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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.
| 551. |
Find the area of the shaded region in the adjacent figure, where ABCD is a square of side 10cm and semicircles are drawn with each side of the square as diameter (usepi=3.14) |
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| 552. |
Let ABC is a right triangle in which AB = 6 cm, BC = 8 cm,angleB=90^(@).BD is the perpendicular from B on AC. The circle through B,C and D is drawn. Construct the tangents from A to this circle. |
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Answer» Solution :Given, ABC is a right triangle in which `AB=6cm, BC=8cm,angleB=90^(@)and BD` is perpendicular to AC. Steps of Construction : 1. Draw the line segments AB = 6 cm and BC= 8 cm perpendicular to each other. JoinAC, thus `DeltaABC` is the right triangle. 2. Take mid-point F of BC as CENTRE, draw a circle with radius 4 cm , passing through B,C and D. 3. Now, join AF and bisect it. Let mid-point of AF is O. 4. Take O as centre and OA as radius, FRAW a circle which intersect the given circle (which passes through B,C and D) at B and M. 5. Now, join AB and AM, which are the required tangents. Justification : Join FM and FB. Then, `angleAMF` is the angle lie in semicircle, so `""angleAMF=90^(@)` `implies""FMbotAM` Since, FM is radius of the circle. So, AM has to be tangent of the circle with centre F. Similarly, AB is also a tangent to the circle with centre F. 
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| 553. |
At a point on level ground, the angle of elevation of the top of a tower is found to be such that its tangent is (5)/(12). On walking 192 m towards the tower, the tangent of the angle of elevation is (3)/(4). Find the height of the tower. |
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| 554. |
Given that AB = 5 cm angle BAC=30^(@), angleABC= 60^(@) , angleBAD = 45^(@) , angleABD = 45^(@)Construct two triangles DeltaABCand DeltaABCin sucha waythatthepointC and Dlie on opposite sideof AB. By drawingthe circumcirleof Delta ABCwritethe positionof the pointD with respect to thecircumcricle . Also statewhat othercharacteristics you are observinghere. |
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| 555. |
Find the area of the triangle formed by joining the midpoints of thesides of thetrianglewhose vertices are (0,-1), (2,1) and (0,3) . Find the ratio of this area tothe areaof the given triangle . |
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| 557. |
Calculate the height of a right circular cone where C.S.A. and base radius are 12320cm^(2) and 56 cms, respectively . |
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| 558. |
If the sum of first 8 terms of arithmetic progressions is 136 and that of first 15 terms is 465, then find the sum of first 25 terms. OR The sum of the 5^(th) and 9^(th) terms of an arithmetic progression is 40 and the sum of the 8^(th) and 14^(th) term is 64, find the sum of first 20 terms. |
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| 559. |
A cone of height 15 cm and diameter 7 cm is mounted on a hemisphere of same diameter. Determine the volume of the solid thus formed. |
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| 560. |
If A (20,10) ,B (0,20)are given , find the co- ordinates of the points which divide segment AB into five congruent parts. |
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| 561. |
In which quadrant, the point which divides the line segment joining the points (5, 4) and (-6, -7) in the ratio 1 : 3 internally lies? |
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| 562. |
Show that cot theta +tan theta =sec theta cosec theta |
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| 563. |
A heap of wheat is in the form of a cone of diameter 16.8 m and height 3.5 m. Find its volume. How much cloth is required to just cover the heap ? |
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| 564. |
Determine the ratio of volume of a cube and a right circular cone that can be fit into the cube whose side is alpha units. |
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| 565. |
The ratio of the volumes of two cones is 4:5 and the ratio of their radii is 2:3. Then, the ratio of their heights is ..... |
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| 566. |
Prove that (cos A)/(1+sinA)+(1+sinA)/(cosA)=2secA. |
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| 567. |
Find the number of tangents that can be drawn to two internally touching circles. |
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| 568. |
Determine the value of the following. log_(25)5 |
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| 569. |
A solid consisting of a right circular cone standing on a hemisphere , is placed upright in a right circular cylinder full of water and touching the bottom. Find the volume of water left in the cylinder , given that the radius of the cylinder is 3 cm and its height is 6 cm The radius of the hemisphere is 2 cm and the height of the cone is 4 cm . (Take pi =(22)/(7)). |
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| 570. |
If two sides of a cyclic quadrilateralare parallel , prove that the other two sides are equal |
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| 571. |
Find the roots of the equation (1)/(x)-(1)/(x-2)=3, x ne 0,2 |
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| 572. |
2 cubes each of volume 64cm^(3)are joined end to end . Find the surface area of the resulting cuboid. |
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| 573. |
Diameter of a right circular cylinder is 14cm and hight is 15cm,find its lateral surface. |
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| 574. |
Constract an equilaterial triangle ABC of sides 5 cm each and then construct its circumcircle . Draw a tangent at Aof the circleand then a point P onit such that AP=5 cm . Draw another tangent to the circle from the point P and observe minutely at point of the circle this tangent intersects. |
Answer» Solution :From the FIGURE , we SEE that ANOTHER tangent from P touches the circle at the POINT C. 
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| 575. |
If alpha and beta are zeros of polynomial f(x) = 2x^2 + 11x + 5, then find (i) alpha^(4) + beta^(4), (ii) 1/alpha + 1/beta -2 alpha beta |
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| 578. |
If circumference of a circle is 44 cm, then what will be the area of the circle ? |
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| 580. |
The polynomials 2x^3- 7x^2 + ax -6 and x^3-8x^2 +(2a + 1)x- 16 leave the same remainder when divided by x- 2. Find the value of a |
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| 581. |
If the point (x , y) , (-5, -2) and (3, -5) are collinear, prove that 3x+8y+31=0. |
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| 582. |
Find the coordinates of the points which divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts. |
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| 583. |
A pen stand is made of wood in the shape of cuboid with three conical depressions to hold the pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depression is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand. |
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| 584. |
Draw a circle with radius 4cm and draw a tangent at any point on the circle. |
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| 585. |
A dia is thrown once, what is the probability of getting a prime number? |
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| 586. |
Attempt this question on graph paper. Write down : the image A'' of A . When A is reflected in the origin. |
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| 587. |
Solve for x and y 41x+53y=135 53x+41y=417 |
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| 588. |
Check whether the following are quadratic equation: x^(2)+3x+1=(x-2)^(2) |
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| 589. |
If A=[{:(,4,-4),(,-3,3):}], B=[{:(,6,5),(,3,0):}] and C=[{:(,2,3),(,-1,-2):}] show that AB=AC. Write the conclusion, if any, that you can draw from the result obtained above. |
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| 590. |
For the A.P. 10, 15,20,…..195, find: (i) the number of terms in the above A.P. (ii) the sum of all its terms. |
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| 591. |
Find the value of 'a' if the division of ax^(3)+9x^(2)+4x-10 by x+3 leaves a remainder of 5. |
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| 592. |
To divide a line segment internally in the ratio 4:7, the number of arcs to be drawn on a ray inclined to the line segment is ....... |
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Answer» 4 |
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| 593. |
Interrup: Speak :: ? |
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Answer» Shout : Yell |
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| 594. |
We have a linear quations 2x + 3y - 8 = 0. Write another linear equation in two variables x and y such that the geometrical representation of the pair so formed is intersecting lines. Now, write two more linear equations so that one forms a pair of parllel lines and the second forms coincident line with the given equation. |
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Answer» (II) 4x + 6Y - 10 = 0 (iii) 6x +9y - 24 = 0 |
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| 595. |
A man sells 60 , 15rs shares of a company paying 12 percent dividend, at21rs each and invests the proceedsin 6rs shares of another company at 9rs each. Find his change in income, if the second company pays a dividend of 8 percent |
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| 596. |
Let f : R -{(-4)/(3)} to -{(4)/(3)} : f (x) =(4x)/((3x+4)) . " Then " f^(-1) (y)=? |
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| 597. |
A survey regarding the heights (in cm) of 51 girls of Class X of a school was conducted and data was obtained as shown in table. Find their median. |
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| 598. |
A sphere, a cylinder and a cone have the same radius and same height. Find the ratio of their volumes. [Hint : Diameter of the sphere is equal to the heights of the cylinder and the cone.] |
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| 599. |
Fill the blank: Roots of the equation x^2=6x are______________ |
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| 600. |
If the first and the third terms of a G.P. are 2 and 8 respectively, find its second term. |
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