratio of the combined share of A and D to the combined share of B and C is 8 : 5. The ratio of the share of B to that of C is 5 : 4. A receives ₹18,400. If x is the difference between the shares of A and B and y is the difference between the shares of C and D, then what is the value of (x - y) (in ₹)?
A person marks an article 36% above the cost price and offers 30% discount on the marked price.
What is the loss or gain percentage?
A loan is to be returned in two equal yearly instalments. If the rate of interest is 10% p.a. compounded annually and each instalment is ₹5,808. then 60% of the total interest (nearest to a ₹) charged in this scheme is:
The curved surface area and the volume of a cylindrical objet are 88 $$cm^{2}$$ and 132 $$cm^{3}$$, respectively. The height (in cm) of the cylindrical objet is:
(Take $$\pi=\frac{22}{7}$$)
In $$\triangle$$LMN , $$LM = 5\sqrt{2}$$ cm, LN = 13 cm and $$\angle LMN = 135^\circ$$. What is the lenth (in m) of MN?
Study the given graph and answer the question that follows.
What is the ratio of the total production of fertilisers by country X in 2017 and country Y in 2020 to the production of fertilisers by country Z in 2019?
S and T are points on the sides PQ and PR . respectively, of $$\triangle$$PQR such that PS $$\times$$ PR = PQ $$\times$$ PT . If $$\angle Q = 96^\circ$$ and $$ \angle PST = \angle PRQ + 34^{\circ}$$, then $$\angle$$QPR = ?
In 6 minutes, $$\frac{4}{13}$$ of a bucket ia filled. How much time will it take to the remaining bucket?
$$\left(\frac{\tan^{3}\theta}{\sec^{2}\theta}+\frac{\cot^{3}\theta}{\csc^{2}\theta}+2\sin\theta\cos\theta\right)\div\left(1+\csc^{2}\theta+\tan^{2}\theta\right), 0^\circ < \theta < 90^\circ$$, is equal to:
If the sum of two positive numbers is 65 and the square root of their product is 26, then the sum of their reciprocals is:
The ratio of the distance between two places A and B to the distance between places B and C is 3 : 5. A man travels from A to B at a speed of x km/h and from B to C at a speed of 50 km/h. If his average speed for the entire journey is 40 km/h, then what is the value of (x - 10) : (x + 1 )?
A and B can do a work in $$26\frac{2}{3}$$ days. Band C together can complete the same work in 48 days, while A and C together can complete the same work in 30 days. How long (in days) will A alone take to complete 60% of the work?
The sum of the interior angles of a regular polygon A is 1260 degrees and each interior angle of a regular polygon B is $$128\frac{4}{7}$$ degrees. The sum of the number of sides of polygons A and B is:
Eight years ago, the ratio of ages of A and B was 5 : 4. The ratio of their present ages is 6 : 5. What will be the sum (in years) of the ages of A and B after 7 years from now?
The base of a right prism is a triangle with sides 16 cm, 30 cm and 34 cm. Its height is 32 cm. The lateral surface area (in $$cm^{2}$$) and the volume (in $$cm^{3}$$) are, respectively:
The graphs of the equations
$$4x+\frac{1}{3}y=\frac{8}{3}$$ and $$\frac{1}{2}x+\frac{3}{4}y+\frac{5}{2} = 0$$ intersect at a point P. The point P also lies on the graph of the equation:
A saves 35% of his income. If his income increases by 20.1% and his expenditure increases by 20%, then by what percentage do his savings increase or decrease? (correct to one decimal place)
The value of $$\left(2\frac{6}{7} of 4\frac{1}{5}\div\frac{2}{3}\right)\times5\frac{1}{9}\div\left(\frac{3}{4}\times2\frac{2}{3} of \frac{1}{2}\div\frac{1}{4}\right)$$ is:
Let x = $$\left(433\right)^{24}-\left(377\right)^{38}+\left(166\right)^{54}$$. What is the units digit of x?
If 7 $$\sin^{2}\theta + 4 \cos^{2}\theta = 5$$ and $$\theta$$ lies in the first quadrant, then what is the value of $$\frac{\sqrt{3}\sec\theta+\tan\theta}{\sqrt{2}\cot\theta-\sqrt{3}\cos\theta}$$?
The surface area of a sphere is 221.76 $$cm^{2}$$• Its volume (in $$cm^{3}$$ ) is (correct to one decimal place):
(Take $$\pi=\frac{22}{7}$$)
If $$2x^{2}+5x+1=0$$, then one of the values of $$x - \frac{1}{2x}$$ is:
If an article is sold for ₹355, there is a loss of 29%. At what price (in ₹) should it be sold to gain 31% of profit?
One cup has juice and water in the ratio 5 : 2, while another cup of the same capacity has them in the ratio 7 : 4, respectively. If contents of both the cups (when full) are poured in a vessel, then what will be the final ratio of water to juice in the vessel?
Study the given histogram and answer the question that follows.
The number of persons weighing 55 kg or more but less than 75 kg is what percentage more than the number of persons weighing 80 kg or more but less than 100 kg (correct to one decimal place)?
In $$\triangle$$ABC, O is the point of intersection of the bisectors of $$\angle$$ B and $$\angle$$A. If $$\angle BOC = 108^\circ$$, then $$\angle$$ BAO = ?
If $$847\times385\times675\times3025 = 3^{a}\times5^{b}\times7^{c}\times11^{d}$$ , then the value of ab-cd is:
The income of A is 80% of B's income and the expenditure of A is 60% of B's expenditure. If the income of A is equal to 90% of B's expenditure, then by what percentage are the savings of A more than B's savings?
A student goes to school at a speed of $$5\frac{1}{2}$$ km/h and returns at a speed of 4 km/h. If he takes $$4\frac{3}{4}$$ hours for the entire journey, then the total distance covered by the student (in km) is:
Study the given pie charts and answer the quesrion that follows.
Total number of students appeared = 1200
Total number of students passed = 900
The number of students who passed the examination from institute C is what percentage of the total number of students who appeared from institutes D and E?
AB and CD are two chords in a circle with centre O and AD is a diameter. AB and CD produced meet at a point P outside the circle. If $$\angle APD = 25^{\circ}$$ and $$\angle DAP = 39^\circ$$, then the measure of $$\angle$$ CBD is:
4 men and 5 women can complete a work in 15 days, whereas 9 men and 6 women can complete it in 1O days. To complete the same work in 7 days, how many women should assist 4 men?
If a $$+$$ b $$+$$ c $$=$$ 1 , ab $$+$$ bc $$+$$ ca $$=$$ $$-22$$ and abc $$=$$ $$-40$$ , then what is the value of $$a^{3} + b^{3} + c^{3}$$ ?
The base of right pyramid is an equilateral triangle, each side of which is 20 cm . Each slant edge is 30 cm . The vertical height (in cm ) of the pyramid is:
If the amount obtained by A by investing ₹9,100 for three years at a rate of 10% p.a. on simple interest is equal to the amount obtained by B by investing a certain sum of money for five years at a rate of 8% p.a. on simple interest, then 90% of the sum invested by B (in ₹) is:
The volume of a solid cylinder is 2002 $$cm^{3}$$ and its height is 13 cm. What is the area (in $$cm^{2}$$) of its base?
(Take $$\pi=\frac{22}{7}$$)
If $$\triangle$$ABC , $$\angle B = 78^\circ$$ , AD is a bisector of $$\angle$$ A meeting BC at D. and AE $$\perp$$ BC at E . If $$\angle DAE = 24^\circ$$, then the measure of $$\angle$$ ACB is:
The ratio of the incomes of A and B in the last year was 4 : 3. The ratios of their individual incomes in the last year and the present year are 3 : 4 and 5 : 6, respectively. If their total income in the present year is ₹24.12 lakhs, then the sum of the income (in ₹ lakhs) of A in the last year and that of B in the present year is:
An article was sold for ₹716 after offering a discount of 10.5%. If a discount of 6.5% is given, then for how much (in ₹) should it be sold?
Let $$0^\circ < \theta < 90^\circ . \left(1+\cot^{2}\theta\right) \left(1+\tan^{2}\theta\right) \times \left(\sin\theta - \csc\theta\right)\left(\cos\theta -\sec\theta\right)$$ is equal to:
The volume of a solid hemisphere is 19,404 $$cm^{3}$$ . Its total surface area (in $$cm^{2}$$) is:
(Take $$\pi=\frac{22}{7}$$)
Study the given graph and answer the question that follows.
The average production of fertilisers by country Z in 2017, 2018 and 2020 is what percentage more than the average production of fertilisers by country X in 2018 and 2020?
If a, b and c are positive numbers such that $$\left(a^{2}+b^{2}\right):\left(b^{2}+c^{2}\right):\left(c^{2}+a^{2}\right)=34:61:45$$, then b$$-$$a : c$$-$$b : c$$-$$a =_______.
Study the given pie charts and answer the question that follows.
Total number of students appeared = 1200
Total number of students passed = 900
The number of students who passed the examination from institute D exceeds the number of students who appeared from institute A is x. The value of x lies between:
A trader gains 25% by selling an article with 20% discount on its marked price. If the cost price of the article increases by 30%, then how much discount (in %) should he offer on the same marked price to gain 15% of profit?
A discount of 10% is offered on the price of an article if the payment is made online. An additional discount of 5% is given to credit card holders. A person wishes to buy a watch priced at ₹60,000 by paying online through credit card. How much does he need to pay (in ₹)?
$$\frac{\left(1+\sec\theta\csc\theta\right)^{2}\left(\sec\theta-\tan\theta\right)^{2}\left(1+\sin\theta\right)}{\left(\sin\theta\sec\theta\right)^{2}+\left(\cos\theta\csc\theta\right)^{2}}, 0^\circ < \theta < 90^\circ$$ is equal to:
Alloy A contains metals x and y only in the ratio 5 : 2, while alloy B contains them in the ratio 3 : 4. Alloy C is prepared by mixing alloys A and B in the ratio 4 : 5. The percentage of x in alloy C is:
If a 10-digit number 75462A97B6 is divisible by 72, then the value of
$$\sqrt{8A - 4B}$$ is:
A, B and C invested their capitals in the ratio 2 : 3 : 5. The ratio of months for which they invested is 4 : 2 : 3, respectively. If the difference between the profit shares of A and B is ₹1,86,000, then C's share of profit (in ₹) is:
The valu of $$\frac{1}{4}+\frac{\left[\left(20.35\right)^{2}-\left(8.35\right)^{2}\right]\times0.0175}{\left(1.05\right)^{2}+\left(1.05\right)\left(27.65\right)}$$ is:
A started a business with a capital of ₹54,000 and admitted B and C after 4 months and 6 months, respectively. At the end of the year, the profit was divided among the three in the ratio 1 : 4 : 5. What is the sum (in ₹) of the capitals invested by B and C?
$$\frac{1+\cos\theta-\sin^{2}\theta}{\sin\theta\left(1+\cos\theta\right)}\times\frac{\sqrt{\sec^{2}\theta+\csc^{2}\theta}}{\tan\theta+\cot\theta}, 0^\circ < \theta < 90^\circ$$ is equal to:
If a + b = 8, ab = 10, then the value of $$a^{3}+b^{3}$$ is:
If $$x=\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}$$, then the value of $$\frac{\sqrt{3}-x}{\sqrt{3}+x}$$ (corrected to two decimal place) is:
A circle is inscribed in $$\triangle$$ PQR touching the sides QR, PR and PQ at the points S , U and T, respectively. PQ = (QR + 5) cm, PQ = (PR + 2) cm . If the perimeter of $$\triangle$$ PQR is 32 cm ,then PR is equal to:
Let x=$$\frac{5\frac{3}{4}-\frac{3}{7}\times15\frac{3}{4}+2\frac{2}{35}\div1\frac{11}{25}}{\frac{3}{4}\div5\frac{1}{4}+5\frac{3}{5}\div3\frac{4}{15}}$$. When y is added to x, the result is $$\frac{7}{13}$$. What is the value of y?
The value of $$\frac{1}{4-\sqrt{15}}-\frac{1}{\sqrt{15}-\sqrt{14}}+\frac{1}{\sqrt{14}-\sqrt{13}}-\frac{1}{\sqrt{13}-\sqrt{12}}+\frac{1}{\sqrt{12}-\sqrt{11}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{10}-3}-\frac{1}{3-\sqrt{3}}$$
If $$\sin A=\frac{5}{13}$$ and 7 $$\cot$$ B = 24 , then the value of $$\left(\sec A \cos B\right) \left(\csc B \tan A\right)$$ is:
The sum of and different between the LCM and HCF of two numbers are 512 and 496, respectively. If one number is 72, then the other number is:
The angle of elevation of the top of a tower 25 $$\sqrt{3}$$ m high from two points on the level ground on its opposite sides are $$4545^{\circ}$$ and $$60^{\circ}$$. What is the distance (in m) between the two points (correct to one decimal place)?
ABCD is a cyclic quadrilateral and BC is a diameter of the circle. If $$\angle DBC = 29^{\circ}$$ , then $$\angle$$ BAD = ?
Three fractions x, y and z are such rhat x > y > z. When the smallest of them is divided by the greatest, the result is $$\frac{9}{16}$$, which exceeds y by 0.0625 . If x+y+z=$$2\frac{3}{12}$$, then what is the value of x+z?
If $$x^{2}-\sqrt{7}x+1=0$$, then what is the value of $$x^{5}+\frac{1}{x^{5}}$$?
The total surface area of a cylinder is 4092 $$cm^{2}$$ and the diameter of its base is 21 cm. What is 50% volume (in $$cm^{3}$$) of the cylinder ( nearest to an integer)
The value of $$\frac{4 \tan^{2}30^{\circ}+\sin^{2}30^{\circ}\cos^{2}45^{\circ}+\sec^{2}48^{\circ}-\cot^{2}42^{\circ}}{\cos37^{\circ}\sin53^{\circ}+\sin37^{\circ}\cos53^{\circ}+\tan18^{\circ}\tan72^{\circ}}$$ is?
The radius of the base of a cylindrical tank is 4 m. If three times the sum of the areas of its two circular faces is twice the area of its curved surface, then the capacity (in kilolitres) of the tank is:
If $$\frac{22\sqrt{2}}{4\sqrt{2} - \sqrt{3 + \sqrt{5}}} = a + \sqrt{5}b$$, with a, b > 0, then what is the value of $$(ab):(a + b)?$$
Two pipes A and B can fill a cistern in $$12\frac{1}{2}$$ hours and 25 hours, respectively. The pipes were opened simultaneously, and it was found that, due to leakage in the bottom, it took one hour 40 minutes more to fill the cistern. If the cistern is full, in how much time (in hours) will the leak alone empty 70% of the cistern?
In $$\triangle ABC, \angle A = 66^\circ$$ and $$\angle B = 50^\circ$$. If the bisectors of $$\angle B$$ and $$\angle C$$ meet at P, then $$\angle BPC - \angle PCA = ?$$
A tap can fill a tank in $$5\frac{1}{2}$$ hours. Because of a leak, it took $$8\frac{1}{4}$$ hours to fill the tank. In how much time (in hours) will the leak alone empty 30% of the tank?
The monthly expenses of a person are $$66\frac{2}{3}\%$$ more than her monthly savings. If her monthly income increases by 44% and her monthly expenses increase by 60%, then there is an increase of ₹1,040 in her monthly savings. What is the initial expendirure (in ₹)?
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