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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.
| 651. |
In the given figure we have angle1=angle3,angle2=angle4 and angle3=angle4 prove that angle1= angle2 |
Answer» Solution : Euclid 's Axiom 1 says the THINGS which are equal to the same things are aqual to one another `therefore ANGLE(1)=angle(3) and anlge(3)=angle(4)` `rarrangle(1)=angle(4)` [by Euclid 's Axiom 1] Now `angle(1)=angle(4)` (proved ) and angle(2)=angle(2)=angle(4)` (given) `RARR angle(1)=angle(2)` [by Euclid 's Axiom 1] HENCE `angle(1)=angle(2)` |
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| 652. |
The ratio of the interest accured on a sum, when invested at simple interest for 2 years and the interest accured on it, if it is invested at compound interest, interest being compounded annually for 3 years at the same rate of interest is 50:91. Find the rate of interest (per annum). |
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Answer» <P> ii) `(P xx r xx 2)/100 /P[(1+r/100)^(3)-1]=50:91`. iii) Solve the above and find r. |
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| 654. |
A land is the shape of rhombus. The perimeter of the land is 160 m and one of the diagonall is 48 m. Find the area of the land. |
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| 655. |
Ashot-putt is a metallic sphere of radius 4.9 cm. If the density of the metalis 7. 8"\ "g"\ "p e r"\ "c m^3, find the mass of the shot-putt |
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| 656. |
ABC is a triangle inscribed in a circle, AC being the diameter of the circle. The length of AC is as much more than the length of BC as the length of BC is more than the length of AB. Find AC:AB. |
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Answer» `5:3` |
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| 657. |
If P={:[(ab,bc),(ca,ab)]:}andI={:[(1,0),(0,1)]:} then show that P^(2)2abP=ba(c^(2)-ab)I. |
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| 658. |
Evaluate : [(3sqrt(8))-(1)/(2)]^(4). |
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| 659. |
A sum of Rs 40 is borrowed at simple interest, it is borrowed at 2% per annum for the first month, 4% per annum for the second month, 6% per annum for the third month, and so on. What is the total interest to be paid at the end of 6 months? (in Rs) |
| Answer» SOLUTION :1.4 | |
| 660. |
Mr. Sharma borrowed a certain sum of money at 10% per annum compounded annually. If by paying Rs 19,360 at the end of the second year and Rs 31,944 at the end of the third year he clears the debt, find the sum borrowed by him. |
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| 661. |
Diameter of a circle is 14, find its area and perimeter. |
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| 662. |
The measures of two angles of a cyclic quadrilateral are 40^(@) and 110^(@)Then, the measures of other two angles of the quadrilateral are .......... |
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Answer» `400^(@) and 110^(@)` |
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| 664. |
Construct a triangle PQR, in which QR=4.5 cm, angleQ=44^(@) and PQ-PR=2 cm. |
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Answer» Solution :Step 1: Draw a LINE segment `QR=4.5 cm` Step 2: Draw `vec(QX)`, such that `angleRQX=44^(@)` Step 3: With Q as the center and radius =2 cm, draw an arc to INTERSECT `vec(QX)` at P. Step 4 : Join P and R, PQR is the REQUIRED TRIANGLE. 
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| 666. |
Euclid s which axiom illustrates the statement that when x+y =15 |
| Answer» Solution :Second axiom states that if equals be added to equals then wholes are EQUAL | |
| 667. |
find the mean of the following data. |
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| 668. |
In the given figure below, if AC = BD then prove that AB = CD. |
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Answer» Solution :We have AC = BD Substracting BC from both sides, we get `AC-BC=BD-BC` (when EQUALS are subtracted from equals, remainder are equal) `rArr""AB = CD` Hence Proved. |
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| 670. |
Mr Ramu has his saving bank acccount with andhra bank given are the entries in his pass book ltvbrgt The interest up to 30-6-2003 at 4(1)/(2)% per annum is _________(approx) |
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Answer» RS 60.70 |
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| 671. |
Calculate the sum of money on which the compound interest (payable annually) for 2 years be four times the simple interest on Rs 4,715 for 5 years, both at the rate of 5 per cent per annum. |
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| 672. |
Examine, whether the following numbers are rational or irrational: (i) 0.9842796 (ii) 6.125125125.. (iii) 1.10100100010000........... |
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| 674. |
Find out whether the followingnumbers are rational or irrational : (a) 2.42857314 (b) 2.02002000…. |
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| 675. |
Find the square root of (2x+7)(x^(2)-9)(2x-5)+9. |
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Answer» Solution :FIRST of all we make the coefficient of x as 1 in each factor by taking some CONSTANT common as : `2(x+(7)/(2))(x+3)(x-3).2(x-(5)/(2))+9` Now, we take the product of 2 factors at a time in such a way that sum of constant terms is same in each pair as : ` (##NTN_MATH_IX_C02_S01_066_S01.png" width="80%"> `=4(x^(2)+(x)/(2)-(21)/(2))(x^(2)+(x)/(2)-(15)/(2))+9` Let `x^(2)+(x)/(2)=a` `=(a-(21)/(2))(a-(15)/(2))+9` `4(a^(2)-18a+(315)/(4))+9` `4(a^(2)-18a)+315+9` `4underset("make perfect SQUARE")(ubrace(a^(2)-18a+81)-81)+324 "" ["add and subtract"(("coeff. of a")/(2))^(2) " to make perfect square"]` `=4(a^(2)-18a+81)-324+324` `=4(a-9)^(2)` Replace the VALUE of a as `x^(2)+(x)/(2)`, we get `4(x^(2)+(x)/(2)-9)^(2)=4((2x^(2)+x-18)/(2))^(2)=(2x^(2)+x-18)^(2)` `therefore " Square root of" (2x+7)(x^(2)-9)(2x-5)+9 i.e., (2x^(2)+x-18)^(2) " is" 2x^(2)+x-18`. |
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| 676. |
Expand :((1)/(2)x-(1)/(3)y-(1)/(5)z)^(2) |
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| 678. |
……….. Should be added to x^(2) - 8, so that the result is exactly divisible by (x+3). |
| Answer» ANSWER :A | |
| 679. |
Find the volume of that largest cone that can be cut from a cube of edge 14 cm. |
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| 680. |
In the given figure, if area of triangle ADE is 60cm^(@), giving reason, the area of : (i) parallelogram ABED, (ii) rectangle ABCF, (iii) triangle ABE. |
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| 681. |
In the followingfigure , ABCis a righttrianglerightangledat A. BCEDACFGand ABMN and squareson the sidesBC,CA and ABrespectively , LinesegementAXbotDEmeetsBC at Y. Show that (i)tirangle MBC = tirangle (MBC) (ii) ar (BXYD) = 2 ar (MBC) (iii) ar (BYXD) = ar(ABMN)(iv)tirangle FCB = tirangle ACE (v)ar (CYXE) = 2 ar (FCB) (vi) ar (CYXE )= ar (ACFG) (vii)ar (BCED) = ar (ABMN) + ar (ACFG) |
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Answer» (ii) `1/2` (iii) AMBN (iv) ` tirangle ACE ` (v) 2 (VI)ACFG ABMN |
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| 682. |
On one page of a telephone directory , there were 200 telephone numbers . The frequency distribution of their unit place digit (for example , in the number 25828573 , the unit place digit is 3 ) is given in the following table . {:("Digit",0,1,2,3,4,5,6,7,8,9),("Frequency",22,26,22,22,20,10,14,28,16,20):} Without looking at the pencil is placed on one of these numbers, i.e., the number is chosen at random. What is the probability that the digit in its unit place is 6 ? |
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| 683. |
Refer to Example 5, Section 14.4, Chapter 14. Findthe probability that a student of the class was born in August. |
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| 684. |
Factorise the following using appropriate identities : 9x^(2) + 6xy + y^(2) |
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| 685. |
If A={:[(-3,5),(2,-1)]:}, then show that A^(2)+4A-7I=O. |
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| 686. |
Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area. |
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| 688. |
Which of the following statements are true ? (i) A line segment has no definite length (ii) A ray has no end point (iii) A line has definite length (iv) A line AB is the same as line BA (v) A ray AB is the same as ray BA (vi) Two distnict points always determine a unique line (vii) Three lines are concurrent if they have a common point (viii)T wo distinct lines cannot have more than one point in common (ix) Two intersecting lines cannot be both parallel to the same line (x) open half line is the same thing as ray (xi) Two lines may intersect in two points (xii) Two lines are parallel only when they have no point in common |
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| 689. |
Answer the following by a number or a word or a sentence : Name the region between and arc of a circle and its corresponding chord. |
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| 691. |
Construct a rhombus whose diagonals are 4 cm and 6 cm in length. Measure each side of the rhombus. |
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Answer» Solution :STEPS OF CONSTRUCTION (i) DRAW a line segment `AC=4` cm. (ii) Draw the perpendicular bisector `XOY` of `AC`, cutting `AC` at `O.` (III) Along `OX` and `OY,` set off `OB=3` cm and `OD=3` cm respectively. (iv) Join `AB, BC, CD` and `AD`. Then, `ABCD` is the required RHOMBUS. 
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| 692. |
Rationalise the denominators of the following: (sqrt6)/(sqrt3-sqrt2) |
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| 693. |
What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m ? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. (Use pi=3.14) |
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| 694. |
A part of the locus of a point P, which is equidstant from two intersecting line as + by + c = 0 and px + qy + r = 0 |
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Answer» `(a - p) x + (b - q) y + (c - x) = 0` `(|px_(1) + qy_(1) + r|)/(sqrt(p^(2) + q^(2)))`, (ii) PERPENDICUALR distance of the point `(x_(1), y_(1))` to the line `ax + by + c = 0` is `(|ax_(1) + qy_(1) + c|)/(sqrt(a^(2) + b^(2)))`, |
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| 695. |
In trianglePQR, PQ = 4, QR = 6 and PR = 5. Then, ........ is the angle with greatest measure in trianglePQR. |
| Answer» Answer :A | |
| 696. |
The total surface area of a closed cylinder with radius 3.5 cm and height 6.5 cm is …….. cm^(2). |
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Answer» 110 |
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| 697. |
Construct a right triangle whose base is 4 cm and the sum of its hypotenuse and the other side is 8 cm. |
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Answer» SOLUTION :STEPS OF CONSTRUCTION (i) Draw a line segment `BC=4` cm. (ii) Construct `angleCBX=90^(@)`. (iii) From B, set off `BD=8` cm. (iv) Join `CD`. (v) Draw the perpendicular bisector of `CD`, intersecting `BD` at `A`. (VI) Join `AC`. Then, `Delta ABC` is the required RIGHT TRIANGLE. Verification : On measuring, we find that `AB+AC=(3+5) cm=8` cm. 
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| 698. |
10 women can complete a job in 12 days . 4 of them started working on the job. After every 4 days, a women joined the group. Every woman joinin the group has equal capcity as any woman in the group. Find the time taken to complete the job ( In days) |
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| 699. |
If cosx=sin43^(@), then the value of x is…………… |
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Answer» `57^(@)` |
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| 700. |
What length of tarpaulin 3m wide be required to make a conical tent of height 8m and base radius 6m? Assume that extra length of material that will be required for stitching margins and wastage in cutting is approxmately 20 cm (use pi = 3.14) |
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