32581 + Interview Questions in Mathematics Page 201 InterviewSolution

10001.	Points A(1,2) and B(3,4) are two ends of a line segment. Find the point which divides AB in the ratio 3:4.
Answer» Points A(1,2) and B(3,4) are two ends of a line segment. Find the point which divides AB in the ratio 3:4.

10001.

Points A(1,2) and B(3,4) are two ends of a line segment. Find the point which divides AB in the ratio 3:4.

Answer»

Points A(1,2) and B(3,4) are two ends of a line segment. Find the point which divides AB in the ratio 3:4.

10002.	The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the following figure is ________.
Answer» The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the following figure is ________.

Discussion

10003.	With respect to the roots of x2–2x–3=0, we can say that
Answer» With respect to the roots of $x^{2} - 2 x - 3 = 0$ , we can say that

Discussion

10004.	If a matrix has 18 elements, what are the possible orders it can have? What, if the has 5 elements?
Answer» If a matrix has $18$ elements, what are the possible orders it can have? What, if the has $5$ elements?

Discussion

10005.	Question 22 Area of a circular garden with diameter 8m is (a) 12.56 m2 (b) 25.12 m2 (c) 50.24 m2 (d) 200.96 m2
Answer» Question 22 Area of a circular garden with diameter 8m is (a) $12.56 m^{2}$ (b) $25.12 m^{2}$ (c) $50.24 m^{2}$ (d) $200.96 m^{2}$

Discussion

10006.	PQR is a triangle right angles at P and M is a point on QR such that pm is perpendicular to QR show that PMsquare=QM*MR
Answer» PQR is a triangle right angles at P and M is a point on QR such that pm is perpendicular to QR show that PMsquare=QM*MR

Discussion

10007.	For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?
Answer» For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?

Discussion

10008.	The total elongation of the structural element fixed, at one end, free at the other end, and of varying cross-section as shown in the figure when subjected to a force P at free end is given by
Answer» The total elongation of the structural element fixed, at one end, free at the other end, and of varying cross-section as shown in the figure when subjected to a force $P$ at free end is given by

Discussion

10009.	23. What is laminar flow?
Answer» 23. What is laminar flow?

Discussion

10010.	Return on investment is given by _______.
Answer» Return on investment is given by _______.

Discussion

10011.	22. In a binomial distribution, the mean is 4 and variance is 3. Then find its mode.
Answer» 22. In a binomial distribution, the mean is 4 and variance is 3. Then find its mode.

Discussion

10012.	In each of the following determine whether the given values are solution of the given equation or not (i)x2−3x+2=0,x=2,x=−1(ii)x2+x+1=0,x=0,x=1(iii)x2−3√3x+6=0,x=√3,x=−2√3(iv)x+1x=136,x=56,x=56,x=43(v)2x2−x+9=x2+4x+3,x=2,x=3(vi)x2−√2x−4=0,x=−√2,x=−2√2(vii)a2x2−3abx+2b2=0,x=ab,x=ba
Answer» In each of the following determine whether the given values are solution of the given equation or not $(i) x^{2} - 3 x + 2 = 0, x = 2, x = - 1 (i i) x^{2} + x + 1 = 0, x = 0, x = 1 (i i i) x^{2} - 3 \sqrt{3 x} + 6 = 0, x = \sqrt{3}, x = - 2 \sqrt{3} (i v) x + \frac{1}{x} = \frac{13}{6}, x = \frac{5}{6}, x = \frac{5}{6}, x = \frac{4}{3} (v) 2 x^{2} - x + 9 = x^{2} + 4 x + 3, x = 2, x = 3 (v i) x^{2} - \sqrt{2 x} - 4 = 0, x = - \sqrt{2}, x = - 2 \sqrt{2} (v i i) a^{2} x^{2} - 3 a b x + 2 b^{2} = 0, x = \frac{a}{b}, x = \frac{b}{a}$

Discussion

10013.	Question 2In an AP, if a = 3.5, d = 0 and n = 101, then an will be:A) 0B) 3.5C) 103.5D) 104.5
Answer» Question 2 In an AP, if a = 3.5, d = 0 and n = 101, then $a_{n}$ will be: A) 0 B) 3.5 C) 103.5 D) 104.5

Discussion

10014.	Find the volume of a cylinder whose height is 10cm and radius is 7 cm.
Answer» Find the volume of a cylinder whose height is 10cm and radius is 7 cm.

Discussion

10015.	A test tube of volume V kept open initially is closed with an air tight cork. The quantity of air inside the test tube is:
Answer» A test tube of volume V kept open initially is closed with an air tight cork. The quantity of air inside the test tube is:

Discussion

10016.	Find the values of k for which the following equation has equal roots: [4 MARKS](k−12)x2+2(k−12)x+2=0
Answer» Find the values of k for which the following equation has equal roots: [4 MARKS] $(k - 12) x^{2} + 2 (k - 12) x + 2 = 0$

Discussion

10017.	Question 3 (iii)Find the LCM and HCF of 8, 9 and 25 by applying the prime factorization method.
Answer» Question 3 (iii) Find the LCM and HCF of 8, 9 and 25 by applying the prime factorization method.

Discussion

10018.	Find the equation of a line which passes through (1,2,3) and also parallel to the planes x-y+2z=5, 3x+y+z=6.
Answer» Find the equation of a line which passes through (1,2,3) and also parallel to the planes x-y+2z=5, 3x+y+z=6.

Discussion

10019.	Question 12If 2 sin2 θ−cos2 θ=2, then find the value of θ.
Answer» Question 12 If $2 s i n^{2} θ - c o s^{2} θ = 2$ , then find the value of $θ$ .

Discussion

10020.	Maximum value of expression f(x) = - x2 + 6x + 7 occur at x = __
Answer» Maximum value of expression f(x) = - $x^{2}$ + 6x + 7 occur at x = __

Discussion

10021.	Use Euclid's division algorithm to find the HCF of(i) 135 and 225(ii) 196 and 38220(iii) 867 and 255(iv) 184, 230 and 276(v) 136, 170 and 255
Answer» Use Euclid's division algorithm to find the HCF of (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 (iv) 184, 230 and 276 (v) 136, 170 and 255

Discussion

10022.	What is/are the point(s) on the line X+Y = 4 that lie(s) at unit distance from the line 4x+3y = 10
Answer» What is/are the point(s) on the line X+Y = 4 that lie(s) at unit distance from the line 4x+3y = 10

Discussion

10023.	In a quadrilateral ABCD, which is not a trapezium, it is known that ∠ DAB = ∠ABC = 600. Moreover, ∠CAB = ∠CBD. Then,
Answer» In a quadrilateral ABCD, which is not a trapezium, it is known that $∠$ DAB = $∠$ ABC = $60^{0}$ . Moreover, $∠$ CAB = $∠$ CBD. Then,

Discussion

10024.	The largest number which divides 70 and 125, leaving remainders 5 and 8 , respectively,is (a) 13 (b) 65 (c) 875 (d) 1750
Answer» The largest number which divides 70 and 125, leaving remainders 5 and 8 , respectively,is (a) 13 (b) 65 (c) 875 (d) 1750

Discussion

10025.	Does the sequence of odd numbers form an AP?
Answer» Does the sequence of odd numbers form an AP?

Discussion

10026.	Solve each of the following systems of equations by the method of cross-multiplication :x+yxy=2, x-yxy=6
Answer» Solve each of the following systems of equations by the method of cross-multiplication : $\frac{x + y}{x y} = 2, \frac{x - y}{x y} = 6$

Discussion

10027.	Question 13The circumcentre of the ΔABC is O. Prove that ∠OBC+∠BAC=90∘.
Answer» Question 13 The circumcentre of the $Δ A B C$ is O. Prove that $∠ O B C + ∠ B A C = 90^{\circ}$ .

Discussion

10028.	Ms. Rana goes for shopping to buy a leather coat which costs Rs.735. The rate of sales tax is 5%. She tells the shopkeeper to reduce the price to such an extent that she has to pay Rs.735, inclusive of sales tax. Find the reduction needed at the price of the coat.
Answer» Ms. Rana goes for shopping to buy a leather coat which costs Rs.735. The rate of sales tax is 5%. She tells the shopkeeper to reduce the price to such an extent that she has to pay Rs.735, inclusive of sales tax. Find the reduction needed at the price of the coat.

Discussion

10029.	If 2 is a root of the quadratic equation 3x2+px-8=0 and the quadratic equation 4x2-2px+k=0 has equal roots, find the value of k.
Answer» If 2 is a root of the quadratic equation $3 x^{2} + p x - 8 = 0$ and the quadratic equation $4 x^{2} - 2 p x + k = 0$ has equal roots, find the value of k.

Discussion

10030.	A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.
Answer» A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.

Discussion

10031.	If the equation 9x2+6kx+4=0 has equal roots, then find the value of k.
Answer» If the equation $9 x^{2} + 6 k x + 4 = 0$ has equal roots, then find the value of $k$ .

Discussion

10032.	Find the roots of the equation x2–4x−9=0 by the method of completing the square.
Answer» Find the roots of the equation $x^{2} - 4 x - 9 = 0$ by the method of completing the square.

Discussion

10033.	Question 1 Find the coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in the ratio 2:3.
Answer» Question 1 Find the coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in the ratio 2:3.

Discussion

10034.	A round cover has a regular hexagonal design as shown in the figure. If the radius of the cover is 14cm , then find the cost of making the shade region at the rate of Rs 0.50 per cm^2 [ use root 3 =1.7]
Answer» A round cover has a regular hexagonal design as shown in the figure. If the radius of the cover is 14cm , then find the cost of making the shade region at the rate of Rs 0.50 per cm^2 [ use root 3 =1.7]

Discussion

10035.	A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is(a) 9, 6(b) 3, −9(c) −3, 9(d) 9, −6
Answer» A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is (a) 9, 6 (b) 3, −9 (c) −3, 9 (d) 9, −6

Discussion

10036.	Here AB ∥ CD. If the altitude of △ACD is 6 cm and CD is 8 cm then the area of △BCD is:
Answer» Here AB $∥$ CD. If the altitude of $△$ ACD is 6 cm and CD is 8 cm then the area of $△$ BCD is:

10036.

Here AB ∥ CD. If the altitude of △ACD is 6 cm and CD is 8 cm then the area of △BCD is:

Answer»

Here AB $∥$ CD. If the altitude of $△$ ACD is 6 cm and CD is 8 cm then the area of $△$ BCD is:

Discussion

10037.	22. If α and β are the zeroes of the polynomial (x-p) (x-q) - r, then p and q would be the zeroes of the polynomial
Answer» 22. If α and β are the zeroes of the polynomial (x-p) (x-q) - r, then p and q would be the zeroes of the polynomial

Discussion

10038.	A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle 30∘ with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree?
Answer» A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle $30^{\circ}$ with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree?

Discussion

10039.	The LCM of (x−1)(x−2) and (x−2)(x−7) is:
Answer» The LCM of $(x - 1) (x - 2) a n d (x - 2) (x - 7)$ is:

Discussion

10040.	If cot θ=13, find the value of 1-cos2 θ2-sin2 θ.
Answer» If $\cot θ = \frac{1}{\sqrt{3}}$ , find the value of $\frac{1 - \cos^{2} θ}{2 - \sin^{2} θ}$ .

Discussion

10041.

The table below classifies the members of a committee according to their ages. Age Number of Members 25 − 30 30 − 35 35 − 40 40 − 45 45 − 50 50 − 55 55 − 60 6 14 16 22 5 4 3 Calculate the mean age of the members of this committee.

Answer»

The table below classifies the members of a committee according to their ages.

Age

Number of Members

25 − 30

30 − 35

35 − 40

40 − 45

45 − 50

50 − 55

55 − 60

6

14

16

22

5

4

3

Calculate the mean age of the members of this committee.

Discussion

10042.	Their is a poynomial 2x to the power 2+4x-3. Alpha and beta are zeroes of it find the value of (i) 1 upon alpa + 1 upon beta(ii) alpha squre upon beta square + beta square upon alpha square
Answer» Their is a poynomial 2x to the power 2+4x-3. Alpha and beta are zeroes of it find the value of (i) 1 upon alpa + 1 upon beta (ii) alpha squre upon beta square + beta square upon alpha square

Discussion

10043.	A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
Answer» A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Discussion

10044.	Which of the following is correct for XeO_2F_2 and PCl_5 ? (1) Both have same hybridisation and shape ( 2) Both have same hybridisation but different geometry (3) Both have different hybridisation but same shape (4) Both have same hybridisation but different shape
Answer» Which of the following is correct for XeO_2F_2 and PCl_5 ? (1) Both have same hybridisation and shape ( 2) Both have same hybridisation but different geometry (3) Both have different hybridisation but same shape (4) Both have same hybridisation but different shape

Discussion

10045.	Prove that sin(50°+θ)-cos(40°-θ)=0
Answer» Prove that sin(50°+θ)-cos(40°-θ)=0

Discussion

10046.	a milkman while supplying milk to the customer adds milk from a measuring cane without adding water which is cylindrial in shape with hemispherical bottom . the radius of the cylinder is 1.75 cm and its height is 10 cm . find the volume of the milk in the cane . what values are shown by him
Answer» a milkman while supplying milk to the customer adds milk from a measuring cane without adding water which is cylindrial in shape with hemispherical bottom . the radius of the cylinder is 1.75 cm and its height is 10 cm . find the volume of the milk in the cane . what values are shown by him

Discussion

10047.	The perimeter of a rectangle is 28 metres and its diagonal is 10 metres. What are the lengths of its sides?
Answer» The perimeter of a rectangle is 28 metres and its diagonal is 10 metres. What are the lengths of its sides?

Discussion

10048.	Show that ΔABC with vertices A(–2, 0), B(0, 2) and C(2, 0) is similar to ΔDEF with vertices D(–4, 0), F(4, 0) and E(0, 4). [CBSE 2017]
Answer» Show that ΔABC with vertices A(–2, 0), B(0, 2) and C(2, 0) is similar to ΔDEF with vertices D(–4, 0), F(4, 0) and E(0, 4). [CBSE 2017]

Discussion

10049.	The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm,(i) Find the area of the metal sheet used to make the bucket.(ii) Why we should avoid the bucket made by ordinary plastic? (use π = 3.14)
Answer» The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, (i) Find the area of the metal sheet used to make the bucket. (ii) Why we should avoid the bucket made by ordinary plastic? (use π = 3.14)

Discussion

10050.	In the following figures, the figure that is not symmetric with respect to any line is :
Answer» In the following figures, the figure that is not symmetric with respect to any line is :

Discussion

Explore topic-wise InterviewSolutions in .

Points A(1,2) and B(3,4) are two ends of a line segment. Find the point which divides AB in the ratio 3:4.

The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the following figure is ________.

With respect to the roots of x2–2x–3=0, we can say that

If a matrix has 18 elements, what are the possible orders it can have? What, if the has 5 elements?

Question 22 Area of a circular garden with diameter 8m is (a) 12.56 m2 (b) 25.12 m2 (c) 50.24 m2 (d) 200.96 m2

PQR is a triangle right angles at P and M is a point on QR such that pm is perpendicular to QR show that PMsquare=QM*MR

For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?

The total elongation of the structural element fixed, at one end, free at the other end, and of varying cross-section as shown in the figure when subjected to a force P at free end is given by

23. What is laminar flow?

Return on investment is given by _______.

22. In a binomial distribution, the mean is 4 and variance is 3. Then find its mode.

Question 2In an AP, if a = 3.5, d = 0 and n = 101, then an will be:A) 0B) 3.5C) 103.5D) 104.5

Find the volume of a cylinder whose height is 10cm and radius is 7 cm.

A test tube of volume V kept open initially is closed with an air tight cork. The quantity of air inside the test tube is:

Find the values of k for which the following equation has equal roots: [4 MARKS](k−12)x2+2(k−12)x+2=0

Question 3 (iii)Find the LCM and HCF of 8, 9 and 25 by applying the prime factorization method.

Find the equation of a line which passes through (1,2,3) and also parallel to the planes x-y+2z=5, 3x+y+z=6.

Question 12If 2 sin2 θ−cos2 θ=2, then find the value of θ.

Maximum value of expression f(x) = - x2 + 6x + 7 occur at x = __

Use Euclid's division algorithm to find the HCF of(i) 135 and 225(ii) 196 and 38220(iii) 867 and 255(iv) 184, 230 and 276(v) 136, 170 and 255

What is/are the point(s) on the line X+Y = 4 that lie(s) at unit distance from the line 4x+3y = 10

In a quadrilateral ABCD, which is not a trapezium, it is known that ∠ DAB = ∠ABC = 600. Moreover, ∠CAB = ∠CBD. Then,

The largest number which divides 70 and 125, leaving remainders 5 and 8 , respectively,is (a) 13 (b) 65 (c) 875 (d) 1750

Does the sequence of odd numbers form an AP?

Solve each of the following systems of equations by the method of cross-multiplication :x+yxy=2, x-yxy=6

Question 13The circumcentre of the ΔABC is O. Prove that ∠OBC+∠BAC=90∘.

Ms. Rana goes for shopping to buy a leather coat which costs Rs.735. The rate of sales tax is 5%. She tells the shopkeeper to reduce the price to such an extent that she has to pay Rs.735, inclusive of sales tax. Find the reduction needed at the price of the coat.

If 2 is a root of the quadratic equation 3x2+px-8=0 and the quadratic equation 4x2-2px+k=0 has equal roots, find the value of k.

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.

If the equation 9x2+6kx+4=0 has equal roots, then find the value of k.

Find the roots of the equation x2–4x−9=0 by the method of completing the square.

Question 1 Find the coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in the ratio 2:3.

A round cover has a regular hexagonal design as shown in the figure. If the radius of the cover is 14cm , then find the cost of making the shade region at the rate of Rs 0.50 per cm^2 [ use root 3 =1.7]

A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is(a) 9, 6(b) 3, −9(c) −3, 9(d) 9, −6

Here AB ∥ CD. If the altitude of △ACD is 6 cm and CD is 8 cm then the area of △BCD is:

22. If α and β are the zeroes of the polynomial (x-p) (x-q) - r, then p and q would be the zeroes of the polynomial

A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle 30∘ with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree?

The LCM of (x−1)(x−2) and (x−2)(x−7) is:

If cot θ=13, find the value of 1-cos2 θ2-sin2 θ.

The table below classifies the members of a committee according to their ages. Age Number of Members 25 − 30 30 − 35 35 − 40 40 − 45 45 − 50 50 − 55 55 − 60 6 14 16 22 5 4 3 Calculate the mean age of the members of this committee.

Their is a poynomial 2x to the power 2+4x-3. Alpha and beta are zeroes of it find the value of (i) 1 upon alpa + 1 upon beta(ii) alpha squre upon beta square + beta square upon alpha square

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Which of the following is correct for XeO_2F_2 and PCl_5 ? (1) Both have same hybridisation and shape ( 2) Both have same hybridisation but different geometry (3) Both have different hybridisation but same shape (4) Both have same hybridisation but different shape

Prove that sin(50°+θ)-cos(40°-θ)=0

a milkman while supplying milk to the customer adds milk from a measuring cane without adding water which is cylindrial in shape with hemispherical bottom . the radius of the cylinder is 1.75 cm and its height is 10 cm . find the volume of the milk in the cane . what values are shown by him

The perimeter of a rectangle is 28 metres and its diagonal is 10 metres. What are the lengths of its sides?

Show that ΔABC with vertices A(–2, 0), B(0, 2) and C(2, 0) is similar to ΔDEF with vertices D(–4, 0), F(4, 0) and E(0, 4). [CBSE 2017]

The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm,(i) Find the area of the metal sheet used to make the bucket.(ii) Why we should avoid the bucket made by ordinary plastic? (use π = 3.14)

In the following figures, the figure that is not symmetric with respect to any line is :