3694 + Interview Questions in Maths in Class 10 Page 58 InterviewSolution

2851.	Attempt this question on graph paper. Write down : the geometrical name of the figure ABB'A'
Answer» ANSWER :ISOSCELES TRAPEZIUM

Discussion

2852.	How many two-digit numbes leave the remainder 1 when divided by 5? Find the sum of all these numbers.
Answer» Solution :The first two-digit number divisible by 5 is `5xx2=10`. The LAST two digit number divisible by 5 is `5xx9=95` ( `:'5xx20=100` is a three digig number) We want two-digit numbers which would LEAV REMAINDER 1 when dividied by 5. `:.` the first two-digit number is `10+1=11` and the last one is `95+1=96` Here `t_(1)=a=11` and `t_(n)=96, d=5` `t_(n)=a+(n-1)d`....(FORMULA) `:.96=11+(n-1)xx5` ...(Substituting the values) `:.96-11=(n-1)xx5` `:.85=(n-1)xx5` `:.n-1=85/5:.n-1=17:.n=17+1:.n=18` Now `S_(n)=n/2[a+l]` `:.S_(18)=18/2(11+96)` .........( `:' a=11` and `t_(18)=96`) `-9xx107` `=963` Ans. There are 18 two-digit numbers which leave remainder 1 when divided by 5. The sum of all these number is 963.

Discussion

2853.	Prove that: 2 sec^(2) theta - sec^(4) theta - 2 "cosec"^(2) theta = cot^(4) theta - tan^(4) theta.
Answer» ANSWER :`COT^(4) theta - TAN^(4) theta ` = RHS.

Discussion

2854.	If sum of the coefficients of thefirst two odd terms of the expansion (x+y)^(n) is 16,then find n
Answer» 10 8 7 6 Solution :PUT y=1and PROCEED

Discussion

2855.	From a point Q ,the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm . The radius of the circle is
Answer» `7CM` `12CM` `15CM` `24.5cm` ANSWER :A

Discussion

2856.	A geometric progression has common ratio = 3 and last term = 486. If the sum of its terms is 728, find its first term.
Answer» ANSWER :2

Discussion

2857.	Find the 41st term of an AP whose 13th term is 79 and 26th term is 157.
Answer» ANSWER :247

Discussion

2858.	Find the distance between two parallel tangents drawn to a circle.
Answer» ANSWER : EQUAL to DIAMETER

Discussion

2859.	Find the roots of the following equations by factorisation. (ii) x(x-1)=30
Answer» ANSWER :`X=6` or `x= -5` are the ROOTS.

Discussion

2860.	If thelengths of twoparallelchords are16 cmand 30 cmrespectively and theradiusof the circleis 7 cm, thendistance of two chords is
Answer» 7 CM 5 cm 14 cm 8 cm ANSWER :B

Discussion

2861.	If the distance of point P from the centre of the circle is 13 cm and the radius of the circle is 5 cm, then length of the tangent drawn from P to the circle is :
Answer» 8 cm 6.5 cm 9 cm 12 cm. Answer :D

Discussion

2862.	A container shpaed like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice creqa. The ice cream is to be filled into cones of height 12 cmand diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Answer» ANSWER :10 CONES

Discussion

2863.	If sin 3 theta = cso ( theta - 6^(@)) where 3 theta and theta - 6^(@) are both acute angles, find the value of theta.
Answer» ANSWER :`THETA = 24^(@)`.

Discussion

2864.	A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder.
Answer» ANSWER :6.5 m

Discussion

2865.	Express sin 81^(@) +tan 81^(@) in terms of trigonometric ratio of angles between 0^(@) and 45^(@)
Answer» Answer :Then `,sin 81^(@) +TAN 81^(@) =COS 9^(@) +COT 9^(@) `

Discussion

2866.	If x=1(1)/(2) is a solution of the equation 2x^(2)+px-6=0, find the value of 'p'.
Answer» ANSWER :`p=1`

Discussion

2867.	Two circles with centre at A and B touch each other at C. Common tangents PQ and RC are drawn. If \|__PAC=50^(@), find \|__PRC and \|__CBQ.
Answer» ANSWER :`130^(@)`.

Discussion

2868.	Consultancy services, worth Rs. 50,000 are transferred from Delhi to Culcutta at the rate of GST 18% and then from Calcutta to Nainital (with profit = Rs. 20,000) at the same rate of GST. Find the output tax at : Nainital [Consider the dealer at Nainital as end - user].
Answer» ANSWER :RS. 00

Discussion

2869.	Consultancy services, worth Rs. 50,000 are transferred from Delhi to Culcutta at the rate of GST 18% and then from Calcutta to Nainital (with profit = Rs. 20,000) at the same rate of GST. Find the output tax at : Delhi [Consider the dealer at Nainital as end - user].
Answer» ANSWER :RS. 9,000

Discussion

2870.	Consultancy services, worth Rs. 50,000 are transferred from Delhi to Culcutta at the rate of GST 18% and then from Calcutta to Nainital (with profit = Rs. 20,000) at the same rate of GST. Find the output tax at : Calcutta [Consider the dealer at Nainital as end - user].
Answer» ANSWER :RS. 12,600

Discussion

2871.	Verify that point P (-2,2), Q (2,2) and R (2,7) are vertices of a right angled triangle .
Answer» Answer :`THEREFORE ` Points P , Q and R are the VERTICES of a right ANGLED triangle.

Discussion

2872.	A motor boat heads upstream a distance of 24km on a river whose current is running at 3km per hours. Assuming that the motor boat maintained a constant speed, what was its speed ?
Answer» ANSWER :9 KMPH

Discussion

2873.	If a+ b+ c=0 what is the value of (a^2 + b^2 + ab)/( b^2 + c^2 + bc) + (c^2 + ca+ a^2)/( b^2 + c^2 + bc) ?
Answer» ANSWER :`2`

Discussion

2874.	Write GP. If a=256, r=-1/2
Answer» ANSWER :`=256, -128, 64, -32`,…….

Discussion

2875.	For the quadratic equation 3x^(2)+5x-2=0, show that : (i) x=(1)/(3) is a solution. (ii) x=3 is not a solution.
Answer» ANSWER :(i) `X=(1)/(3)` is a solution of the given EQUATION. (ii) `x=3` is not a solution of the given equation.

Discussion

2876.	GiventhatPQ = 4 cm , QR= 6 cm . Constructthe recatnglePQRS . Alsodrawthe diagonalsoftherectangle and withoutdrawingthe circumcirclewritethe positionof thecentreof thecircumcirleof Delta PQRandfind thelengthof cirumradius. Afterall by drawingthe cirumcircleof Delta PQRvarifyyour answer .
Answer» ANSWER :`SQRT(13) CM`

Discussion

2877.	If Q((a)/(3),4) is the mid-point of the line segement joining the points A(-6, 5) and B(-2, 3), then the value of 'a' is
Answer» 4 `-6` `-8` `-12` ANSWER :D

Discussion

2878.	In the following frequency distribution, find the median class. What is the value of model marks ?
Answer» 155.25 156.25 157.25 159.25 Solution :Here, `l=155,f_(1)=30,f_(0)=25,f_(2)=15` and `h=5` Mode, `""M_(o)=l+h((f_(1)-f_(0))/(2f_(1)-f_(0)-f_(2)))=155+(30-25)/(60-25-15)XX5` `=155+(5)/(20)xx5` `=155+1.25=156.25` Thus (b) is CORRECT option.

Discussion

2879.	The radius of conical tent is 7 meters and its height is 10 meters. Calculate the length of canvas used in making the tent if the width of canvas is 2 m [ Use pi= (22)/7]
Answer» ANSWER :134.2 m

Discussion

2880.	Find a relation between x and y such that the point (x, y) is equidistant from the points (-2, 8) and (-3, -5)
Answer» ANSWER :X + 13Y – 17 = 0

Discussion

2881.	A man saved Rs 200 during the first month, Rs 225 in the second month and in this way he increases his savings by Rs 25 every month. Find in what time his saving will be Rs 13325.
Answer» ANSWER :26 MONTHS

Discussion

2882.	Using a ruler and compasses only: Construct a triangle ABC with the following data: AB = 3*5 cm, BC =6 cm and angle ABC=120^(@)
Answer» ANSWER :`30^@`

Discussion

2883.	Two dice are rolled simultaneously. Find the probability of : getting a multiple of 3 as the sum.
Answer» ANSWER :`1/3`

Discussion

2884.	An integer is chosen between 0 and 100. what is the probability that it is divisible by 10?
Answer» 1/10 1/11 1/100 1/99 Answer :`1/(11)`

Discussion

2885.	A man invests 7770rs in a company paying 5 percent dividend when a share of nominal value of 100rs sells at a premium of 5rs. Find. (i) the number of shares bought (ii) annual income (iii) percentage income
Answer» ANSWER :`(i)74` `(II)370rs` `(III) 4.76%`

Discussion

2886.	A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, if would have taken 1 hour less for the same journey. Find the speed of the train.
Answer» ANSWER :40 KMPH

Discussion

2887.	if L is the point of trisection nearer to B of the side BC of the triangle ABC, prove that 2AB^(2)+ AC^(2)= 3AL^(2)+CL^(2)
Answer»

Discussion

2888.	Find the roots of the quadratic equation 6x^2 - x - 2 = 0.
Answer» ANSWER :`2/3 and 1`

Discussion

2889.	Find the roots of the equation x+(1)/(x)=3, x ne 0
Answer» ANSWER :`(3+sqrt(5))/(2) and (3-sqrt(5))/(2)`

Discussion

2890.	How many number from 1 to 50 are there each of which is not exactly divisible by 4 but also contain 4 as a digit in it?
Answer» 5 4 7 8 Solution :The REQUIRED NUMBERS are 4,24,40,44,48 There are five such NUMBER which contain 4 as a digit in each and also divisible by4.

Discussion

2891.	Line L has intercepts a and b on the coordinate axes. When the axes are rotated through a fixed given angle keeping the origin fixed, the same line L has intercepts P and q, then
Answer» `1/p^2+1/q^2` `1/p^2-1/q^2` `p^2+ q^2=1` None Answer :A

Discussion

2892.	A toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of the conical portion is 12 cm and its height is 8 cm. Determine the surface area and the volume of the toy (pi = 3.14).
Answer» ANSWER :`753 .6 CM ^(3)`

Discussion

2893.	2 cubes each of volume 64cm^(3) joined end to end. Find the surface area of the resulting cuboid.
Answer» ANSWER :`160 cm^2`

Discussion

2894.	Find the roots of the quadratic equations by factorisation: 3x^(2)-5x+2=0
Answer» ANSWER :`1;(2)/(3)`

Discussion

2895.	Choose the correct answer and give justification for each. (ii) From a point Q, the length of the tangent to a circle is 24 cm. and the distance of Q from the centre is 25 cm. The radius of the circle is7cm12cm15cm24.5cm
Answer» `7CM` `12CM` `15CM` `24.5cm` ANSWER :A

Discussion

2896.	Findthe ratio in whichthe points (-1,k) divides the line joining the points(-3,10) and (6,-8)
Answer» ANSWER :HENCE , REQUIRED RATIO = ,:N = 2:7

Discussion

2897.	Whatdo you observe ?
Answer» ANSWER :Weobserve that the AREA FORMED by above all TRIANGLES is ZERO .

Discussion

2898.	The speed of sound is 332 metres per second. A gun is fired. Describe the locus of all the people on the earth's surface, who hear the sound exactly after one second ?
Answer» ANSWER :332 m

Discussion

2899.	Mukul invests 9000rs in a company paying a dividend of 6% per annum whena share of face value 100rs stands at 150rs. What is his annual income ? If he sells 50% of his shares at 200rs each , what is his gain in this transaction ?
Answer» ANSWER :`360RS, 1500RS`

Discussion

2900.	Find the value of ‘K’ for which the points are collinear (8, 1), (K, -4), (2, -5)
Answer» ANSWER :K=3

Discussion

Explore topic-wise InterviewSolutions in .

Attempt this question on graph paper. Write down : the geometrical name of the figure ABB'A'

How many two-digit numbes leave the remainder 1 when divided by 5? Find the sum of all these numbers.

Prove that: 2 sec^(2) theta - sec^(4) theta - 2 "cosec"^(2) theta = cot^(4) theta - tan^(4) theta.

If sum of the coefficients of thefirst two odd terms of the expansion (x+y)^(n) is 16,then find n

From a point Q ,the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm . The radius of the circle is

A geometric progression has common ratio = 3 and last term = 486. If the sum of its terms is 728, find its first term.

Find the 41st term of an AP whose 13th term is 79 and 26th term is 157.

Find the distance between two parallel tangents drawn to a circle.

Find the roots of the following equations by factorisation. (ii) x(x-1)=30

If thelengths of twoparallelchords are16 cmand 30 cmrespectively and theradiusof the circleis 7 cm, thendistance of two chords is

If the distance of point P from the centre of the circle is 13 cm and the radius of the circle is 5 cm, then length of the tangent drawn from P to the circle is :

A container shpaed like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice creqa. The ice cream is to be filled into cones of height 12 cmand diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

If sin 3 theta = cso ( theta - 6^(@)) where 3 theta and theta - 6^(@) are both acute angles, find the value of theta.

A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder.

Express sin 81^(@) +tan 81^(@) in terms of trigonometric ratio of angles between 0^(@) and 45^(@)

If x=1(1)/(2) is a solution of the equation 2x^(2)+px-6=0, find the value of 'p'.

Two circles with centre at A and B touch each other at C. Common tangents PQ and RC are drawn. If |__PAC=50^(@), find |__PRC and |__CBQ.

Consultancy services, worth Rs. 50,000 are transferred from Delhi to Culcutta at the rate of GST 18% and then from Calcutta to Nainital (with profit = Rs. 20,000) at the same rate of GST. Find the output tax at : Nainital [Consider the dealer at Nainital as end - user].

Consultancy services, worth Rs. 50,000 are transferred from Delhi to Culcutta at the rate of GST 18% and then from Calcutta to Nainital (with profit = Rs. 20,000) at the same rate of GST. Find the output tax at : Delhi [Consider the dealer at Nainital as end - user].

Consultancy services, worth Rs. 50,000 are transferred from Delhi to Culcutta at the rate of GST 18% and then from Calcutta to Nainital (with profit = Rs. 20,000) at the same rate of GST. Find the output tax at : Calcutta [Consider the dealer at Nainital as end - user].

Verify that point P (-2,2), Q (2,2) and R (2,7) are vertices of a right angled triangle .

A motor boat heads upstream a distance of 24km on a river whose current is running at 3km per hours. Assuming that the motor boat maintained a constant speed, what was its speed ?

If a+ b+ c=0 what is the value of (a^2 + b^2 + ab)/( b^2 + c^2 + bc) + (c^2 + ca+ a^2)/( b^2 + c^2 + bc) ?

Write GP. If a=256, r=-1/2

For the quadratic equation 3x^(2)+5x-2=0, show that : (i) x=(1)/(3) is a solution. (ii) x=3 is not a solution.

GiventhatPQ = 4 cm , QR= 6 cm . Constructthe recatnglePQRS . Alsodrawthe diagonalsoftherectangle and withoutdrawingthe circumcirclewritethe positionof thecentreof thecircumcirleof Delta PQRandfind thelengthof cirumradius. Afterall by drawingthe cirumcircleof Delta PQRvarifyyour answer .

If Q((a)/(3),4) is the mid-point of the line segement joining the points A(-6, 5) and B(-2, 3), then the value of 'a' is

In the following frequency distribution, find the median class. What is the value of model marks ?

The radius of conical tent is 7 meters and its height is 10 meters. Calculate the length of canvas used in making the tent if the width of canvas is 2 m [ Use pi= (22)/7]

Find a relation between x and y such that the point (x, y) is equidistant from the points (-2, 8) and (-3, -5)

A man saved Rs 200 during the first month, Rs 225 in the second month and in this way he increases his savings by Rs 25 every month. Find in what time his saving will be Rs 13325.

Using a ruler and compasses only: Construct a triangle ABC with the following data: AB = 3*5 cm, BC =6 cm and angle ABC=120^(@)

Two dice are rolled simultaneously. Find the probability of : getting a multiple of 3 as the sum.

An integer is chosen between 0 and 100. what is the probability that it is divisible by 10?

A man invests 7770rs in a company paying 5 percent dividend when a share of nominal value of 100rs sells at a premium of 5rs. Find. (i) the number of shares bought (ii) annual income (iii) percentage income

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, if would have taken 1 hour less for the same journey. Find the speed of the train.

if L is the point of trisection nearer to B of the side BC of the triangle ABC, prove that 2AB^(2)+ AC^(2)= 3AL^(2)+CL^(2)

Find the roots of the quadratic equation 6x^2 - x - 2 = 0.

Find the roots of the equation x+(1)/(x)=3, x ne 0

How many number from 1 to 50 are there each of which is not exactly divisible by 4 but also contain 4 as a digit in it?

Line L has intercepts a and b on the coordinate axes. When the axes are rotated through a fixed given angle keeping the origin fixed, the same line L has intercepts P and q, then

A toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of the conical portion is 12 cm and its height is 8 cm. Determine the surface area and the volume of the toy (pi = 3.14).

2 cubes each of volume 64cm^(3) joined end to end. Find the surface area of the resulting cuboid.

Find the roots of the quadratic equations by factorisation: 3x^(2)-5x+2=0

Choose the correct answer and give justification for each. (ii) From a point Q, the length of the tangent to a circle is 24 cm. and the distance of Q from the centre is 25 cm. The radius of the circle is7cm12cm15cm24.5cm

Findthe ratio in whichthe points (-1,k) divides the line joining the points(-3,10) and (6,-8)

Whatdo you observe ?

The speed of sound is 332 metres per second. A gun is fired. Describe the locus of all the people on the earth's surface, who hear the sound exactly after one second ?

Mukul invests 9000rs in a company paying a dividend of 6% per annum whena share of face value 100rs stands at 150rs. What is his annual income ? If he sells 50% of his shares at 200rs each , what is his gain in this transaction ?

Find the value of ‘K’ for which the points are collinear (8, 1), (K, -4), (2, -5)

Two circles with centre at A and B touch each other at C. Common tangents PQ and RC are drawn. If |PAC=50^(@), find |PRC and |__CBQ.