24740 + Interview Questions in Mathematics Page 54 InterviewSolution

2651.	Question 7 (iv)Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC.(d) What do you observe?
Answer» Question 7 (iv) Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC. (d) What do you observe?

Discussion

2652.	Question 180(i)Simplify[(12)2−(14)3]−1×2−3
Answer» Question 180(i) Simplify ${[{(\frac{1}{2})}^{2} - {(\frac{1}{4})}^{3}]}^{- 1} \times 2^{- 3}$

2652.

Question 180(i)Simplify[(12)2−(14)3]−1×2−3

Answer»

Question 180(i)

Simplify

${[{(\frac{1}{2})}^{2} - {(\frac{1}{4})}^{3}]}^{- 1} \times 2^{- 3}$

Discussion

2653.	If 8:2 is greater than 5:a, then the value of a is greater than _____.
Answer» If 8:2 is greater than 5: $a$ , then the value of a is greater than _____.

Discussion

2654.	The population of my country increases at 5% per annum. What type of increase is this?
Answer» The population of my country increases at 5% per annum. What type of increase is this?

Discussion

2655.	The curved surface area of a hemisphere of diameter 28 cm is
Answer» The curved surface area of a hemisphere of diameter 28 cm is

Discussion

2656.	In the adjoining figure, BM⊥AC and DN⊥AC. If BM=DN, prove that AC bisects BD.
Answer» In the adjoining figure, $B M ⊥ A C$ and $D N ⊥ A C$ . If $B M = D N$ , prove that $A C$ bisects $B D$ .

2656.

In the adjoining figure, BM⊥AC and DN⊥AC. If BM=DN, prove that AC bisects BD.

Answer»

In the adjoining figure, $B M ⊥ A C$ and $D N ⊥ A C$ . If $B M = D N$ , prove that $A C$ bisects $B D$ .

Discussion

2657.

Working in pairs give antonyms of the following words. kind- hearted unscrupulous forgiving stern benevolent credulous generous pious suspicious sympathetic understanding wild innocent penitent clever brutal cunning caring sentimental trusting protective concerned honourable embittered

Answer»

Working
in pairs give antonyms of the following words.

kind- hearted	unscrupulous	forgiving	stern	benevolent	credulous
generous	pious	suspicious	sympathetic	understanding	wild
innocent	penitent	clever	brutal	cunning	caring
sentimental	trusting	protective	concerned	honourable	embittered

Discussion

2658.	Consider the below figure. Here, z = ___.
Answer» Consider the below figure. Here, $z$ = ___.

Discussion

2659.	Prove that ʃdx/√(1+x²)=log\|x+√(x²+1)\|
Answer» Prove that ʃdx/√(1+x²)=log\|x+√(x²+1)\|

Discussion

2660.	A cylindrical container of diameter 42 m and height 24 m is full of diesel. The diesel is emptied into a rectangular pool of length 132 m and breadth 56 m. Find the height of which diesel rises in pool.
Answer» A cylindrical container of diameter 42 m and height 24 m is full of diesel. The diesel is emptied into a rectangular pool of length 132 m and breadth 56 m. Find the height of which diesel rises in pool.

Discussion

2661.	Find the value of a and b, if they are the zeroes of polynomial x^2 + ax + b.
Answer» Find the value of a and b, if they are the zeroes of polynomial x^2 + ax + b.

Discussion

2662.	Solve for x: log3(x3)+log1/9(x)<1
Answer» Solve for $x$ : $l o g_{3} (\frac{x}{3}) + l o g_{1 / 9} (x) < 1$

2662.

Solve for x: log3(x3)+log1/9(x)<1

Answer»

Solve for $x$ :

$l o g_{3} (\frac{x}{3}) + l o g_{1 / 9} (x) < 1$

Discussion

2663.	Simultaneous linear equations 1) Twice one number minus three times the second is equal to 2 ; and the sum of the number is 11 find number. 2). The sum of a two digit number and the number obtained on reversing the digits is 165 .If the digits differ by 3, find the number.
Answer» Simultaneous linear equations 1) Twice one number minus three times the second is equal to 2 ; and the sum of the number is 11 find number. 2). The sum of a two digit number and the number obtained on reversing the digits is 165 .If the digits differ by 3, find the number.

2663.

Simultaneous linear equations 1) Twice one number minus three times the second is equal to 2 ; and the sum of the number is 11 find number. 2). The sum of a two digit number and the number obtained on reversing the digits is 165 .If the digits differ by 3, find the number.

Answer»

Simultaneous linear equations

1) Twice one number minus three times the second is equal to 2 ; and the sum of the number is 11 find number.

2). The sum of a two digit number and the number obtained on reversing the digits is 165 .If the digits differ by 3, find the number.

Discussion

2664.	In a ΔABC, if AB=AC and ∠B=70∘, find ∠A.
Answer» In a $Δ A B C, i f A B = A C a n d ∠ B = 70^{\circ}, f i n d ∠ A .$

Discussion

2665.	ntABCD is a parallelogram and P is the midpoint of the side BC. Prove using vector algebra ( not by geometric process) that AC and DP meet in a common point of trisection.n
Answer» ntABCD is a parallelogram and P is the midpoint of the side BC. Prove using vector algebra ( not by geometric process) that AC and DP meet in a common point of trisection.n

Discussion

2666.	In the experiment of finding volume of a solid by immersing it into water, the initial reading of the water level in the graduated cylinder was 16.2 ml. On immersing the given solid completely into water, the water level rose to 19.7ml. Find the volume of the solid
Answer» In the experiment of finding volume of a solid by immersing it into water, the initial reading of the water level in the graduated cylinder was 16.2 ml. On immersing the given solid completely into water, the water level rose to 19.7ml. Find the volume of the solid

Discussion

2667.	Factorise:35x2-195x+4
Answer» Factorise: $\frac{3}{5} x^{2} - \frac{19}{5} x + 4$

Discussion

2668.	If →b is the vector whose initial point divides the joining 5→i and 5→j in the ratio λ:1 and terminal point is at origin. If \|→b\|≤√37, then set of values of λ is
Answer» If $\to b$ is the vector whose initial point divides the joining $5 \to i$ and $5 \to j$ in the ratio $λ : 1$ and terminal point is at origin. If $\| \to b \| \leq \sqrt{37},$ then set of values of $λ$ is

Discussion

2669.	P is any point on the diagonal AC of a parallelogram ABCD. Prove that ar(∆ADP) = ar(∆ABP).
Answer» P is any point on the diagonal AC of a parallelogram ABCD. Prove that ar(∆ADP) = ar(∆ABP).

Discussion

2670.	Which of the following fractions is equal to 1√5−√7?
Answer» Which of the following fractions is equal to $\frac{1}{\sqrt{5} - \sqrt{7}}$ ?

Discussion

2671.	Can we construct a quadrilateral PQRS with PQ = 3 cm, RS = 3 cm, PS = 7.5 cm, PR = 8cm and SQ = 4 cm. Justify your result.
Answer» Can we construct a quadrilateral PQRS with PQ = 3 cm, RS = 3 cm, PS = 7.5 cm, PR = 8cm and SQ = 4 cm. Justify your result.

Discussion

2672.	A soft drink is available in two packs-(i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?
Answer» A soft drink is available in two packs-(i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?

Discussion

2673.	In a Δ ABC, P and Q are respectively the mid-points of AB and BC and R is the mid-point of AP. Prove that:(i) ar (Δ PBQ) = ar (Δ ARC)(ii) ar (Δ PRQ) = 12 ar (Δ ARC)(iii) ar (Δ RQC) = 38 ar (Δ ABC).
Answer» In a Δ ABC, P and Q are respectively the mid-points of AB and BC and R is the mid-point of AP. Prove that: (i) ar (Δ PBQ) = ar (Δ ARC) (ii) ar (Δ PRQ) = $\frac{1}{2}$ ar (Δ ARC) (iii) ar (Δ RQC) = $\frac{3}{8}$ ar (Δ ABC).

Discussion

2674.	Question 1Write True or False and justify your answer :Two chords AB and CD of a circle are each at a distance of 4 cm from the centre, then AB = CD.
Answer» Question 1 Write True or False and justify your answer : Two chords AB and CD of a circle are each at a distance of 4 cm from the centre, then AB = CD.

Discussion

2675.	Ice cream rates for 12 months in 2018 are given below: January - Rs.190 , February - Rs.210 , March - Rs.250 , April - Rs.200 , May - Rs.225 , June - Rs.265 , July - Rs.270 , August - Rs.240 , September - Rs.217, October - Rs.203 , November - Rs.180, December - Rs.170 Find the Mean rate of the ice cream for the year 2018.
Answer» Ice cream rates for 12 months in 2018 are given below: January - Rs.190 , February - Rs.210 , March - Rs.250 , April - Rs.200 , May - Rs.225 , June - Rs.265 , July - Rs.270 , August - Rs.240 , September - Rs.217, October - Rs.203 , November - Rs.180, December - Rs.170 Find the Mean rate of the ice cream for the year 2018.

2675.

Ice cream rates for 12 months in 2018 are given below: January - Rs.190 , February - Rs.210 , March - Rs.250 , April - Rs.200 , May - Rs.225 , June - Rs.265 , July - Rs.270 , August - Rs.240 , September - Rs.217, October - Rs.203 , November - Rs.180, December - Rs.170 Find the Mean rate of the ice cream for the year 2018.

Answer»

Ice cream rates for 12 months in 2018 are given below:

January - Rs.190 , February - Rs.210 , March - Rs.250 , April - Rs.200 , May - Rs.225 , June - Rs.265 ,

July - Rs.270 , August - Rs.240 , September - Rs.217, October - Rs.203 , November - Rs.180, December - Rs.170

Find the Mean rate of the ice cream for the year 2018.

Discussion

2676.	Explain the meaning of diminishing marginal rate of substitution with the help of a numerical example.
Answer» Explain the meaning of diminishing marginal rate of substitution with the help of a numerical example.

Discussion

2677.	If AD and PM are medians of ΔABC and ΔPQR respectively, where ΔABC ~ ΔPQR; prove that ABPQ=ADPM.
Answer» If AD and PM are medians of ΔABC and ΔPQR respectively, where ΔABC ~ ΔPQR; prove that $\frac{A B}{P Q} = \frac{A D}{P M}$ .

Discussion

2678.	What universal set(s) would you propose for each of the following?(i) The set of right triangles.(ii) The set of isosceles triangles.
Answer» What universal set(s) would you propose for each of the following? $(i)$ The set of right triangles. $(i i)$ The set of isosceles triangles.

Discussion

2679.	23. 7 white balls and 3 black balls are placed in a row at random.the probabilty that no two black balls are ajacent is
Answer» 23. 7 white balls and 3 black balls are placed in a row at random.the probabilty that no two black balls are ajacent is

Discussion

2680.	ABCD is a rhombus If area (ABCD)=24 cm2 and AC=8 cm, find the measure of the side of the rhombus.
Answer» ABCD is a rhombus If area $(A B C D) = 24 c m^{2}$ and AC=8 cm, find the measure of the side of the rhombus.

Discussion

2681.	Among a cylinder (of radius r and height h=r), a cone (of radius r and height h=r) and a sphere of radius r the __ will have the maximum volume.
Answer» Among a cylinder (of radius r and height h=r), a cone (of radius r and height h=r) and a sphere of radius r the __ will have the maximum volume.

Discussion

2682.	If x + 1 is a factor of the polynomial 2x3 + ax2 + 4x + 1, then a = _________.
Answer» If x + 1 is a factor of the polynomial 2x³ + ax² + 4x + 1, then a = _________.

Discussion

2683.	AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD=∠ABEand∠EPA=∠DPB (See the given figure). Show thatΔDAP≅ΔEBP
Answer» AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that $∠ B A D = ∠ A B E a n d ∠ E P A = ∠ D P B$ (See the given figure). Show that $Δ D A P ≅ Δ E B P$

Discussion

2684.	Question 58 Fill in the blanks to make the statements true. The measure of each exterior angle of a regular pentagon is ___.
Answer» Question 58 Fill in the blanks to make the statements true. The measure of each exterior angle of a regular pentagon is ___.

Discussion

2685.	Factorise x3+x+2 Please answer as soon as possible because I have my exams tomorrow.
Answer» Factorise x3+x+2 Please answer as soon as possible because I have my exams tomorrow.

Discussion

2686.	Solve for x in the equation log[log(2+log2(x+1))]=0
Answer» $Solve for x in the equation$ $l o g [l o g (2 + l o g_{2} (x + 1))] = 0$

Discussion

2687.	Question 8 (ii)Express 121 as the sum of 11 odd numbers.
Answer» Question 8 (ii) Express 121 as the sum of 11 odd numbers.

Discussion

2688.	□ PTNM is a rectangle. Write the names of the pairs of supplementary angles.
Answer» $□$ PTNM is a rectangle. Write the names of the pairs of supplementary angles.

Discussion

2689.	Which of these triangles can actually be constructed?
Answer» Which of these triangles can actually be constructed?

Discussion

2690.	In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle. If the radius of the larger circle is 5 cm then Find the radius of the smaller circle. [CBSE 2013C]
Answer» In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle. If the radius of the larger circle is 5 cm then Find the radius of the smaller circle. [CBSE 2013C]

Discussion

2691.	Two lines are perpendicular to each other. Then the angle between the lines is
Answer» Two lines are perpendicular to each other. Then the angle between the lines is

Discussion

2692.	ABCD is a parallelogram and E and F are the centroids of triangles ABD and BCD respectively, then EF =(a) AE(b) BE(c) CE(d) DE
Answer» ABCD is a parallelogram and E and F are the centroids of triangles ABD and BCD respectively, then EF = (a) AE (b) BE (c) CE (d) DE

Discussion

2693.	Numbers 1 to 10 is written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of getting a number greater than 6?
Answer» Numbers 1 to 10 is written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of getting a number greater than 6?

Discussion

2694.	In the following figure, if the chords AB and CD are equal to 6 cm then the distance of the chords from the centre of the circle of radius 5 cm will be:
Answer» In the following figure, if the chords AB and CD are equal to 6 cm then the distance of the chords from the centre of the circle of radius 5 cm will be:

2694.

In the following figure, if the chords AB and CD are equal to 6 cm then the distance of the chords from the centre of the circle of radius 5 cm will be:

Answer»

In the following figure, if the chords AB and CD are equal to 6 cm then the distance of the chords from the centre of the circle of radius 5 cm will be:

Discussion

2695.	If 35x×812×656132x=37, then x =(a) 3(b) −3(c) 13(d) -13
Answer» If $\frac{3^{5 x} \times 81^{2} \times 6561}{3^{2 x}} = 3^{7}$ , then x = (a) 3 (b) −3 (c) $\frac{1}{3}$ (d) $- \frac{1}{3}$

Discussion

2696.	A circle is inscribed in a regular hexagon. If the line AB measures 12 cm and passes through the centre of the circle, what is the area of the circle (in cm2)?
Answer» A circle is inscribed in a regular hexagon. If the line AB measures 12 $c m$ and passes through the centre of the circle, what is the area of the circle (in $c m^{2}$ )?

Discussion

2697.	63.If P(0,1,2) , Q(4, -2, 1) and R(0,0,0) are three points , then angle PRQ is = ?
Answer» 63.If P(0,1,2) , Q(4, -2, 1) and R(0,0,0) are three points , then angle PRQ is = ?

Discussion

2698.	If kx + 3y = 14 passes through the point (1,2k), find the value of k. __
Answer» If kx + 3y = 14 passes through the point (1,2k), find the value of k. __

Discussion

2699.	Which of the following equations does not pass through point (3,3)
Answer» Which of the following equations does not pass through point (3,3)

Discussion

2700.	In the given figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT = 60∘ , find ∠PRQ
Answer» In the given figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT = 60^∘ , find ∠PRQ

Discussion

Explore topic-wise InterviewSolutions in .

Question 7 (iv)Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC.(d) What do you observe?

Question 180(i)Simplify[(12)2−(14)3]−1×2−3

If 8:2 is greater than 5:a, then the value of a is greater than _____.

The population of my country increases at 5% per annum. What type of increase is this?

The curved surface area of a hemisphere of diameter 28 cm is

In the adjoining figure, BM⊥AC and DN⊥AC. If BM=DN, prove that AC bisects BD.

Working in pairs give antonyms of the following words. kind- hearted unscrupulous forgiving stern benevolent credulous generous pious suspicious sympathetic understanding wild innocent penitent clever brutal cunning caring sentimental trusting protective concerned honourable embittered

Consider the below figure. Here, z = ___.

Prove that ʃdx/√(1+x²)=log|x+√(x²+1)|

A cylindrical container of diameter 42 m and height 24 m is full of diesel. The diesel is emptied into a rectangular pool of length 132 m and breadth 56 m. Find the height of which diesel rises in pool.

Find the value of a and b, if they are the zeroes of polynomial x^2 + ax + b.

Solve for x: log3(x3)+log1/9(x)&lt;1

Simultaneous linear equations 1) Twice one number minus three times the second is equal to 2 ; and the sum of the number is 11 find number. 2). The sum of a two digit number and the number obtained on reversing the digits is 165 .If the digits differ by 3, find the number.

In a ΔABC, if AB=AC and ∠B=70∘, find ∠A.

ntABCD is a parallelogram and P is the midpoint of the side BC. Prove using vector algebra ( not by geometric process) that AC and DP meet in a common point of trisection.n

In the experiment of finding volume of a solid by immersing it into water, the initial reading of the water level in the graduated cylinder was 16.2 ml. On immersing the given solid completely into water, the water level rose to 19.7ml. Find the volume of the solid

Factorise:35x2-195x+4

If →b is the vector whose initial point divides the joining 5→i and 5→j in the ratio λ:1 and terminal point is at origin. If |→b|≤√37, then set of values of λ is

P is any point on the diagonal AC of a parallelogram ABCD. Prove that ar(∆ADP) = ar(∆ABP).

Which of the following fractions is equal to 1√5−√7?

Can we construct a quadrilateral PQRS with PQ = 3 cm, RS = 3 cm, PS = 7.5 cm, PR = 8cm and SQ = 4 cm. Justify your result.

A soft drink is available in two packs-(i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?

In a Δ ABC, P and Q are respectively the mid-points of AB and BC and R is the mid-point of AP. Prove that:(i) ar (Δ PBQ) = ar (Δ ARC)(ii) ar (Δ PRQ) = 12 ar (Δ ARC)(iii) ar (Δ RQC) = 38 ar (Δ ABC).

Question 1Write True or False and justify your answer :Two chords AB and CD of a circle are each at a distance of 4 cm from the centre, then AB = CD.

Explain the meaning of diminishing marginal rate of substitution with the help of a numerical example.

If AD and PM are medians of ΔABC and ΔPQR respectively, where ΔABC ~ ΔPQR; prove that ABPQ=ADPM.

What universal set(s) would you propose for each of the following?(i) The set of right triangles.(ii) The set of isosceles triangles.

23. 7 white balls and 3 black balls are placed in a row at random.the probabilty that no two black balls are ajacent is

ABCD is a rhombus If area (ABCD)=24 cm2 and AC=8 cm, find the measure of the side of the rhombus.

Among a cylinder (of radius r and height h=r), a cone (of radius r and height h=r) and a sphere of radius r the __ will have the maximum volume.

If x + 1 is a factor of the polynomial 2x3 + ax2 + 4x + 1, then a = _________.

AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD=∠ABEand∠EPA=∠DPB (See the given figure). Show thatΔDAP≅ΔEBP

Question 58 Fill in the blanks to make the statements true. The measure of each exterior angle of a regular pentagon is ___.

Factorise x3+x+2 Please answer as soon as possible because I have my exams tomorrow.

Solve for x in the equation log[log(2+log2(x+1))]=0

Question 8 (ii)Express 121 as the sum of 11 odd numbers.

□ PTNM is a rectangle. Write the names of the pairs of supplementary angles.

Which of these triangles can actually be constructed?

In two concentric circles, a chord of length 8 cm of the larger circle touches the smaller circle. If the radius of the larger circle is 5 cm then Find the radius of the smaller circle. [CBSE 2013C]

Two lines are perpendicular to each other. Then the angle between the lines is

ABCD is a parallelogram and E and F are the centroids of triangles ABD and BCD respectively, then EF =(a) AE(b) BE(c) CE(d) DE

Numbers 1 to 10 is written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of getting a number greater than 6?

In the following figure, if the chords AB and CD are equal to 6 cm then the distance of the chords from the centre of the circle of radius 5 cm will be:

If 35x×812×656132x=37, then x =(a) 3(b) −3(c) 13(d) -13

A circle is inscribed in a regular hexagon. If the line AB measures 12 cm and passes through the centre of the circle, what is the area of the circle (in cm2)?

63.If P(0,1,2) , Q(4, -2, 1) and R(0,0,0) are three points , then angle PRQ is = ?

If kx + 3y = 14 passes through the point (1,2k), find the value of k. __

Which of the following equations does not pass through point (3,3)

In the given figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT = 60∘ , find ∠PRQ

Solve for x: log3(x3)+log1/9(x)<1