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InterviewSolution
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.
| 2151. |
P and Q have co-ordinates (0, 5) and (-2, 4). Find the image of Q on reflection in the axis found in (a). |
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| 2152. |
Find the value of k for which the lines (k+1) x + 3ky +15=0 and 5x+ky +5=0 are coincident. |
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| 2153. |
Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed. |
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| 2154. |
Find the number of straight lines and the number of triangles in the complex figure given below . |
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Answer» Number of straight lines are : AB,BC, CD, DA, AC, BD, EH, AH, DH So there are 9 straight lines in the diagram . Now count triangles : Number of small triangles are (containing one component) AGH, GHD, AFD, DGF, FBE and FCE = 6 Number of triangles with two components: AHF, DHF, AHD, AFD, AFB, DFC , FBC = 7 Number of triangles with four components: ABC, ADC, CDB adn ADB = 4 `therefore` TOTAL number of triangle CONTAINED in the figure= 6+7+4 =17 |
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| 2155. |
Divide 40608 rs into two parts such that if one part is invested in 8%100rsshares at 8%discount and the other part is invested in 9% Rs 100 shares at 8% premium , the annual incomes from both the investments are equal. |
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| 2156. |
Which of the following is not a quadratic equation? |
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Answer» `4X^(2)+2x+2=0` |
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| 2157. |
From the top of a building 16 high the angular elevation of the top of a hill is 60^(@) and the angular depression of the foot of the hill is 30^(@), find the height of the hill. |
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| 2158. |
Find five numbers in A.P. whose sum is 12 1/2and the ratio of the first to the last terms is 2:3. |
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| 2159. |
Determine whether following points are collinear. A(-4,4), K (2-,5/2), N(4,-2) |
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| 2160. |
Without performing division, state whether the following rational numbers will have a terminating decimal form or a non-terminating, repeating decimal form. 36/100 |
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| 2161. |
Without actually performing the long division state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion 77/210 |
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| 2162. |
Without performing division, state whether the following rational numbers will have a terminating decimal form or a non-terminating, repeating decimal form. 9/15 |
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| 2163. |
A' is the image of A(2,3) when reflected in the x-axis. Write down the co-ordinates of A' . |
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| 2164. |
Point P (h,k) divides a line segment between the exes in the ratio 1:2 Find the lengths (intercepts) on the axes made by this segment. Also find the area of triangle formed by the line segment and the axes. |
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Answer» Solution :Let AB be the line segment joining A (0.y) and B (x,0) between the axes. P (h,k) divides the line segment in the ratio `1:2.` Now, question arises that whether `PA:PB=1:2` or `PB:PA=1:2` or `PB:PA = 1:2` The answer of this is that always we take the FORMER part of ratio towards the X-axis and latter part of ratio towards the Y-axis.  So, here we will take `""PB,PA=1:2` `THEREFORE` By using section FORMULA, `h=(1(0)+2(x))/(1+2)implies""h=(2x)/(3)impliesx=(3H)/(2)` and `k=(1(y)+2(0))/(1+2)implies""k=(y)/(3)impliesy=3k` So, length of intercept on the X-axis `=OB=x=(3h)/(2)` and the length of intercept on the Y-axis =OA = y = 3k. `therefore` Area of `DeltaAOB=1/2xxOBxxOA=1/2(3h)/(2)xx3k=9/4hk` SQUARE units |
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| 2165. |
When f(x)=x^(3)+ax^(2)-bx-8 is divided by x-2, the remainder is zero and when divided by x+1, the remainder is -30. Find the values of 'a' and 'b'. |
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| 2166. |
Without performing division, state whether the following rational numbers will have a terminating decimal form or a non-terminating, repeating decimal form. 23/(2^(3).5^2) |
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| 2167. |
Without actually performing the long division state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion 129/(2^(2)5^(7)7^(5)) |
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| 2168. |
Without performing division, state whether the following rational numbers will have a terminating decimal form or a non-terminating, repeating decimal form. 15/1600 |
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| 2169. |
Without performing division, state whether the following rational numbers will have a terminating decimal form or a non-terminating, repeating decimal form. 29/343 |
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| 2170. |
Without performing division, state whether the following rational numbers will have a terminating decimal form or a non-terminating, repeating decimal form. 11/12 |
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| 2171. |
Without performing division, state whether the following rational numbers will have a terminating decimal form or a non-terminating, repeating decimal form. 64/455 |
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| 2172. |
Without performing division, state whether the following rational numbers will have a terminating decimal form or a non-terminating, repeating decimal form. 13/3125 |
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| 2173. |
Find the value of angleBAC in the given triangle . |
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| 2174. |
Find the value of x which satisfies the inequation : -2le1/2-(2x)/3le15/6, x inW Also , graph the solution on a number line. |
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| 2175. |
If the area of the triangle formed by the three points is zero, then the points lie on a |
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Answer» stragth LINE |
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| 2176. |
Iftan2A= cot(A-18^@ )where2Aisanacute angle, findthe value of A. |
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| 2177. |
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in English alphabets in the surnames was obtained as follows : {:("No of letters",1-4,4-7,7-10,10-13,13-16,16-19),("No of surnames",6,30,40,16,4,4):} Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames. |
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| 2178. |
Prove that sqrt(11) is irrational. |
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Answer» Solution :Let, if possible, `sqrt(11)` be rational and its simplest form be`(a)/(b).` Then a and b are INTEGERS and having no common FACTOR other than 1 and `b ne 0`. Now, `sqrt(11) = (a)/(b)` `rArr` `11 = (a^(2))/(b^(2))` `rArr` `a^(2) = 11b^(2)""`...(1) `therefore` As `11b^(2)` is divisible by 11. `rArr` `a^(2)` is divisible by 11. `rArr` a is divisible by 11. Let a = 11c, for some integer c. From EQUATION (1) `(11c)^(2) = 11b^(2)` `rArr` `b^(2) = 11c^(2)` But `11c^(2)` is divisible by 11. `therefore b^(2)` is divisible by 11. `rArr` b is divisible by 11. Let b = 11d, for some integer d. Thus, 11 is a common factor of a and b both. But it contradicts the fact that a and b have no common factor other than 1. So, our supposition is wrong. Hence, `sqrt(11)` is irrational. `""`Hence Proved. |
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| 2179. |
Solve each the following pairs of equations by reducing them to a pair of linear equations. (iii) 2/(sqrtx)+ 3/sqrty =2 4/sqrtx - 9/sqrty = -1 |
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| 2181. |
A person invests Rs 20,000 at 20% Rs. 150 shares at a premium of Rs. 50. The income from theses shares in is Rs. _______. |
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Answer» 1000 (ii) `MV=FV+` Premium. (III) Find the number of shares. `("Number of shares"xxFV)` (IV) Income `=(xx"(Rate of dividend)")/100` |
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| 2182. |
The maximum number of tangents drawn from an external point to a circle is : |
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Answer» 0 |
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| 2183. |
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm. |
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| 2185. |
Find the values of k for each of the following quadratic equations, so that they have two equal roots. (i) 2x^(2)+kx+3=0 (ii)kx(x-2)+6=0 |
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| 2186. |
Underground water sump is popular in India. It is usually used for large water sump storage and can be built cheaply using cement-like materials. Underground water sump are typically chosen by people who want to save space. The water in the underground sump is not affected by extreme weather conditions. The underground sump maintain cool temperatures in both winter and summer. A builder wants to build a sump to store water in an apartment. The volume of the rectangular sump will be modelled by V(x)=x^(3)+x^(2)-4x-4. What is the storage capacity of this sump ? |
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Answer» 3000 litre Thus (C) is CORRECT option. |
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| 2187. |
Underground water sump is popular in India. It is usually used for large water sump storage and can be built cheaply using cement-like materials. Underground water sump are typically chosen by people who want to save space. The water in the underground sump is not affected by extreme weather conditions. The underground sump maintain cool temperatures in both winter and summer. A builder wants to build a sump to store water in an apartment. The volume of the rectangular sump will be modelled by V(x)=x^(3)+x^(2)-4x-4. He planned in such a way that its base dimensions are (x + 1) and (x + 2) . How much he has to dig ? |
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Answer» `(x+1)` `V(x)=x^(3)+x^(2)-4x-4=x^(2)(x+1)-4(x+1)` `=(x+1) (x^(2)-4)=(x+1)(x-2) (x+2)` If `(x+1)` and `(x+2)` are two dimension , 3rd dimension will be `(x-2)`. THUS he has to DIG `(x-2)`. Thus (b) is correct OPTION. |
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| 2188. |
Underground water sump is popular in India. It is usually used for large water sump storage and can be built cheaply using cement-like materials. Underground water sump are typically chosen by people who want to save space. The water in the underground sump is not affected by extreme weather conditions. The underground sump maintain cool temperatures in both winter and summer. A builder wants to build a sump to store water in an apartment. The volume of the rectangular sump will be modelled by V(x)=x^(3)+x^(2)-4x-4. If x = 4 meter, what is the volume of the sump? |
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Answer» `30m^(3)` `V(4) =(4+1) (4-2)(4+2) =5xx2xx6=60m^(3)` Thus (d) is correct option. |
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| 2189. |
Underground water sump is popular in India. It is usually used for large water sump storage and can be built cheaply using cement-like materials. Underground water sump are typically chosen by people who want to save space. The water in the underground sump is not affected by extreme weather conditions. The underground sump maintain cool temperatures in both winter and summer. A builder wants to build a sump to store water in an apartment. The volume of the rectangular sump will be modelled by V(x)=x^(3)+x^(2)-4x-4. If x = 4 and the builder wants to paint the entire inner portion on the sump, what is the total area to be painted ? |
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Answer» `52m^(2)` `x+1=4+1=5` `x+2=4+2=6` `x-2=4-2=2` `S=2(5xx2+2xx6+6xx5)` `=2(10+12+30)=2(52)=104m^(2)` Thus (d) is correct option. |
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| 2190. |
Underground water sump is popular in India. It is usually used for large water sump storage and can be built cheaply using cement-like materials. Underground water sump are typically chosen by people who want to save space. The water in the underground sump is not affected by extreme weather conditions. The underground sump maintain cool temperatures in both winter and summer. A builder wants to build a sump to store water in an apartment. The volume of the rectangular sump will be modelled by V(x)=x^(3)+x^(2)-4x-4. If the cost of paint is Rs. 25/ per square metre, what is the cost of painting ? |
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Answer» 3900 Rs THUS (b) is CORRECT OPTION. |
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| 2191. |
Find the sum of all the two digit numbers which are either multiples of 2 or 3. |
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| 2192. |
Construct a triangle PQR where PQ=6 cm QR=7 cm, and PR = 8 cm. Then, construct another triangle whose sides are (4)/(5)th the corresponding sides of PQR. |
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| 2193. |
When a registered dealer sells goods to another registered dealer under GST, then this trading is termed as ...... |
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Answer» BB |
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| 2194. |
Prove that the points A(9,0) , B(9,6) , C(-9 , 6) and D(-9,0) are the vertices of a rectangle . |
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| 2195. |
Solve the following equation : (2x)/(3)-(3y)/(2)=-2 (x)/(2)+(4y)/(3)=(25)/(3). |
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| 2196. |
Check whether the following equations are consistent or inconsistent. Solve them graphically. 2x+y-6=0 and 4x-2y-4=0. |
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| 2197. |
At one end A of a diameter AB of a circle of radius 13 cm , tangent ,XAY is drawn to the circle . A chord CD is parallel to XY and is at a distance of 18 cm from A . What will be the length of CD? |
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| 2198. |
State with reason, whether the following are true of false. A, B and C are matrices of order 2 xx 2. A.(B-C)=A.B-A.C |
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| 2199. |
How is Mohit related to Niharika? I. Mohit is the only son of Niharika's mother in-law. II. Sarita is Mohit's only sister. |
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Answer» Solution :I STATES that Mohit is the only son of Niharika.s mother-in-law i.e. Mohit is Niharika.s husband. However, the relation between Mohit and Niharika can not be FOUND from II. So I alone is SUFFICIENT to ANSWER the GIVEN question. |
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| 2200. |
A line intersecting a circle in two points is called a ……….. |
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