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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 79651. |
\begin{array} { l } { \text { In Fig. } 6.36 , \frac { Q R } { Q S } = \frac { Q T } { P R } \text { and } \angle 1 = \angle 2 . \text { Show } } \\ { \text { In Fig. } 6.36 , \frac { Q R } { Q S } = \frac { Q T } { P R } \text { and } \angle 1 = \angle 2 . \text { Show } } \\ { \text { that } \Delta P Q S - \Delta T Q R \text { . } } \end{array} |
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Answer» Two Triangles are said to be similar if their i)corresponding angles are equal and ii)corresponding sides are proportional.(the ratio between the lengths of corresponding sides are equal) •Similarity of triangles should be expressed symbolically using correct correspondence of their vertices. SOLUTION: In ΔPQR, ∠1 = ∠2∠PQR = ∠PRQ [GIVEN]∴ PR = PQ ……………..…(1) [Sides opposite to equal angles of a triangle are also equal]Given: QR/QS = QT/PRQR/QS = QT/PQ QS/QR = PQ/QT…... …(ii) [Taking reciprocals] [From eq (i)]In ΔPQS and ΔTQR,QS/QR = PQ/QT [From eq (ii)] ∠PQS = ∠TQR [ common]∴ ΔPQS ~ ΔTQR [By SAS similarity criterion] Hence, proved |
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| 79652. |
2. A ray of light is incident on a medium with angle of incidence i' and is retracted into aversus sin r is as shown.second medium with angle of refraction r'. The graph of sÄąnFind the ratio of the velocity of light in the first medium to the velocity of light in thesecond mediumsin rsin i |
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| 79653. |
IfA .-3,-1, 0, 4, 6, 8, 10), Đ-|-4,-2, 3, 4, 5, 6, and C-(6,-4,-2, 2, 4, 6},show that Au(Bnc) (A UB)(AUC) |
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| 79654. |
16Quantitative, Data Interpretation & Dataetation & Data Sufficiency13. If 2A = 3B = 4C then A:B:C is :A 2:3:4B. 4:3:2C. 6:4:3D. 3:4:6 |
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| 79655. |
The age of Ramesh mother is four time the age of Rameshafter five years the age os mother will be thrice the age ofRamesh. Find thier ages ? |
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Answer» let the age of Ramesh mother be x,and the age of Ramesh be y. when the age of Ramesh mother is four times the age if Ramesh then,y=4x --------(1) when the age of Ramesh mother is thrice the age of Ramesh but after 5 years then,(y+5)=3(x+5)y+5 = 3x + 153x - y =5 - 153x - y = -10from equation (1) we get that 3x - (4x) = -103x - 4x = -10-x = -10x = 10therefore y = 4x = 4(10) = 40. therefore Ramesh mother age is 40 while Ramesh age is 10. |
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| 79656. |
The cost price of a refrigerator is 32,000It is purchased on credit at 12.5% compoundinterest. Find the following:a. The amount to be paid after 2 yearsb. The compound interest |
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| 79657. |
) The sum of the reciprocals of two consecutive odd natural numbers is1235Find thoseBumbers. |
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Answer» Please hit the like button if this helped you |
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| 79658. |
(1) The sum of the reciprocals of two consecutive odd natural numbers is 35 Find those12numbers(2) A box consists of 100 shirts of which 88 are good, 8 have minor defects and 4 havemajor defects. Ramesh, a shopkeeper will buy only those shirts which are good; butKewal', another shopkeeper, will not buy shirts with major defects. A shirt is takenout of the box at random. What is the probability that,(i) Ramesh will buy the selected shirt?(ii) Kewal will buy the selected shirt? |
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Answer» Ramesh will buy the shirt= probablity is 88/100 44/50 22/25so the probablity is of 22/25kewal will buy the shirt= 92/100 46/50 23/25so the probablity is 23/25 Like my answer if you find it useful! |
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| 79659. |
la) Mansi has 8 stamp albums. There are 25 stamps in each album. Her brotherVinamra has 246 stamps more than Mansi. How many stamps does Vinamrahave? |
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Answer» Total stamps of mansi= 8x25 =200Vinamra has 246 more tan mansi= 200 + 246=446 Number of stamps Mansi has = 25×8 = 200 Vinamra has 246 stamps more than Mansi. So, Number of stamps Vinamra has = 200+246 =446. |
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| 79660. |
wano 4. Manav is fond of collecting post office stamps. He hasto 879 of them. His brother Pranav has 394 stamps. Howmany stamps do they have altogether? |
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Answer» In total they both have879+3941273 stampsthanks in the total together both (879+394)=1273 Stamp's. sort note pranav mistry std 11 |
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| 79661. |
A metre of cloth costs ₹107 1/2 7 Find the cost f 2 1/5 m of cloth. |
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Answer» one meter is of 107.52 1/5=2.2 is of 2.2×107.5=236.5 |
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| 79662. |
e T 1L Db !(nH) —a=~s =+ |
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Answer» (a+b)^2=( a+b)( a+b)= a^2 + ab + ba+ b^2= = a^2 + 2ab + b^2 |
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| 79663. |
(b) Mno, + NO+H,O Basiemedium |
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| 79664. |
1l.Whatvalues of a would make the given quadri-lateral a parallelogram(a) 5(c) 5(b) 55b-4/3b + 6434(d) 539 |
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Answer» Diagonal bisect each other in a parallelogram.So 5b-4=3b+62b=10b=5Now,3b-4=2a3*5-5 =2a10=2aa=5 Wrong answer |
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| 79665. |
Rehana borrowed a sum of 10,400 to open a bookshop, at the rate of 4.5% per annum for 3Find the compound interest paid by her after 3 years. |
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| 79666. |
3.Rom is 7 years younger than Ravi's. In four years time, Ram will be half of Ravi's ago. Theof their acres now is... mer than and with a n reis |
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Answer» Let Ravi's present age be x.Ram's age = x - 7 In 4 yearsRavi's age = x + 4Ram's age = (x + 4) - 7Ram's age = (1/2) Ravi's age=> (x + 4) - 7 = (1/2)(x + 4) x - 3 = (1/2)(x + 4) 2(x - 3) = x + 4 2x - 6 = x + 4 x = 10 Ravi's age = 10 yrsRam's age = 3 yrs |
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| 79667. |
ganpat used organic fertilizer in one fifth part of his field and chemical fertilizer in one fourth part of his field in the remaining 55 acres,he use vermiculture manure find the total area of his field |
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Answer» Total area = 11/4 the part = 55 acrestotal 1 part = 55*4220acres |
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| 79668. |
Is of two consecutive odd natural numbers is . Find those1235numbers. |
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Answer» suppose two numbers are a-d and a+d1/(a-d)+1/(a+d)=12/35(a+d+a-d)/(a^2-d^2)=12/352a/(a^2-d^2)=12/35a/(a^2-d^2)=6/35so a=6 and d=1so numbers are 5 and 7 |
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| 79669. |
12(1) The sum of the reciprocals of two consecutive odd natural numbers isnumbers |
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Answer» Let the two consecutive odd natural numbers are x and x+2. As given sum of reciprocal of two consecutive odd natural number is 12/35 . Writing the statement in terms of equation: →1 /x + 1/(x+2) = 12/35 →35× (2 x +2) = 12× (x² +2 x) → 70 x + 70 = 12 x² + 24 x → [ Using Distributive property: a× (b+c) = a ×b + a× c] Taking variable and constant on one side of equation → 12 x² + 24 x - 70 x - 70 =0 → 12 x² - 46 x - 70=0 → 2 × (6 x² - 23 x -35) =0 → 6 x² - 23 x -35=0 Splitting the middle term → 6 x² - 30 x + 7 x - 35=0 → 6 x × ( x -5) + 7 × (x -5) =0 → (6 x +7)(x-5) =0 → 6 x +7 =0 ∧ x -5 =0 x ≠ can't be the solution as x is a natural number. and x = 5. So, x = 5 and 5+2 =7 are those two numbers. |
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| 79670. |
a b c = 1 , \text { show that } \frac { 1 } { 1 + a + b ^ { - 1 } } + \frac { 1 } { 1 + b + c ^ { - 1 } } + \frac { 1 } { 1 + c + a ^ { - 1 } } = 1 |
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Answer» abc=1 ⟹c=1/ab 1/(1+a+1/b)+1/(1+b+1/c)+1/(1+c+1/a) =1/(1+a+1/b)+1/(1+b+ab)+1/(1+1/ab+1/a) =b/(1+b+ab)+1/(1+b+ab)+ab/(1+b+ab) =1+b+ab/(1+b+ab) =1 |
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| 79671. |
wapnesh wants to mail three parcels to three village schools. He findghat the postal charges are Rs 42, Rs 63 and Rs 294. He wants to buy stampsly of one denomination. Find the greatest denomination of stampsust buy to mail the three parcels. |
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| 79672. |
litres of petrol?7. If 50 metres of a cloth costs Rs.3725, how much cloth can be purchased for Rd.1788 |
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Answer» Cloth which can be purchased by 1 rupee =50/3725 Cloth which can be purchased by 1788 rupees =50*1788/3725 =24 |
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| 79673. |
) 22. 1 litre of petrol costs 16. Find thecost of 31litreof petrol. |
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| 79674. |
(L1.J2UULUU --22.A person pays * 75000 as income tax. If the tax paid is 24% of his taxable income, findhis taxable income.mno norcon nurchased it for 37100 at a |
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Answer» Let taxable income be x As given tax paid = 75000 and its 24% of taxable income Then,(24/100)*x = 75000x = 3125*100x = 312500 Therefore, taxable income is Rs 312500 |
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| 79675. |
1. Find the equation of a line passing throughorigin and having gradient (i.e., slope):341l |
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Answer» line passing through origin is y=mxy=6xy=-3/4x4y=-3x |
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| 79676. |
(i) a3 = 15 तथा 5]0 न 125 दिया है। / और ८८ ज्ञात कीजिए।g -n e o "~ |
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Answer» a3 = 15 S10 = 125 a3 = a + 2d = 15 S10 = 10/2 (2a+9d) = 125 2a+9d = 25 2a+9d-2a-4d = 125-30 5d = 95 d = 19 a + 38 = 15 a = -23 a10 = a + 9d = -23 + 9(19) = -23+171 = 148 |
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| 79677. |
Rajendra and Rehana own a business. Rehana receives 25% ofthe profit in each month ItRehana received2080 in particular month, what is the total profit in that month ? |
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Answer» Percentage of profit Rehana receives= 25%Rehana received money= rs. 2080Let the whole profit be x.25% of x = 208025x/100 = 2080x = 2080*100/25 = rs. 8320 |
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| 79678. |
A man earns12,000 and spends 10,500. If he saves rest of the money, findpercentage of his savings. |
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Answer» Money he saves is 12000-10500= 1500 Percentage of his saving = 1500×100/12000% =150000/12000% =12.5% Bhai how 150 is divide by 12 Thanks |
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| 79679. |
Sulochanabai owns 42 acres of farm land. If she planted wheat onof theland, on how many acres has she planted wheat ? |
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| 79680. |
If A, B, C are the angles in a triangle, then prove thatSin A+ Sin-+ SinC=1+ 4 Sin--A Sin--B Sinn-2 |
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| 79681. |
3-13 +1a=-1, b=2(1)(2) ,a=1, b = 2(3)(4)a=2,b=-1a=-2, b-1 |
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| 79682. |
How Much Petrol?Isha has Rs 1000 with her. She wants to buypetrol. One litre of petrol costs Rs 47. How manylitres can she buy? |
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| 79683. |
How Much Petrol?Isha has Rs 1000 with her. She wants to buypetrol. One litre of petrol costs Rs 47. How manylitres can she buy?Money with Isha Rs 1000Cost of 1litreRs 47Litres of petrol she can buy Rs 1000Rs 47-?Isha can buy_litres ofpetrol |
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| 79684. |
How Much Petrol?Isha has Rs 1000 with her. She wants to buypetrol. One litre of petrol costs Rs 47. How many elitres can she buy? |
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| 79685. |
(2) There are three dealers A, B and C in Maharashtra. Suppose, the tradcof each of them in september 2018 was as shown in the following taThe rate of GST on each transaction was 5%.Read the table and answer the questions below it.Tax-balancewith theGovt.Rs. 1000GST GST paid atTax paidDealer collected the timc of ITC to theGovt.on the salepurchaseA Rs. 5000Rs. 6000 Rs. 5000 Rs. 0p- | Rs. 5000 | Rs. 4000 | Rs. 4000 | Rs. 1000 | Rs. OC Rs. 5000 Rs. 5000 Rs. 5000 Rs. 0Rs. 0(i) How much amount did the dealer A get by salc?(ii) For how much amount did the dealer B buy the articles ?(ili) How much is the balance of CGSI and SGST left with the govermmentthat was paid by A? |
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Answer» ANS:-1) Rs. 60002) Rs. 40003) Rs. 1000 |
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| 79686. |
The relative velocity between two layers of fluid,separated by 0.1 mm is 2 cm/s. Calculate thevelocity gradient.(Ans : 200/s) |
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| 79687. |
Write each of the following in power no\frac{7}{20} \times \frac{7}{20} \times \frac{7}{20} \times \frac{7}{20} |
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| 79688. |
In right triangle ABC, right angled at C, M isthe mid-point of hypotenuse AB. C is joinedto M and produced to a point D such thatDM - CM. Point D is joined to point B(see Fig. 7.23). Show that:(ii) DBC is a right angle.(iii) Δ DBC Δ ACB(iv) CM AB2 |
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| 79689. |
l the coordinates of the pointsand (2,-3)To conduct Sports Day activities, inyour rectangular shaped school3.ground ABCD, lines have beendrawn with chalk powder atdistance of 1m each 100 flower potshave been placed at a distance of mfrom each other along AD, as showin Fig. 7.12 Niharika runshthedistance AD on the 2nd line andposts a green flag. Preet runsthe distance AD on the cighth line12and posts a red flag. What is thedistance between both the flags? ir-1Rashmi has to post a blue flag exactly A3 4 5 0halfway between the line segmentjoining the two flags, where shouldshe post her flag?Fig. 7.12 |
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| 79690. |
UD1) Alka spends 90% of the money that she receives every month, and saves Rs. 120.How much money does she get monthly?Find the thumber |
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Answer» 1200 she get monthly 100 % = 90 % + 10 % =90 % + 120 = 100 %100 % = (90/100*120) + 120100 % = 1080 + 120 = 1200 Salary of Alka=1200. 1200 is the correct answer |
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| 79691. |
A business man saves 9,876 every month.How much money will he save in 11 years? |
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Answer» ₹9876*12months*11years=₹1303632 |
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| 79692. |
The car that Ravi owns can go 150km in 15 litres of petrol. How for can it go with90 litres of petrol? |
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Answer» In 15 litres car can go 150 km In 1 litres car can go 150km/15 = 10 km In 90 litres car can go 90 × 10 = 900 km |
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| 79693. |
Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11 |
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Answer» thanks |
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| 79694. |
(1) The sum of the reciprocals of the two consecutive the odd natural nuthose numbers.mbers is 12/35. Find |
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Answer» please like my answer if you find it useful |
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| 79695. |
sinA+sinB-sinc=4sinA/2sinB/2cosC/2 |
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| 79696. |
2*3^(1/3)*(2*3^(2/3)) |
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| 79697. |
((-a^2 %2B c^2)^3 %2B (a^2 - b^2)^3 %2B (b^2 - c^2)^3)/((-a %2B c)^3 %2B (a - b)^3 %2B (b - c)^3) |
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| 79698. |
(1) 90°clination with positive direction of -axis isExercise 5.2what is the slope of a line whose inclination with positive directio(ii) 0°what is the inclination of a line whose slope is (0) 0Find the slope of a line joining the points(ii) 115.5) with the origin (ii) (sin cose) and (sin 8.What is the slope of a line perpendicular to the line joining A[5.1) andthe mid-point of the segment joining (4.2) and (-6,4).Show that the given points are collinear: (-3.1). (7.2) and (12,5)If the three points (3.-1), (,3) and (1.-3) are collinear, find the value of a.The line through the points (-2.a) and (9,3) has slope Find the value of aThe line through the points (-2,6) and (4.8) is perpendicular to the line through thepoints (8.12) and (x. 24). Find the value of x.Show that the given points form a right angled triangle and check whether theysatisfies pythagoras theorem10,5). M(9.12) and N (3.14)(i) A(1.-4). B2.-3) and C(4.-7)Coordinate Geometry |
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Answer» the anwer must be equal |
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| 79699. |
How Much Petrol?Isha has Rs 1000 with her. She wants to buypetrol. One litre of petrol costs Rs 47. How manylitres can she buy?Money with Isha ะ: Rs 1 000Cost of 1litre Rs 47Litres of petrol she can buy Rs 1000 + Rs 47-?Isha can buylitres of petrol. |
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| 79700. |
How Much Petrol?Isha has Rs 1000 with her. She wants to buypelrol. One litre of petrol costs Rs 47. Howmanylitres can she buy?Money with Isha Rs 1000Cost of 1 lite = Rs 47Litres of petrol she can buy - Rs 1000 Rs 47-?Isha can buylitres of petrol. |
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