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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.
| 1502. |
The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 175 times. What is the probability that it was not correct on a given day ? |
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| 1503. |
The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 175 times. What is the probability that on a given day it was correct. |
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| 1505. |
Draw a line segment 6.4 cmlong and draw its perpendicular bisector. Measure the length of each part. |
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Answer» Solution :STEPS OF CONSTRUCTION (i) Draw a ling segment `AB=6.4` cm. (ii) With `A` as centre and a radius equal to more than half of `AB`, draw two arcs, one above `AB` and the other below `AB.` (iii) With `B` as centre and the same radius, draw two arcs, cutting the previously drawn arcs at points `C` and `D` respectively. (iv) Join `CD` is the required perpendicular bisector of AB at the point O. On measuring, we find that `OA=3.2` cm and `OB=3.2` cm Also, `angleAOC=angle BOC=90^(@)` JUSTIFICATION : Join AC, AD, BC and BD. In `Delta CAD` and `Delta CBD`, we have `AC=BC` (arcs of equal RADII) `AD=BD` (arcs of equal radii) `CD=CD` (common) `:. Delta CAD cong Delta CBD` (SSS-criteria) `:. angle ACO = angle BCO` (c.p.c.t.). Now, in `Delta AOC` and `Delta BOC`, we have `AC=BC` (arcs of equal radii) `angleACO=angle BCO` (PROVED above) `CO=CO` (common) `:. Delta AOC cong Delta BOC` (SAS-criteria). Hence, `AO=BO` and `angleAOC=angleBOC`. But, `angleAOC+angleBOC=180^(@)` (LINEAR pair axiom) `:. angle AOC=angle BOC=90^(@)`. Hence, COD is the perpendicular disector of `angleAOB`. 
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| 1506. |
Find the mean and median of all the positive factors of 72. |
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| 1509. |
A piece of work can be done by 9 men and 15 women in 24 days. In how many days can 15men and 15 women do the same work ? |
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| 1513. |
In the given figure, AD is perpendicular to BC and EF || BC, if /_ EAB = /_ FAC, show that triangles ABD and ACD are congruent. Also, find the values of x and y if AB = 2x + 3, AC = 3y + 1, BD = x and DC = y + 1. |
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| 1514. |
Construct a rhombus PQRS, such that PQ=3.2 cm and PR=4.2 cm. |
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Answer» SOLUTION :Step 1: Draw a line SEGEMENT PQ=3.2 cm. Step 2: Taking P as the center and radius equal to 4.2 cm, draw an arc and taking Q as center, radius as 3.2 cm draw another arc to cut the previous arc at R. Step 3: With R and P as CENTERS and the radii equal to 3.2 cm each, draw two arcs to met at S. Step 4: Join PS, RS and QR to form rhombus PQRS. 
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| 1515. |
Show that the points (-1,-1) , (6,8) , (8,8) and (1,6) , when joined in the given order form a rhombus . |
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| 1516. |
Determine which of the following polynomials has (x+1) a factor : x^(4) + x^(3) + x^(2) + x +1 |
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| 1517. |
Evalutate the following expression as a computer does I (dxxa)/(b-cxxe) II (r )/((pxxq)-cxxe) The values of I and II are: |
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Answer» `(a)/(B)-CE,(r )/(pq)-ce` |
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| 1518. |
In the given figure, AB and CD are the parallel chords of a circle with centre O. Such that AB = 8 cm and CD = 6 cm. If OMbotAB and OLbotCD distance becween LM is 7 cm. Find the radius of the circle ? |
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| 1519. |
The paint in a certain container is sufficient to paint an area equal to 9.375 m^(2). How many bricks of dimensions 22.5 cm times 10 cm times 7.5 cm can be painted out of this container ? |
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| 1520. |
Mohan invested Rs.24,000 in 8% Rs.400 shares at Rs.320. He sold them at Rs.360 after one year. Find the total profit he earned. (in Rs.) |
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Answer» 6540 Dividend rate = `8%` ANNUAL inocome/share = Rs.32 Market value/share = Rs.320 `"NUMBER of shares bought"=(24,000)/(320)=75` `THEREFORE` Profit earned (in Rs.) = `75(360-320+32)="Rs.5400."` |
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| 1522. |
Draw a histogram from the following data: |
Answer» Solution :Given table is in the INCLUSIVE form. First we will convert it into the exclusive form. So the frequency table in the exclusive form is as follows:  Scale : LET 1 cm = 10 units on X-axis 1 cm = 5 units on Y-axis 
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| 1523. |
Examine whether x+2 is a factor of x^(3) + 3x^(2) + 5x + 6 and of 2x + 4. |
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| 1525. |
Express the following rational numbers in decimal form. (2)/(5) |
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| 1526. |
ABCD is a parallelogram and angleA = 60^(@). Find the remaining angles. |
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| 1527. |
Rohit borrows Rs 86,000 from Arun for two years at 5% per annum simple interest. He immediately lends out this money to Akshay at 5% compound interest compounded annually for the same period. Calculate Rohit's profit in the transaction at the end of two years. |
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| 1528. |
If 4sin^(2)x^(@)-3=0" and "x^(@) is an acute angle, find : (i) sinx^(@) "(ii) "x^(@) |
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| 1529. |
Calculate the total approximate interest earned by ravi up to 31-12-2006 .The rates of interest which change from time to time are as follows (i) 5% per annum up to 3-8-2006 (ii) 4.5 % per annum from 1-9-2006 to 31-12-2006 |
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Answer» RS 395 |
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| 1530. |
If both the diagonals of a quadrilateral divides it into four triangles of equal area, then the quadrilateral is a rhombus. |
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| 1531. |
What can you say about the position of the points (1,2), (1,3), (1,-4), (1,0) and (1,8). Locate on a graph sheet. |
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| 1532. |
The ratio of radi of two sphere is 2: 3 Find the ratioof their surface areas and volumes. |
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| 1533. |
In the following equations, find whether variables x, y, z etc. represent rational or irrational numbers w^(2)=27 |
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| 1534. |
In the following equations, find whether variables x, y, z etc. represent rational or irrational numbers u^(2)=(17)/(4) |
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| 1535. |
In the following equations, find whether variables x, y, z etc. represent rational or irrational numbers t^(4)=256 |
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| 1536. |
Without actually dividing find which of the following are terminating decimals. (11)/(18) |
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| 1537. |
If the lateral surface of a cylinder is 94. 2\ c m^2and its heightis 5 cm, then find(i) radius of its base (ii) its volume. |
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Answer» (II) 141.3 `cm^(3)` |
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| 1538. |
If two sides of a triangle measure 4 cm and 6 cm find all possible measurements (positive Integers) of the third side. How many distinct triangles can be obtained? |
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| 1539. |
In the following equations, find whether variables x, y, z etc. represent rational or irrational numbers x^(2)=7 |
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| 1540. |
In the following equations, find whether variables x, y, z etc. represent rational or irrational numbers y^(2)=16 |
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| 1541. |
In the following equations, find whether variables x, y, z etc. represent rational or irrational numbers z^(2)=0.02 |
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| 1542. |
Write an algorithm to find the factors of a given number |
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| 1543. |
A patientin a hospital is given soup daily in a cylindrical bowl of diameter 7cm. Ifthe bowl is filled with soup to a height of 4cm, how much soup the hospitalhas to prepare daily to serve 250 patients? |
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| 1544. |
Which of the following needs a proof? |
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Answer» AXIOM |
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| 1545. |
A certain quantity of wood costs Rs. 250 "per "m^(3). A solid cubical block of such wood is bougth for Rs. 182.25. Calculate the volume of the block and edge of the cube. |
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| 1546. |
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram. |
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| 1547. |
A sum of money lent out at C.I. at a certain rate per annum becomes three times of itself in 8 years. Find in how many years will the money become twenty-seven times of itself at the same rate of interest p.a. |
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| 1548. |
X and Y can do a piece of work in 4 days and 6 days resepectively. If Y works on the first day and they work on alternate days, in how many days will twice the amount of work be complete? |
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Answer» `9(2)/(3)` (i) The amount of work done by P and Q in one day in 40% of `(1)/(7) and 90% (1)/(9)` (ii) The amount of work done by P and Q in one of is 70% of `(1)/(7)` and 90% of `(1)/(9)` respectively. (III) Now find the part of work doneby P,Q adn R in one day and PROCEEDS. |
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| 1549. |
Construct trianglePQR in which QR=3.4 cm, angleP=50^(@) and PQ - PR = 1.2 cm. |
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Answer» Solution :Step 1: DRAW the ray, `QX`. Step 2: Mark the point S on `bar(QX)`, such that `QS=1.2 cm.` Step 3: Construct an angle equal to `180-1/2(180-50)=115^(@)` at S, such that `angleQSY=115^(@)`. Step 4: With `Q` as the center and radius = `3.4 cm`, draw an arc to meet `SY` at `R.` Step 5: Join `Q` and `R`. Step 6: Draw the perpendicular bisector of `SR` intersecting `QX` at `P`. Step 7: Join `PR`. `PQR` is the required TRIANGLE. 
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| 1550. |
Add the following polynomials and find the degree of the resultant polynomials (i)p(x) =6x^(2) -7x +2"" , q(x) =6x^(2) -7x +15 (ii)h(x) =7x^(3) -6x+1"", f(x) =7x^(3) +17x -9 (iii)f(x) =16x^(4) -5x^(2) +9 "", g(x) =-6x^(3) +7x-15 |
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