32581 + Interview Questions in Mathematics Page 135 InterviewSolution

6701.	The height of a cone is 40 cm. A small cone is cut off at the top by a plane parallel to the base. If the volume of the small cone be 164 of the volume of the given cone, at what height ( in cm) above the base is the section made ?
Answer» The height of a cone is 40 cm. A small cone is cut off at the top by a plane parallel to the base. If the volume of the small cone be $\frac{1}{64}$ of the volume of the given cone, at what height ( in cm) above the base is the section made ?

Discussion

6702.	Question 1 (iii)State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:
Answer» Question 1 (iii) State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:

Discussion

6703.	The sum of the reciprocals of Rehman's ages (in years) 3 years ago and 5 years from now is 13. Find his present age.
Answer» The sum of the reciprocals of Rehman's ages (in years) $3$ years ago and $5$ years from now is $\frac{1}{3}$ . Find his present age.

Discussion

6704.	In ΔABC , right angled at B. Find the value of (ABAC)2 + (BCAC)2
Answer» In ΔABC , right angled at B. Find the value of $(\frac{A B}{A C})^{2}$ + $(\frac{B C}{A C})^{2}$

6704.

In ΔABC , right angled at B. Find the value of (ABAC)2 + (BCAC)2

Answer»

In ΔABC , right angled at B. Find the value of

$(\frac{A B}{A C})^{2}$ + $(\frac{B C}{A C})^{2}$

Discussion

6705.	Show graphically that each one of the following systems of equations has infinitely many solutions:x − 2y + 11 = 03x − 6y + 33 = 0
Answer» Show graphically that each one of the following systems of equations has infinitely many solutions: x − 2y + 11 = 0 3x − 6y + 33 = 0

Discussion

6706.	50 bells B1,B2,B3,.......B50 start ringing together. The bells ring after every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.....50 sec respectively. Answer the following questions. 1. Bells B1,B2.....B7 ring together after how many seconds ?
Answer» 50 bells $B_{1}, B_{2}, B_{3}, . . . . . . . B_{50}$ start ringing together. The bells ring after every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.....50 sec respectively. Answer the following questions. 1. Bells $B_{1}, B_{2} . . . . . B_{7}$ ring together after how many seconds ?

Discussion

6707.	Sum of the digits of two digit number is 24 times the sum of their reciprocals. If the sum of their reciprocals is 5/12, the number is::
Answer» Sum of the digits of two digit number is 24 times the sum of their reciprocals. If the sum of their reciprocals is 5/12, the number is::

Discussion

6708.	Simplify the expression: cosecθcotθ
Answer» Simplify the expression: $\frac{c o s e c θ}{cot θ}$

Discussion

6709.	For what values of,n2-1 is divisible by 8.
Answer» For what values of,n²-1 is divisible by 8.

Discussion

6710.	Which of the following is NOT a composite number?
Answer» Which of the following is NOT a composite number?

Discussion

6711.	If a + b + c = 8 and ab + bc + ca = 20, find the value of a3+b3+c3–3abc.
Answer» If a + b + c = 8 and ab + bc + ca = 20, find the value of $a^{3} + b^{3} + c^{3} - 3 a b c$ .

Discussion

6712.	At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha. Find the present age of both Asha and Nisha.
Answer» At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha. Find the present age of both Asha and Nisha.

Discussion

6713.	If x is a positive integer such that the distance between points P (x, 2) and Q (3, –6) is 10 units, then x =
Answer» If x is a positive integer such that the distance between points P (x, 2) and Q (3, –6) is 10 units, then x =

Discussion

6714.	Can we find the length of the sides of a triangle if we know the ratios of the sides
Answer» Can we find the length of the sides of a triangle if we know the ratios of the sides

Discussion

6715.	The distance of the plane r→.27i^+37j^-67k^=1 from the origin is (a) 1(b) 7(c) 17(d) none of these
Answer» The distance of the plane $\vec{r} . (\frac{2}{7} \hat{i} + \frac{3}{7} \hat{j} - \frac{6}{7} \hat{k}) = 1$ from the origin is (a) 1 (b) 7 (c) $\frac{1}{7}$ (d) none of these

Discussion

6716.

Heights of students of Class X are given in the foloowing frequency distribution: Height (in cm) 150−155 155−160 160−165 165−170 170−175 Number of students 15 8 20 12 5 Find the modal height. Also, find the mean height. Compare and interpret the two measures of central tendency. [CBSE 2014]

Answer»

Heights of students of Class X are given in the foloowing frequency distribution:

Height (in cm)	150−155	155−160	160−165	165−170	170−175
Number of students	15	8	20	12	5

Find the modal height.

Also, find the mean height. Compare and interpret the two measures of central tendency. [CBSE 2014]

Discussion

6717.	A man arranges to pay off a debt of Rs. 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.
Answer» A man arranges to pay off a debt of Rs. 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.

Discussion

6718.	The radius of a circle and the tangent at the __ are perpendicular.
Answer» The radius of a circle and the tangent at the __ are perpendicular.

Discussion

6719.	28. If the value of CFSE for Ni is delta o than it is for Pd should be
Answer» 28. If the value of CFSE for Ni is delta o than it is for Pd should be

Discussion

6720.	Is there any real value of 'a' for which the equation x2 + 2x + (a2 + 1) = 0 has real roots?
Answer» Is there any real value of 'a' for which the equation x² + 2x + (a² + 1) = 0 has real roots?

Discussion

6721.

If a coin is tossed 3 times, what is the probability of getting atleast one tail? A. 18B.58C.14D.78

Answer»

If a coin is tossed 3 times, what is the probability of getting atleast one tail?

A. $\frac{1}{8}$

B. $\frac{5}{8}$

C. $\frac{1}{4}$

D. $\frac{7}{8}$

Discussion

6722.	The number which should be added to x2+6x+5 so that the resulting polynomial is completely divisible by x+3 _______. 4
Answer» The number which should be added to $x^{2} + 6 x + 5$ so that the resulting polynomial is completely divisible by $x + 3$ _______. 4

Discussion

6723.	In ∆ABC, ∠C is an obtuse angle. AD ⊥ BC and AB2 = AC2 + 3 BC2. Prove that BC = CD.
Answer» In ∆ABC, ∠C is an obtuse angle. AD ⊥ BC and AB² = AC² + 3 BC². Prove that BC = CD.

Discussion

6724.	A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30∘.
Answer» A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is $30^{\circ}$ .

Discussion

6725.	prove that a rectangle that circumscribed a circle is a square.
Answer» prove that a rectangle that circumscribed a circle is a square.

Discussion

6726.	In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.Using distance formula, find which of them is correct.
Answer» In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct.

6726.

In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.Using distance formula, find which of them is correct.

Answer»

In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.

Using distance formula, find which of them is correct.

Discussion

6727.	A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is (i) A card of spade or an ace (ii) A black king (iii) Neither a jack nor a king (iv) Either a king or a queen
Answer» A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is (i) A card of spade or an ace (ii) A black king (iii) Neither a jack nor a king (iv) Either a king or a queen

Discussion

6728.	In ΔABC, DE \|\| BC. Then which of the following is stated by Basic Proportionality Theorem?
Answer» In $Δ A B C$ , DE \|\| BC. Then which of the following is stated by Basic Proportionality Theorem?

Discussion

6729.	In the figure: ∠PSQ=90∘,PQ = 10 cm, QS = 6 cm and RQ = 9 cm.Calculate the length of PR.
Answer» In the figure: $∠ P S Q = 90^{\circ},$ PQ = 10 cm, QS = 6 cm and RQ = 9 cm. Calculate the length of PR.

6729.

In the figure: ∠PSQ=90∘,PQ = 10 cm, QS = 6 cm and RQ = 9 cm.Calculate the length of PR.

Answer»

In the figure: $∠ P S Q = 90^{\circ},$

PQ = 10 cm, QS = 6 cm and RQ = 9 cm.

Calculate the length of PR.

Discussion

6730.	Given that - x < 3 ; which of the following represent the same inequation
Answer» Given that - x < 3 ; which of the following represent the same inequation

Discussion

6731.	Question 5Determine, algebraically, the vertices of the triangle formed by the lines3x – y = 32x – 3y = 2x + 2y = 8
Answer» Question 5 Determine, algebraically, the vertices of the triangle formed by the lines 3x – y = 3 2x – 3y = 2 x + 2y = 8

Discussion

6732.	Question 4 (i) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (i) 2, 4, 8, 16 …
Answer» Question 4 (i) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (i) 2, 4, 8, 16 …

Discussion

6733.	If cot θ=34, prove that sec θ-cosec θsec θ+cosec θ=17.
Answer» If $\cot θ = \frac{3}{4}$ , prove that $\sqrt{\frac{\sec θ - cosec θ}{\sec θ + cosec θ}} = \frac{1}{\sqrt{7}}$ .

Discussion

6734.	52. Urn a contains 6 red balls and 4 black balls and urn b contains 4 red balls and 6 black balls then one ball is drawn from a and placed in b and again one ball is drawn from b and placed in a now finally one ball is drawn at random from urm a what is the probability that it is red.?
Answer» 52. Urn a contains 6 red balls and 4 black balls and urn b contains 4 red balls and 6 black balls then one ball is drawn from a and placed in b and again one ball is drawn from b and placed in a now finally one ball is drawn at random from urm a what is the probability that it is red.?

Discussion

6735.	A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of ₹25 per metre. [CBSE 2014]
Answer» A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of ₹25 per metre. [CBSE 2014]

Discussion

6736.	A Dealer in Mumbai sold an Audi car to a dealer in Pune for ₹45 Lakhs and the Dealer in Pune sold it to the customer making a ₹3 Lakhs profit on it. If the rate of GST is 28%, how much GST will be paid to the Central Goverment in this transaction by the dealer in Pune?
Answer» A Dealer in Mumbai sold an Audi car to a dealer in Pune for ₹45 Lakhs and the Dealer in Pune sold it to the customer making a ₹3 Lakhs profit on it. If the rate of GST is 28%, how much GST will be paid to the Central Goverment in this transaction by the dealer in Pune?

Discussion

6737.	Y is equals to x sin x square then find the value of DY by DX
Answer» Y is equals to x sin x square then find the value of DY by DX

Discussion

6738.	If α and β are the zeros of the quadratic polynomial f(x) = x2 − 5x + 4, find the value of 1α+1β-2αβ.
Answer» If α and β are the zeros of the quadratic polynomial f(x) = x² − 5x + 4, find the value of $\frac{1}{α} + \frac{1}{β} - 2 αβ$ .

Discussion

6739.	The abscissa of the point of intersection of less than type and of the more than types cumulative frequency curves of a grouped data gives its (a) mean (b) median (c) mode (d) all the three above
Answer» The abscissa of the point of intersection of less than type and of the more than types cumulative frequency curves of a grouped data gives its (a) mean (b) median (c) mode (d) all the three above

Discussion

6740.	A man arranges to pay off a debt of 36000 by 40 monthly instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid. Find the value of the first instalment.
Answer» A man arranges to pay off a debt of 36000 by 40 monthly instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid. Find the value of the first instalment.

Discussion

6741.	If (x2−y2)=18 and (x−y)=3, find the value of 16x2y2.
Answer» If $(x^{2} - y^{2}) = 18$ and $(x - y) = 3$ , find the value of $16 x^{2} y^{2}$ .

Discussion

6742.	Which of the following cannot be the probability of an event? [CBSE 2013C] (a) 1.5(b) 35(c) 25%(d) 0.3
Answer» Which of the following cannot be the probability of an event? [CBSE 2013C] (a) 1.5 (b) $\frac{3}{5}$ (c) 25% (d) 0.3

Discussion

6743.	Find the zeros of the quadratic polynomial x2−8x+12.
Answer» $Find the zeros of the quadratic polynomial x^{2} - 8 x + 12.$

Discussion

6744.	Write the first five terms and obtain the corresponding series, whose sequence is a1=a2=2, an=an−1−1, n>2.
Answer» Write the first five terms and obtain the corresponding series, whose sequence is $a_{1} = a_{2} = 2, a_{n} = a_{n - 1} - 1, n > 2$ .

Discussion

6745.	Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.(i) From the information shown in the figure,in ∆ABC and ∆PQR∠ABC ≅ ∠PQRseg BC ≅ seg QR ∠ACB≅ ∠PRQ∴ ∆ABC ≅ ∆PQR ....... 3243432 test∴ ∠BAC ≅ 3243432 .......corresponding angles of congruent triangles.seg AB≅ 1234and 1234 ≅ seg PR...corresponding sides of congruent triangles(ii) From the information shown in the figure,in ∆PTQ and ∆STRseg PT ≅ seg ST ∠PTQ≅ ∠STR...... vertically opposite angles∴ ∆PTQ ≅ ∆STR ....... 3243432 test ∴ ∠TPQ≅ 1234and 1234 ≅ ∠TRS...corresponding angles of congruent trianglesseg PQ ≅ 3243432 corresponding sides of congruent triangles
Answer» Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles. (i) From the information shown in the figure, in $∆$ ABC and $∆$ PQR $∠$ ABC $≅ ∠$ PQR seg BC $≅$ seg QR $∠$ ACB $≅$ $∠$ PRQ $∴ ∆$ ABC $≅$ $∆$ PQR ....... $3243432$ test $∴ ∠$ BAC $≅$ $3243432$ .......corresponding angles of congruent triangles. $\begin{array}{l} seg AB ≅ 1234 \\ and 1234 ≅ seg PR \end{array}\} . . . corresponding sides of congruent triangles$ (ii) From the information shown in the figure, in $∆$ PTQ and $∆$ STR seg PT $≅$ seg ST $∠$ PTQ $≅$ $∠$ STR...... vertically opposite angles $∴ ∆$ PTQ $≅$ $∆$ STR ....... $3243432$ test $\begin{array}{l} ∴ ∠ TPQ ≅ 1234 \\ and 1234 ≅ ∠ TRS \end{array}\} . . . corresponding angles of congruent triangles$ seg PQ $≅$ $3243432$ corresponding sides of congruent triangles

Discussion

6746.	If x2+k4x+k-1+2=0 has equal roots, then k =(a) -23, 1(b) 23, -1(c) 32, 13(d) -32, -13
Answer» If $x^{2} + k (4 x + k - 1) + 2 = 0$ has equal roots, then k = (a) $- \frac{2}{3}, 1$ (b) $\frac{2}{3}, - 1$ (c) $\frac{3}{2}, \frac{1}{3}$ (d) $- \frac{3}{2}, - \frac{1}{3}$

Discussion

6747.	Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on the outer circle, construct the pair of tangents to the inner circle. [CBSE 2017]
Answer» Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on the outer circle, construct the pair of tangents to the inner circle. [CBSE 2017]

Discussion

6748.	12. The number of integer solution (x,y) of the equation\|2x-y\|+\|x-y\|=1
Answer» 12. The number of integer solution (x,y) of the equation\|2x-y\|+\|x-y\|=1

Discussion

6749.	If p and q are zeroes of quadratic polynomial (x^2)-6x+a , find the value of a if 3p+2q=20
Answer» If p and q are zeroes of quadratic polynomial (x^2)-6x+a , find the value of a if 3p+2q=20

Discussion

6750.	Find the least number of flowers which can be planted in 5, 6, or 9 rows equally.
Answer» Find the least number of flowers which can be planted in 5, 6, or 9 rows equally.

Discussion

Explore topic-wise InterviewSolutions in .

The height of a cone is 40 cm. A small cone is cut off at the top by a plane parallel to the base. If the volume of the small cone be 164 of the volume of the given cone, at what height ( in cm) above the base is the section made ?

Question 1 (iii)State whether the pair of triangles in the below figure is similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:

The sum of the reciprocals of Rehman's ages (in years) 3 years ago and 5 years from now is 13. Find his present age.

In ΔABC , right angled at B. Find the value of (ABAC)2 + (BCAC)2

Show graphically that each one of the following systems of equations has infinitely many solutions:x − 2y + 11 = 03x − 6y + 33 = 0

50 bells B1,B2,B3,.......B50 start ringing together. The bells ring after every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.....50 sec respectively. Answer the following questions. 1. Bells B1,B2.....B7 ring together after how many seconds ?

Sum of the digits of two digit number is 24 times the sum of their reciprocals. If the sum of their reciprocals is 5/12, the number is::

Simplify the expression: cosecθcotθ

For what values of,n2-1 is divisible by 8.

Which of the following is NOT a composite number?

If a + b + c = 8 and ab + bc + ca = 20, find the value of a3+b3+c3–3abc.

At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha. Find the present age of both Asha and Nisha.​

If x is a positive integer such that the distance between points P (x, 2) and Q (3, –­6) is 10 units, then x =

Can we find the length of the sides of a triangle if we know the ratios of the sides

The distance of the plane r→.27i^+37j^-67k^=1 from the origin is (a) 1(b) 7(c) 17(d) none of these

A man arranges to pay off a debt of Rs. 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.

The radius of a circle and the tangent at the __ are perpendicular.

28. If the value of CFSE for Ni is delta o than it is for Pd should be

Is there any real value of 'a' for which the equation x2 + 2x + (a2 + 1) = 0 has real roots?

If a coin is tossed 3 times, what is the probability of getting atleast one tail? A. 18B.58C.14D.78

The number which should be added to x2+6x+5 so that the resulting polynomial is completely divisible by x+3 _______. 4

In ∆ABC, ∠C is an obtuse angle. AD ⊥ BC and AB2 = AC2 + 3 BC2. Prove that BC = CD.

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30∘.

prove that a rectangle that circumscribed a circle is a square.

A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is (i) A card of spade or an ace (ii) A black king (iii) Neither a jack nor a king (iv) Either a king or a queen

In ΔABC, DE || BC. Then which of the following is stated by Basic Proportionality Theorem?

In the figure: ∠PSQ=90∘,PQ = 10 cm, QS = 6 cm and RQ = 9 cm.Calculate the length of PR.

Given that - x &lt; 3 ; which of the following represent the same inequation

Question 5Determine, algebraically, the vertices of the triangle formed by the lines3x – y = 32x – 3y = 2x + 2y = 8

Question 4 (i) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (i) 2, 4, 8, 16 …

If cot θ=34, prove that sec θ-cosec θsec θ+cosec θ=17.

52. Urn a contains 6 red balls and 4 black balls and urn b contains 4 red balls and 6 black balls then one ball is drawn from a and placed in b and again one ball is drawn from b and placed in a now finally one ball is drawn at random from urm a what is the probability that it is red.?

A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of ₹25 per metre. [CBSE 2014]

A Dealer in Mumbai sold an Audi car to a dealer in Pune for ₹45 Lakhs and the Dealer in Pune sold it to the customer making a ₹3 Lakhs profit on it. If the rate of GST is 28%, how much GST will be paid to the Central Goverment in this transaction by the dealer in Pune?

Y is equals to x sin x square then find the value of DY by DX

If α and β are the zeros of the quadratic polynomial f(x) = x2 − 5x + 4, find the value of 1α+1β-2αβ.

The abscissa of the point of intersection of less than type and of the more than types cumulative frequency curves of a grouped data gives its (a) mean (b) median (c) mode (d) all the three above

A man arranges to pay off a debt of 36000 by 40 monthly instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid. Find the value of the first instalment.

If (x2−y2)=18 and (x−y)=3, find the value of 16x2y2.

Which of the following cannot be the probability of an event? [CBSE 2013C] (a) 1.5(b) 35(c) 25%(d) 0.3

Find the zeros of the quadratic polynomial x2−8x+12.

Write the first five terms and obtain the corresponding series, whose sequence is a1=a2=2, an=an−1−1, n&gt;2.

If x2+k4x+k-1+2=0 has equal roots, then k =(a) -23, 1(b) 23, -1(c) 32, 13(d) -32, -13

Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on the outer circle, construct the pair of tangents to the inner circle. [CBSE 2017]

12. The number of integer solution (x,y) of the equation|2x-y|+|x-y|=1

If p and q are zeroes of quadratic polynomial (x^2)-6x+a , find the value of a if 3p+2q=20

Find the least number of flowers which can be planted in 5, 6, or 9 rows equally.

At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha. Find the present age of both Asha and Nisha.

If x is a positive integer such that the distance between points P (x, 2) and Q (3, –6) is 10 units, then x =

Given that - x < 3 ; which of the following represent the same inequation

Write the first five terms and obtain the corresponding series, whose sequence is a1=a2=2, an=an−1−1, n>2.