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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.
| 3101. |
A card is drawn at random from a well-shuffled pack of 52 cards. What is the probability of getting |
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Answer» `(3)/(4)` `(1)/(13).` |
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| 3102. |
Solvegraphically the system of linear equations4x - 5y+16=0 and2x+y - 6 = 0 .Determinethe verticesof the vertices of the triangle formedby theselinesand thex-axis. |
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Answer» Solution :On a graph PAPER, draw horizontlline `X'OX ` and verticalline `YOY'`as the x - axisand the y - axis respectively. Graphof `4x-5y+ 16 = 0 ` `4 x-5y+16 = 0 rArr5y=4x+16` ` ""rArry =((4x +16))/( 5)""` ... (i) Putting` x = - 4 ` in (i), we get`y = 0 ` Putting` x =1 ` in(i), we get`y =4` Putting` x =6` in (i), we get `y = 8` Thus, we havethe followingtable for` 4x -5y+ 16 = 0`  Now,plotthe points` A(-4, 0), B(1, 4)andC(6, 8)` on the graph paper. JoinAB and BC to get thegraphline ABC. Extendit onboth ways. Thus,the line ABC is the graph of `4x - 5y + 16 = 0` Graphof `2x+ y-6 = 0` ` 2x + y - 6 = 0 rArry =( 6 -2x )""`... (ii) Putting` x = 0 ` in(ii),we get` y =6 `. Putting ` x =2 `in (ii), we get` y =2 ` Putting ` x =3 `in(ii), we get`y = 0 ` Thus, we havethe followingtable for `2x+ y -6 = 0`  On the samegraphpaper as above, plot the points `P(0, 6), Q(2, 2 ) and R(3, 0)` Join PQand QR to get the graph line PQR. Extendit onboth ways. Thus, theline PQR is the graphof ` 2x + y - 6 = 0`  The two graphslines ABC and PQR intesectat the point ` B (1, 4 )`. ` thereforex= 1AND y =4` is thesolution of the givensystem ofequations. These lines from`Delta BAR` withthe x -axis , whose verticesare ` B(1, 4), A(-4, 0) and R(3, 0)` |
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| 3103. |
While calculating median of grouped data the following entries were found l=860, h=20 cf= frequency of preceding class 40 N N=50 and median =868, find the frequency of the median class. |
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| 3104. |
837, 612, 549, 422, 342, 216 |
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Answer» 837 |
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| 3105. |
The ratio of 11th term to 18th term of an AP is 2:3. Find the ratio of 5th term to the 21st term, also the ratio of the sum of the first 5 terms to the sum of the first 21 terms. |
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| 3106. |
A number series arranged in some sequence is given, One term in the series is wrong, which is given as one of the alternatives under it. Find the wrong term in each case. 0, 1, 3, 6, 10, 15, 21, 28, 37, 45 |
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Answer» 0 |
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| 3107. |
A number series arranged in some sequence is given, One term in the series is wrong, which is given as one of the alternatives under it. Find the wrong term in each case. 3, 5, 10, 12, 24, 26, 52, 54, 109, 110 |
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Answer» 12 |
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| 3108. |
A number series arranged in some sequence is given, One term in the series is wrong, which is given as one of the alternatives under it. Find the wrong term in each case. 2, 0, 5, 8, 17, 24, 37, 48 |
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Answer» 2 |
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| 3109. |
A number series arranged in some sequence is given, One term in the series is wrong, which is given as one of the alternatives under it. Find the wrong term in each case. 6, 4, 10, 5, 16, 6, 26, 7, 52, 8 |
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Answer» 4 |
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| 3110. |
As observed from the top of a 75m high lighthouse from the sea-level, the angles of depression of two ships are 30^(@) and 45^(@). If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships |
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| 3111. |
Gopal is worrying that his neighbour can peep into his living room from the top floor of his house. He has decided to build a fence that is high enough to block the view from their top floor window. What should be the height of the fence? The measurements are given in the figure. |
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| 3112. |
Some people collected money to be donated in some orphanages. A part of the donation is fixed and remainingdepends on the number of children in the orphanage. Ifthey donated ₹ 9,500 in the orphanage having 50 children and ₹ 13,250 with75 children, find the fixed part of the donation and the amount donated for each child .Whatvalues do these people possess ? |
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| 3113. |
If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y. |
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| 3114. |
Given matrix A=[{:(,4sin30^@ cos 0^@),(,cos 0^@4 sin 30^@):}] and B=[{:(,4),(,5):}]. If AX=B. write the order of matrix X. |
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| 3115. |
Water in a canal. 6m wide and 1.5 mdep. Is flowig with a speed of 10 km//h . How much area will it irrigate in 30 minutes if 8 cm of standing water is needed ? |
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| 3116. |
A shopkeeper sells x units of books and y units of stationery. If he makes a profit of Rs.2 On each book and Rs. 3 on each unit of stationery, then the profitfunction is ______ |
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Answer» `p=2x-3Y` (ii) PROFIT on books is RS. 2x and profit on stationary is Rs. 3y. (III) Profitfunction = Profit on books + Profit on stationary. |
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| 3117. |
Let ABC be a right-triangle where AB= 6 cm, BC= 8 cm, and B = 90° . BD is the perpendicular from B on AC. The circle through B, C, and Dis drawn. Given below are the steps of construction of a pair of tangents from A to this circle. Which of the following steps is incorrect? Step 1: Draw a line segment AB = 6 cm and BC = 8 cm perpendicular to each other. Join AC. Step 2: Draw the perpendicular bisector of BC which meets BC at O. Step 3: With O as centre and OB as radius. draw a circle which intersects AC at D. Thus BD bot AC. Step 4: With A as centre and AO as radius draw an arc cutting the circle at M. Step 5: Join AM. Thus AB and AM are the required tangents. |
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Answer» STEP 2 only |
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| 3118. |
An exterior angle of a regular polygon having n sides is more than that of the polygon having n^2 sides by 50^@. Then findthe number of the sides of each polygon |
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| 3119. |
In what ratio does 4x +3y-13 0 divide the line segment joining (2, 1) and (1, 4)? |
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| 3120. |
A right circular cone is 3.6 cm high and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Find its height. |
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| 3121. |
In the given figure LM||AB M AL = x - 3, AC = 2x, BM = x - 2 and BC = 2x + 3 find the value of x |
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| 3122. |
Directions (Questions 21 to 25): Given below are five patterns represented by circles A, B and C which indicate the logical relationship between and among the respective descriptions. On the basis of descrip tion given for A, B and Crespectively in the questions decide which of the given patterns (a), (b), (c), (d) and (e) best indicates the logical relationship. (A) Apple (B) Fruit (C) Orange |
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| 3123. |
Directions (Questions 21 to 25): Given below are five patterns represented by circles A, B and C which indicate the logical relationship between and among the respective descriptions. On the basis of descrip tion given for A, B and Crespectively in the questions decide which of the given patterns (a), (b), (c), (d) and (e) best indicates the logical relationship. (A) Doctor (B) Male (c) Actor |
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| 3124. |
Solve the following pair of linear equation by elimination method: x/2 + (2y)/3 = 1 and x - y/3 = 3. |
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| 3125. |
If P=[{:(,2,6),(,3,9):}] and Q=[{:(,3,x),(,y,2):}]. find x and y such that PQ=null matrix. |
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| 3126. |
In traangle ABC , AB =AC and E is any point on the extended BC . If the circumcircle ofDeltaABC intersect AE at the point D then that angleACD=angleAEC. |
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Answer» Solution :In `DeltaABC`, AB=AC, `thereforeangleABC=angleACB` ………….(1) Now , ABCD is a CYCLIC QUADRILATERAL, `thereforeangleABC+angleADC=180^(@)` or , `angleACB+angleADC=180^(@)` ……..(2) [from (1)] , Again , `angleACB+angleACE=1" straight angles " =180^(@)` ........(3) From (2) and (3) we GET , `angleACB+angleADC=angleACB+angleACE` or, `angleADC=angleACE" or " angleDCE+angleDEC=angleACD+angleDCE" or " angleDEC=angleACD` `thereforeangleACD=angleDEC` Hence `angleACD=angleAEC` 
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| 3127. |
Evaluate each of the following in terms of x and y, if it is given that x = log_(2)3 and y = log_(2)5 log_(2)7.5 |
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| 3128. |
Shri. Batliwala sold shares of 30,350 and purchased shares of 69,650 in a day. He paid brokerage at the rate of 0.1 on sale and purchase. 18% GST was charged on brokerge. Find his total expenditure on brokerage and tax. |
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| 3129. |
Find the 99^(th)term of the series: 7 (3)/(4) , 9 (1)/(2) , 11(1)/(4),……. |
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| 3130. |
Find the value of k, so that line joining the points A (3,k) and B(2,7) is parallel to line joiningthe points C(-1,4) and D(0,6). |
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| 3131. |
In the given figure DeltaODC ~ DeltaOAB, /_BOC = 100^@,/_ODC = 60^@, then /_OAB ……. (40^@) |
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| 3132. |
Which of the following is a polynomial |
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Answer» `x^(2)-5x+3sqrt(x)` |
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| 3133. |
In the given figure quadrilateral ABCD is circumscribed and AD_|_DC. Find x if radius of circle is 10 cm. |
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| 3134. |
The value of sum_(n=1)^(10) n is: |
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Answer» 10 |
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| 3135. |
A die is thrown once. Find the probability of getting a number less than or equal to 4. |
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| 3136. |
If [{:(,4,-2),(,4,0):}]+3A=[{:(,-2,-2),(,1,-3):}] find A. |
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| 3137. |
The point A(-3, 2) is reflected in the x-axis to the point A'. Point A' is then reflected in the origin to point A". Write down the co-ordinates of A". |
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| 3138. |
The point A(-3, 2) is reflected in the x-axis to the point A'. Point A' is then reflected in the origin to point A". Write down a single transformation that maps A onto A". |
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| 3139. |
A right triangle has sides 'a' and 'b' where a>b . If the right angle is bisected then find the distance between orthocentres of the smaller triangles using coordinate geometry. |
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| 3140. |
To construct a triangle similar to a given triangle ABC with its sides (8)/(5)th the corresponding sides of triangle A, B, C draw a ray BX such that CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on the ray BX |
| Answer» ANSWER :B | |
| 3141. |
By determing the mean-proportional there can be construted ______ of area equal to the area of a given rectangle. |
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Answer» a rhombus |
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| 3143. |
From the top of a 7m high buildings, the angle of elevation of the top of a cable tower is 60^@ and the angle of depression of its foot is 45^@. Determine the height of the tower. |
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| 3144. |
In the given figure ABC is a right angled triangle with AB=6 cm, and BC=8 cm. A circle with centre O has been inscribed inside the triangle. Find the radius of the circle. |
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Answer» Solution :Let x be the radius of the circle. In right triangle ABC, `AC^(2)=AB^(2)+BC^(2)""`(by Pythagoras Th.) `implies""AC^(2)=6^(2)+8^(2)` `implies""AC^(2)=36+64` `implies""AC^(2)=100` `implies""AC=10` Now in QUADRILATERAL OPBR `angleB=angleP=angleR=90^(@)` each Hance, `""angleROP=90^(@)""`(sum of all angles of a quadrilateral is 360^(@)) and also `""OP=OR""`(each radii) HENCE, OPBR is a square with each side x cm. Hence, `""BP=RB=xcm` Therefore, CR=(8-x) and PA=(6-x) Since, the tangents from an EXTERNAL point to a circle are equal in length `:.AQ=AP=(6-X) and CQ=CR=(8-x)` Now,`""AC=AQ+CQ` `implies""10=6-x+8x` `implies""10=14-2x` `implies""x=2cm` |
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| 3145. |
The sum of three numbers in A.P. is 15. and the sum of the squares of the extreme terms is 58. Find the numbers. |
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| 3146. |
Using ruler and compasses only, draw an equilateral triangle of side 4.5 cm and draw its inscribed circle. Measure the radius of the circle. |
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| 3147. |
Two solid cylinders, one with diameter 60 cm and height 30 cm and the other with radius 30 cm and height 60 cm, are melted and recasted into a third solid cylinder of height 10 cm. Find the diameter of the cylinder formed. |
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| 3148. |
Point P lies on segment AB such that 3 AB = 10 AP.In which ratio does the point P divide AB internally ? |
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| 3149. |
Diagonals of a trapezium ABCD with AB || DC, intersect each other at the point ‘O’.If AB = 2CD, find the ratio of areas of triangles AOB and COD. |
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| 3150. |
Find the centre of a circle passing through the point (6, -6), (3, -7) and (3,3). |
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