32581 + Interview Questions in Mathematics Page 24 InterviewSolution

1151.	D, E, F are the mid points of the sides BC, CA and AB respectively of an equilateral △ ABC. Then △ DEF is congruent to triangle –
Answer» D, E, F are the mid points of the sides BC, CA and AB respectively of an equilateral $△$ ABC. Then $△$ DEF is congruent to triangle –

1151.

D, E, F are the mid points of the sides BC, CA and AB respectively of an equilateral △ ABC. Then △ DEF is congruent to triangle –

Answer»

D, E, F are the mid points of the sides BC, CA and AB respectively of an equilateral $△$ ABC. Then $△$ DEF is congruent to triangle –

Discussion

1152.	If the points (k,2-2k), (1-k, 2k) and (-k-4, 6-2k) are collinear, the possible values of k are ..............
Answer» If the points (k,2-2k), (1-k, 2k) and (-k-4, 6-2k) are collinear, the possible values of k are ..............

Discussion

1153.	Consider the figure where ∠AOB=90∘ and ∠ABC=30∘. Then, ∠CAO = ___.
Answer» Consider the figure where $∠ A O B = 90^{\circ}$ and $∠ A B C = 30^{\circ} .$ Then, $∠ C A O$ = ___.

Discussion

1154.	Find the LCM. (i) 36,42(ii) 15,25,30(iii) 18,42,48(iv) 4,12,20(v) 24,40,80,120
Answer» Find the LCM. (i) $36, 42$ (ii) $15, 25, 30$ (iii) $18, 42, 48$ (iv) $4, 12, 20$ (v) $24, 40, 80, 120$

Discussion

1155.	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

1156.	Let Bi(i=1,2,3) be three independent events in a sample space. The probability that only B1 occur is α, only B2 occurs is β and only B3 occurs is γ. Let p be the probability that none of the events Bi occurs and these 4 probabilities satisfy the equations (α−2β)p=αβ and (β−3γ)p=2βγ (All the probabilities are assumed to lie in the interval (0,1)). Then P(B1)P(B3) is equal to
Answer» Let $B_{i} (i = 1, 2, 3)$ be three independent events in a sample space. The probability that only $B_{1}$ occur is $α$ , only $B_{2}$ occurs is $β$ and only $B_{3}$ occurs is $γ$ . Let $p$ be the probability that none of the events $B_{i}$ occurs and these 4 probabilities satisfy the equations $(α - 2 β) p = α β$ and $(β - 3 γ) p = 2 β γ$ (All the probabilities are assumed to lie in the interval $(0, 1))$ . Then $\frac{P (B_{1})}{P (B_{3})}$ is equal to

Discussion

1157.	ntIf (x+a)/(b+c) + (x+b)/(c+a) + (x+c)/(a+b) + 3 = 0, a>0, b>0, c>0, then the value of x isn
Answer» ntIf (x+a)/(b+c) + (x+b)/(c+a) + (x+c)/(a+b) + 3 = 0, a>0, b>0, c>0, then the value of x isn

Discussion

1158.	Question 4Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Answer» Question 4 Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Discussion

1159.	In an isosceles triangle, length of the congruent sides is 13 cm and its base is 10 cm. Find the distance between the vertex opposite the base and the centroid.
Answer» In an isosceles triangle, length of the congruent sides is 13 cm and its base is 10 cm. Find the distance between the vertex opposite the base and the centroid.

Discussion

1160.	If two circles touch each other externally or internally then the two centres and point of contact are collinear . Prove it
Answer» If two circles touch each other externally or internally then the two centres and point of contact are collinear . Prove it

Discussion

1161.	Solve the following quadratic equations by factorization method: [4 MARKS]4x2−4ax+(a2−b2)=0
Answer» Solve the following quadratic equations by factorization method: [4 MARKS] $4 x^{2} - 4 a x + (a^{2} - b^{2}) = 0$

Discussion

1162.	The sum of an A.P whose first term is i+1, second term is j-2 and the last term is k, is equal to
Answer» The sum of an A.P whose first term is i+1, second term is j-2 and the last term is k, is equal to

Discussion

1163.	Question 2 (i) Fill in the blanks: (i) A tangent to a circle intersects it at ___ point(s).
Answer» Question 2 (i) Fill in the blanks: (i) A tangent to a circle intersects it at ___ point(s).

Discussion

1164.	Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1), find the third vertex.
Answer» Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1), find the third vertex.

Discussion

1165.	If the sum of three consecutive terms of an increasing AP is 66 and the product of the first and third of these term is 468 , then the third term is
Answer» If the sum of three consecutive terms of an increasing AP is 66 and the product of the first and third of these term is 468 , then the third term is

Discussion

1166.	If the system of equations 2x + 3y = 5, 4x + ky = 10 has infinitely many solutions, then k =(a) 1(b) ½(c) 3(d) 6
Answer» If the system of equations 2x + 3y = 5, 4x + ky = 10 has infinitely many solutions, then k = (a) 1 (b) ½ (c) 3 (d) 6

Discussion

1167.	Sum of the zeros of a quadratic polynomial p(x)=x2−bx+c is equal to __.
Answer» Sum of the zeros of a quadratic polynomial p(x)= $x^{2} - b x + c$ is equal to __.

Discussion

1168.	If sec θ + tan θ = p, prove that sin θ = p2-1p2+1
Answer» If sec θ + tan θ = p, prove that sin θ = $\frac{p^{2} - 1}{p^{2} + 1}$

Discussion

1169.	A circle is inscribed in ΔABC touching the sides AB, BC and CA at points D, E and F respectively. If AB= 10 cm, BC = 12 cm and CA = 8 cm, then the lengths of AD, BE and CF respectively will be
Answer» A circle is inscribed in ΔABC touching the sides AB, BC and CA at points D, E and F respectively. If AB= 10 cm, BC = 12 cm and CA = 8 cm, then the lengths of AD, BE and CF respectively will be

1169.

A circle is inscribed in ΔABC touching the sides AB, BC and CA at points D, E and F respectively. If AB= 10 cm, BC = 12 cm and CA = 8 cm, then the lengths of AD, BE and CF respectively will be

Answer»

A circle is inscribed in ΔABC touching the sides AB, BC and CA at points D, E and F respectively. If AB= 10 cm, BC = 12 cm and CA = 8 cm, then the lengths of AD, BE and CF respectively will be

Discussion

1170.	Solve the following quadratic equations by factorization:1x-3+2x-2=8x; x≠0, 2, 3
Answer» Solve the following quadratic equations by factorization: $\frac{1}{x - 3} + \frac{2}{x - 2} = \frac{8}{x}; x \neq 0, 2, 3$

Discussion

1171.	27 If m(z)= z+az+bz+6 leaves remainders 3 and 0 when divided by (z-3) and (z-2) respectively, then find the values of a and b.
Answer» 27 If m(z)= z+az+bz+6 leaves remainders 3 and 0 when divided by (z-3) and (z-2) respectively, then find the values of a and b.

Discussion

1172.	In an interference experiment, the ratio of amplitudes of coherent waves is a1a2=13. The ratio of maximum and minimum intensities of fringes will be
Answer» In an interference experiment, the ratio of amplitudes of coherent waves is $\frac{a_{1}}{a_{2}} = \frac{1}{3}$ . The ratio of maximum and minimum intensities of fringes will be

Discussion

1173.	The ratio of income of two gentlemen is 9:7 and the ratio of their expenditure are 4:3. If each of them manages to save Rs. 2000 per month, find the difference in their monthly income.
Answer» The ratio of income of two gentlemen is 9:7 and the ratio of their expenditure are 4:3. If each of them manages to save Rs. 2000 per month, find the difference in their monthly income.

Discussion

1174.	In the given figure, E is any point in the interior of the circle with centre O. Chord AB=AC. If ∠OBE=20°, then find the value of x.
Answer» In the given figure, $E$ is any point in the interior of the circle with centre $O$ . Chord $A B = A C$ . If $∠ O B E = 20 °$ , then find the value of $x$ .

Discussion

1175.	The interior of a building is in the form of a cylinder of base radius 12 m and height 3.5 m, surmounted by a cone of equal base and slant height 12.5 m. Find the internal curved surface area and the capacity of the building.
Answer» The interior of a building is in the form of a cylinder of base radius 12 m and height 3.5 m, surmounted by a cone of equal base and slant height 12.5 m. Find the internal curved surface area and the capacity of the building.

Discussion

1176.	Ajeet and Baljeet are partners in a firm. Their capitals are ₹ 9,00,000 and ₹ 6,00,000 respectively. During the year ended 31st March, 2019 the firm earned a profit of ₹ 4,50,000. Assuming that the normal rate of return is 20%, calculate value of goodwill of the firm:(i) By Capitalisation Method; and(ii) By Super Profit Method if the goodwill is valued at 2 years' purchase of super profit.
Answer» Ajeet and Baljeet are partners in a firm. Their capitals are ₹ 9,00,000 and ₹ 6,00,000 respectively. During the year ended 31st March, 2019 the firm earned a profit of ₹ 4,50,000. Assuming that the normal rate of return is 20%, calculate value of goodwill of the firm: (i) By Capitalisation Method; and (ii) By Super Profit Method if the goodwill is valued at 2 years' purchase of super profit.

Discussion

1177.	Question 1 Renu purchases two bags of fertilizer of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertilizer exact number of times.
Answer» Question 1 Renu purchases two bags of fertilizer of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertilizer exact number of times.

1177.

Question 1 Renu purchases two bags of fertilizer of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertilizer exact number of times.

Answer»

Question 1

Renu purchases two bags of fertilizer of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertilizer exact number of times.

Discussion

1178.	If ɑ and β are zeros of the quadratic polynomial 2x2−x+4, then (1α+1)(1β+1) = ______
Answer» If ɑ and β are zeros of the quadratic polynomial $2 x^{2} - x + 4$ , then $(\frac{1}{α} + 1) (\frac{1}{β} + 1)$ = ______

Discussion

1179.	A bag contains 6 black, 7 red and 2 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is black or white.
Answer» A bag contains 6 black, 7 red and 2 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is black or white.

Discussion

1180.	The angle of elevation of the top of a tower as observed form a point in a horizontal plane through the foot of the tower is 32°. When the observer moves towards the tower a distance of 100 m, he finds the angle of elevation of the top to be 63°. Find the height of the tower and the distance of the first position from the tower. [Take tan 32° = 0.6248 and tan 63° = 1.9626]
Answer» The angle of elevation of the top of a tower as observed form a point in a horizontal plane through the foot of the tower is 32°. When the observer moves towards the tower a distance of 100 m, he finds the angle of elevation of the top to be 63°. Find the height of the tower and the distance of the first position from the tower. [Take tan 32° = 0.6248 and tan 63° = 1.9626]

Discussion

1181.	If x tan 45o cos 60o = sin 60o cot 60o then x = ? (a) 1 (b)12 (c) 1√2 (d) √3
Answer» If x tan $45^{o}$ cos $60^{o}$ = sin $60^{o}$ cot $60^{o}$ then x = ? (a) 1 (b) $\frac{1}{2}$ (c) $\frac{1}{\sqrt{2}}$ (d) $\sqrt{3}$

1181.

If x tan 45o cos 60o = sin 60o cot 60o then x = ? (a) 1 (b)12 (c) 1√2 (d) √3

Answer»

If x tan $45^{o}$ cos $60^{o}$ = sin $60^{o}$ cot $60^{o}$ then x = ?

(a) 1 (b) $\frac{1}{2}$ (c) $\frac{1}{\sqrt{2}}$ (d) $\sqrt{3}$

Discussion

1182.	A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 105 cm and the diameter of the hemispherical ends is 36 cm each, find the cost of polishing the surface of the solid at the rate of 21 paise per square cm. [4 MARKS]
Answer» A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 105 cm and the diameter of the hemispherical ends is 36 cm each, find the cost of polishing the surface of the solid at the rate of 21 paise per square cm. [4 MARKS]

Discussion

1183.	If a chord of a circle of radius 28 cm makes an angle of 90 ° at the centre, then the area of the major segment is(a) 392 cm2(b) 1456 cm2(c) 1848 cm2(d) 2240 cm2
Answer» If a chord of a circle of radius 28 cm makes an angle of 90 ° at the centre, then the area of the major segment is (a) 392 cm² (b) 1456 cm² (c) 1848 cm² (d) 2240 cm²

Discussion

1184.	Determine the ratio in which a line 2x + y – 4 = 0 divides another line segment joining points A(2, – 2) and B(3, 7).
Answer» Determine the ratio in which a line 2x + y – 4 = 0 divides another line segment joining points A(2, – 2) and B(3, 7).

Discussion

1185.	Can you please give examples for linear, quadratic and cubic polynomials in which they do not have zeroes of the polynomial at all ? Graphs along with it would be helpful.
Answer» Can you please give examples for linear, quadratic and cubic polynomials in which they do not have zeroes of the polynomial at all ? Graphs along with it would be helpful.

Discussion

1186.	The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
Answer» The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Discussion

1187.	Find four rational number between the -37 and 29 using the formula
Answer» Find four rational number between the -37 and 29 using the formula

Discussion

1188.	tan 2 alpha=1-alpha 2 sec alfa+tancube alpha cosec alpha
Answer» tan 2 alpha=1-alpha 2 sec alfa+tancube alpha cosec alpha

Discussion

1189.	Simplify: 5 + (− 5) + 5 + (− 5) + ...(i) When the number of terms is 20 (ii) When the number of terms is 25
Answer» Simplify: 5 + (− 5) + 5 + (− 5) + ... (i) When the number of terms is 20 (ii) When the number of terms is 25

Discussion

1190.	Which of the following are Pair of Linear Equation in two variables?
Answer» Which of the following are Pair of Linear Equation in two variables?

Discussion

1191.	In any triangle ABC, tanA2−tanB2tanA2+tanB2
Answer» In any triangle ABC, $\frac{t a n \frac{A}{2} - t a n \frac{B}{2}}{t a n \frac{A}{2} + t a n \frac{B}{2}}$

Discussion

1192.	There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes wil they meet again at the starting point?
Answer» There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes wil they meet again at the starting point?

Discussion

1193.	Find the length of the hypotenuse of a right-angled triangle whose perpendicular sides are 5, 13.
Answer» Find the length of the hypotenuse of a right-angled triangle whose perpendicular sides are 5, 13.

Discussion

1194.	Alankrit Ltd. purchased machinery of ₹ 10,00,000 from Grand Iron Works Ltd. and paid as follows:(a) Issued 50,000 Equity Shares of ₹ 10 each at a premium of ₹ 2.(b) Gave an acceptance of ₹ 3,00,000 payable after 3 months; and(c) Balance by issuing post-dated cheque of two months of ₹ 1,00,000.Pass the Journal entries in the books of Alankrit Ltd. and Grand Iron Works Ltd.
Answer» Alankrit Ltd. purchased machinery of ₹ 10,00,000 from Grand Iron Works Ltd. and paid as follows: (a) Issued 50,000 Equity Shares of ₹ 10 each at a premium of ₹ 2. (b) Gave an acceptance of ₹ 3,00,000 payable after 3 months; and (c) Balance by issuing post-dated cheque of two months of ₹ 1,00,000. Pass the Journal entries in the books of Alankrit Ltd. and Grand Iron Works Ltd.

Discussion

1195.	If the radius of the hemisphere is 3r. Find its curved surface area.
Answer» If the radius of the hemisphere is $3 r .$ Find its curved surface area.

Discussion

1196.	Find the common difference of the A.P. and write the next two terms: (i) 51,59,67,75,… (ii) 75,57,59,51,… (iii) 1.8,2.0,2.2,2.4,… (iv) 0,14,12,34,… (v) 119,136,153,170,…
Answer» Find the common difference of the A.P. and write the next two terms: (i) $51, 59, 67, 75, \dots$ (ii) $75, 57, 59, 51, \dots$ (iii) $1.8, 2.0, 2.2, 2.4, \dots$ (iv) $0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, \dots$ (v) $119, 136, 153, 170, \dots$

Discussion

1197.	If \|A\| denotes the value of the determinant of a square matrix of order 3, then \|–2A\| = ___________.
Answer» If \|A\| denotes the value of the determinant of a square matrix of order 3, then \|–2A\| = ___________.

Discussion

1198.	A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm2. (Use π = 3.1416)
Answer» A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm². (Use π = 3.1416)

Discussion

1199.	Mohit's mother is 47 years older than him. The product of their ages 8 years from now will be 860. The equation representing this situation is .
Answer» Mohit's mother is 47 years older than him. The product of their ages 8 years from now will be 860. The equation representing this situation is .

Discussion

1200.	The value of x for which the numbers 2x+1, 5x+1, and 11x+1 are in G.P is ___ (x is a natural number).
Answer» The value of x for which the numbers 2x+1, 5x+1, and 11x+1 are in G.P is ___ (x is a natural number).

Discussion

Explore topic-wise InterviewSolutions in .

D, E, F are the mid points of the sides BC, CA and AB respectively of an equilateral △ ABC. Then △ DEF is congruent to triangle –

If the points (k,2-2k), (1-k, 2k) and (-k-4, 6-2k) are collinear, the possible values of k are ..............

Consider the figure where ∠AOB=90∘ and ∠ABC=30∘. Then, ∠CAO = ___.

Find the LCM. (i) 36,42(ii) 15,25,30(iii) 18,42,48(iv) 4,12,20(v) 24,40,80,120

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

ntIf (x+a)/(b+c) + (x+b)/(c+a) + (x+c)/(a+b) + 3 = 0, a>0, b>0, c>0, then the value of x isn

Question 4Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

In an isosceles triangle, length of the congruent sides is 13 cm and its base is 10 cm. Find the distance between the vertex opposite the base and the centroid.

If two circles touch each other externally or internally then the two centres and point of contact are collinear . Prove it

Solve the following quadratic equations by factorization method: [4 MARKS]4x2−4ax+(a2−b2)=0

The sum of an A.P whose first term is i+1, second term is j-2 and the last term is k, is equal to

Question 2 (i) Fill in the blanks: (i) A tangent to a circle intersects it at ___ point(s).

Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1), find the third vertex.

If the sum of three consecutive terms of an increasing AP is 66 and the product of the first and third of these term is 468 , then the third term is

If the system of equations 2x + 3y = 5, 4x + ky = 10 has infinitely many solutions, then k =(a) 1(b) ½(c) 3(d) 6

Sum of the zeros of a quadratic polynomial p(x)=x2−bx+c is equal to __.

If sec θ + tan θ = p, prove that sin θ = p2-1p2+1

A circle is inscribed in ΔABC touching the sides AB, BC and CA at points D, E and F respectively. If AB= 10 cm, BC = 12 cm and CA = 8 cm, then the lengths of AD, BE and CF respectively will be

Solve the following quadratic equations by factorization:1x-3+2x-2=8x; x≠0, 2, 3

27 If m(z)= z+az+bz+6 leaves remainders 3 and 0 when divided by (z-3) and (z-2) respectively, then find the values of a and b.

In an interference experiment, the ratio of amplitudes of coherent waves is a1a2=13. The ratio of maximum and minimum intensities of fringes will be

The ratio of income of two gentlemen is 9:7 and the ratio of their expenditure are 4:3. If each of them manages to save Rs. 2000 per month, find the difference in their monthly income.

In the given figure, E is any point in the interior of the circle with centre O. Chord AB=AC. If ∠OBE=20°, then find the value of x.

The interior of a building is in the form of a cylinder of base radius 12 m and height 3.5 m, surmounted by a cone of equal base and slant height 12.5 m. Find the internal curved surface area and the capacity of the building.

Question 1 Renu purchases two bags of fertilizer of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertilizer exact number of times.

If ɑ and β are zeros of the quadratic polynomial 2x2−x+4, then (1α+1)(1β+1) = ______

A bag contains 6 black, 7 red and 2 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is black or white.

If x tan 45o cos 60o = sin 60o cot 60o then x = ? (a) 1 (b)12 (c) 1√2 (d) √3

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 105 cm and the diameter of the hemispherical ends is 36 cm each, find the cost of polishing the surface of the solid at the rate of 21 paise per square cm. [4 MARKS]

If a chord of a circle of radius 28 cm makes an angle of 90 ° at the centre, then the area of the major segment is(a) 392 cm2(b) 1456 cm2(c) 1848 cm2(d) 2240 cm2

Determine the ratio in which a line 2x + y – 4 = 0 divides another line segment joining points A(2, – 2) and B(3, 7).

Can you please give examples for linear, quadratic and cubic polynomials in which they do not have zeroes of the polynomial at all ? Graphs along with it would be helpful.

The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Find four rational number between the -37 and 29 using the formula

tan 2 alpha=1-alpha 2 sec alfa+tancube alpha cosec alpha

Simplify: 5 + (− 5) + 5 + (− 5) + ...(i) When the number of terms is 20 (ii) When the number of terms is 25

Which of the following are Pair of Linear Equation in two variables?

In any triangle ABC, tanA2−tanB2tanA2+tanB2

Find the length of the hypotenuse of a right-angled triangle whose perpendicular sides are 5, 13.

If the radius of the hemisphere is 3r. Find its curved surface area.

Find the common difference of the A.P. and write the next two terms: (i) 51,59,67,75,… (ii) 75,57,59,51,… (iii) 1.8,2.0,2.2,2.4,… (iv) 0,14,12,34,… (v) 119,136,153,170,…

If |A| denotes the value of the determinant of a square matrix of order 3, then |–2A| = ___________.

A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm2. (Use π = 3.1416)

Mohit's mother is 47 years older than him. The product of their ages 8 years from now will be 860. The equation representing this situation is .

The value of x for which the numbers 2x+1, 5x+1, and 11x+1 are in G.P is ___ (x is a natural number).