32581 + Interview Questions in Mathematics Page 56 InterviewSolution

2751.	If the product of the zeroes of the quadratic polynomial x2 – 3ax + 2a2 – 1 is 7, then a = _______.
Answer» If the product of the zeroes of the quadratic polynomial x² – 3ax + 2a² – 1 is 7, then a = _______.

Discussion

2752.	Find a cubic polynomial with the sum of the product of its zeroes taken two at a time and product of its zeroes are 5, - 6,-20 respectively.
Answer» Find a cubic polynomial with the sum of the product of its zeroes taken two at a time and product of its zeroes are 5, - 6,-20 respectively.

Discussion

2753.	In ΔABC, ∠B = 35°, ∠C = 65° and the bisector of ∠BAC meets BC in X. Arrange AX, BX and CX in descending order.
Answer» In ΔABC, ∠B = 35°, ∠C = 65° and the bisector of ∠BAC meets BC in X. Arrange AX, BX and CX in descending order.

Discussion

2754.	Solve the following system of linear equations graphically :3x + y − 11 = 0, x − y − 1 = 0.Shade the region bounded by these lines and y-axis. Also, find the area of the region bounded by the these lines and y-axis.
Answer» Solve the following system of linear equations graphically : 3x + y − 11 = 0, x − y − 1 = 0. Shade the region bounded by these lines and y-axis. Also, find the area of the region bounded by the these lines and y-axis.

Discussion

2755.	What is the value of sin45∘sin30∘cos45∘cos30∘?
Answer» What is the value of $\frac{sin 45^{\circ} sin 30^{\circ}}{cos 45^{\circ} cos 30^{\circ}}$ ?

Discussion

2756.	If sin θ=45 and cos θ=35, then the value of tan θ= .
Answer» $If s i n θ = \frac{4}{5} and c o s θ = \frac{3}{5}, then the value of t a n θ =$ .

Discussion

2757.	Find the point on x-axis which is equidistant from points A(−1, 0) and B(5, 0). [CBSE 2013C]
Answer» Find the point on x-axis which is equidistant from points A(−1, 0) and B(5, 0). [CBSE 2013C]

Discussion

2758.	Solve the equation 5x2– 6x– 2 = 0 by the method of completing the square. Find the positive root.
Answer» Solve the equation 5 $x^{2}$ – 6 $x$ – 2 = 0 by the method of completing the square. Find the positive root.

Discussion

2759.	Nick tosses three coins simultaneously. What is the probability of getting at least two heads?
Answer» Nick tosses three coins simultaneously. What is the probability of getting at least two heads?

Discussion

2760.	Volume of a right circular cone of radius ′r ′ and height ′h ′ = .
Answer» Volume of a right circular cone of radius $^{'} r^{'}$ and height $^{'} h^{'}$ = .

Discussion

2761.	Question 2 (iii)Write whether the given statement is true or false. Justify your answer.Every quadratic equation has at least two roots.
Answer» Question 2 (iii) Write whether the given statement is true or false. Justify your answer. Every quadratic equation has at least two roots.

Discussion

2762.	The following graph represents
Answer» The following graph represents

2762.

The following graph represents

Answer»

The following graph represents

Discussion

2763.	The value of Δ=∣∣∣cos15∘sin15∘sin75∘cos75∘∣∣∣ is[1 mark]
Answer» The value of $Δ = ∣ ∣ ∣ \begin{matrix} cos 15^{\circ} & sin 15^{\circ} sin 75^{\circ} & cos 75^{\circ} \end{matrix} ∣ ∣ ∣$ is [1 mark]

Discussion

2764.	If the degree of is to be 5, what should be the degree of p(x)?
Answer» If the degree of is to be 5, what should be the degree of p(x)?

2764.

If the degree of is to be 5, what should be the degree of p(x)?

Answer»

If the degree of is to be 5, what should be the degree of p(x)?

Discussion

2765.	If a and b are roots of the equations x2−x+1=0, then write the value of a2+b2
Answer» If a and b are roots of the equations $x^{2} - x + 1 = 0$ , then write the value of $a^{2} + b^{2}$

Discussion

2766.	PQ is a tangent to a circle with centre O at the point P. If Δ OPQ is an isosceles triangle, then ∠OQP is equal to(a) 30°(b) 45°(c) 60°(d) 90°
Answer» PQ is a tangent to a circle with centre O at the point P. If Δ OPQ is an isosceles triangle, then ∠OQP is equal to (a) 30° (b) 45° (c) 60° (d) 90°

Discussion

2767.	Find the sum of all integers between 100 and 550, which are divisible by 9.
Answer» Find the sum of all integers between 100 and 550, which are divisible by 9.

Discussion

2768.	Find the algebraic expression to compute the third number of an arithmetic sequence, using the first and the second numbers.
Answer» Find the algebraic expression to compute the third number of an arithmetic sequence, using the first and the second numbers.

Discussion

2769.	A cone of height 36 cm and base radius 9 cm is reshaped into a sphere. Find the radius of the sphere formed.
Answer» A cone of height 36 cm and base radius 9 cm is reshaped into a sphere. Find the radius of the sphere formed.

Discussion

2770.	If 3 cot A = 4, check whether 1-tan2 A1+tan2 A=cos2 A-sin2 A or not.
Answer» If 3 cot A = 4, check whether $\frac{1 - \tan^{2} A}{1 + \tan^{2} A} = \cos^{2} A - \sin^{2} A$ or not.

Discussion

2771.	The cost of painting the curved surface area of a cylindrical pillar of height 10 m and radius 3.5 m at ₹ 10 per sq. meter is: (Take pi=227)
Answer» The cost of painting the curved surface area of a cylindrical pillar of height 10 m and radius 3.5 m at ₹ 10 per sq. meter is: (Take pi= $\frac{22}{7}$ )

Discussion

2772.	Determine the degree of each of the following polynomials.(i) 4x−5x2+6x32x(ii) y2(y−y3)(iii) (3x−2)(2x3+3x2)
Answer» Determine the degree of each of the following polynomials. (i) $\frac{4 x - 5 x^{2} + 6 x^{3}}{2 x}$ (ii) $y^{2} (y - y^{3})$ (iii) $(3 x - 2) (2 x^{3} + 3 x^{2})$

2772.

Determine the degree of each of the following polynomials.(i) 4x−5x2+6x32x(ii) y2(y−y3)(iii) (3x−2)(2x3+3x2)

Answer»

Determine the degree of each of the following polynomials.

(i) $\frac{4 x - 5 x^{2} + 6 x^{3}}{2 x}$

(ii) $y^{2} (y - y^{3})$

(iii) $(3 x - 2) (2 x^{3} + 3 x^{2})$

Discussion

2773.	Equal chords are equidistant from the center. Prove this. In the Proof, which principle are you making use of :
Answer» Equal chords are equidistant from the center. Prove this. In the Proof, which principle are you making use of :

Discussion

2774.	1- Why π is irrational and 22/7 is rational ?
Answer» 1- Why π is irrational and 22/7 is rational ?

Discussion

2775.	A window of a house is h metre above the ground . From the window , the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be α and β respectively. Prove that the height of the house is h1 + tan α tan β metres.
Answer» A window of a house is h metre above the ground . From the window , the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be $α$ and $β$ respectively. Prove that the height of the house is $h (1 + \tan α \tan β)$ metres.

Discussion

2776.	What portion of a circular paper would form a right circular cone of total surface area 84π cm2 and radius 6 cm?
Answer» What portion of a circular paper would form a right circular cone of total surface area $84 π c m^{2}$ and radius 6 cm?

Discussion

2777.	Q.5If a polynomial G(x), is divided by (x – 14) and (x – 71), then the remainders are 71 and 14 respectively. The remainder when G(x) is divided by (x – 14) (x – 71), is
Answer» Q.5 If a polynomial G(x), is divided by (x – 14) and (x – 71), then the remainders are 71 and 14 respectively. The remainder when G(x) is divided by (x – 14) (x – 71), is

Discussion

2778.	AD is the median of △ ABC. Area of △ABC : △ADB = ____.
Answer» AD is the median of △ ABC. Area of △ABC : △ADB = ____.

Discussion

2779.	If \|z + 2\| = \|z – 2\|, then the locus of z is ____________.
Answer» If \|z + 2\| = \|z – 2\|, then the locus of z is ____________.

Discussion

2780.	Prove the centroid their of triangles
Answer» Prove the centroid their of triangles

Discussion

2781.	Let A = [aij] and B = [bij] be a square matrices of order 3 such that bi1 = 2 ai1, bi2 = 3 ai2 and bi3 = 4 ai3, i = 1, 2, 3If \|A\| = 5, then \|B\| = _____________.
Answer» Let A = [a_ij] and B = [b_ij] be a square matrices of order 3 such that b_i₁ = 2 a_i₁, b_i₂ = 3 a_i₂ and b_i₃ = 4 a_i₃, i = 1, 2, 3 If \|A\| = 5, then \|B\| = _____________.

Discussion

2782.	Pass necessary Journal entries for the issue of debentures in the following cases:(a) ₹ 40,000; 12% Debentures of ₹ 100 each issued at a premium of 5% redeemable at par.(b) ₹ 70,000; 12% Debentures of ₹ 100 each issued at a premium of 5% redeemable at ₹ 110.
Answer» Pass necessary Journal entries for the issue of debentures in the following cases: (a) ₹ 40,000; 12% Debentures of ₹ 100 each issued at a premium of 5% redeemable at par. (b) ₹ 70,000; 12% Debentures of ₹ 100 each issued at a premium of 5% redeemable at ₹ 110.

Discussion

2783.	The number of points of inflection, number of point of intersections with x−axis and the number of points of local maximum for the curve y=x+tanx are given by l,m and n respectively ∀x∈(−π2,π2), then
Answer» The number of points of inflection, number of point of intersections with $x -$ axis and the number of points of local maximum for the curve $y = x + tan x$ are given by $l, m$ and $n$ respectively $\forall x \in (- \frac{π}{2}, \frac{π}{2}),$ then

Discussion

2784.	In the given figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that AD bisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is(a) 72°(b) 73°(c) 74°(d) 95°
Answer» In the given figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that AD bisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is (a) 72° (b) 73° (c) 74° (d) 95°

Discussion

2785.	What is the degree of following equation? (k+1)x2+32x=7, where k = -1
Answer» What is the degree of following equation? $(k + 1) x^{2} + \frac{3}{2} x = 7$ , where k = -1

2785.

What is the degree of following equation? (k+1)x2+32x=7, where k = -1

Answer»

What is the degree of following equation?

$(k + 1) x^{2} + \frac{3}{2} x = 7$ , where k = -1

Discussion

2786.	Find out the wrong number in the series given below :6,13,27,55,110,223
Answer» Find out the wrong number in the series given below : $6, 13, 27, 55, 110, 223$

Discussion

2787.	Choose the correct answer of the following question:The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes is(a) 64 : 27 (b) 16 : 9 (c) 4 : 3 (d) 163 : 93 [CBSE 2013C]
Answer» Choose the correct answer of the following question: The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes is (a) 64 : 27 (b) 16 : 9 (c) 4 : 3 (d) 16³ : 9³ [CBSE 2013C]

Discussion

2788.	In the given figure, m(arc WY) = 44°, m(arc ZX) = 68°, then(1) Find the measure of ∠ ZTX.(2) If WT = 4.8, TX = 8.0,YT = 6.4, find TZ.(3) If WX = 25, YT = 8,YZ = 26, find WT.
Answer» In the given figure, m(arc WY) = 44°, m(arc ZX) = 68°, then (1) Find the measure of ∠ ZTX. (2) If WT = 4.8, TX = 8.0, YT = 6.4, find TZ. (3) If WX = 25, YT = 8, YZ = 26, find WT.

Discussion

2789.	If the lines represented by the equations 3x – y – 5 = 0 and 6x – 2y – p = 0 are parallel, then p is equal to ________.
Answer» If the lines represented by the equations 3x – y – 5 = 0 and 6x – 2y – p = 0 are parallel, then p is equal to ________.

Discussion

2790.	If α, β are the zeros of the polynomial f(x) = ax2 + bx + c, then 1α2+1β2=(a) b2-2aca2(b) b2-2acc2(c) b2+2aca2(d) b2+2acc2
Answer» If α, β are the zeros of the polynomial f(x) = ax² + bx + c, then $\frac{1}{α^{2}} + \frac{1}{β^{2}} =$ (a) $\frac{b^{2} - 2 a c}{a^{2}}$ (b) $\frac{b^{2} - 2 a c}{c^{2}}$ (c) $\frac{b^{2} + 2 a c}{a^{2}}$ (d) $\frac{b^{2} + 2 a c}{c^{2}}$

Discussion

2791.	Let n(U) = 700, n(A) = 200, n(B) = 300 and n(A∩B)=100, Then n(Ac∩Bc)=
Answer» Let n(U) = 700, n(A) = 200, n(B) = 300 and $n (A \cap B) = 100$ , Then $n (A^{c} \cap B^{c}) =$

2791.

Let n(U) = 700, n(A) = 200, n(B) = 300 and n(A∩B)=100, Then n(Ac∩Bc)=

Answer»

Let n(U) = 700, n(A) = 200, n(B) = 300 and $n (A \cap B) = 100$ ,

Then $n (A^{c} \cap B^{c}) =$

Discussion

2792.	29. Prove that the intercepts of a tangent between a pair of parallel tangents to a circle subtend a right angle at the centre of the circle.
Answer» 29. Prove that the intercepts of a tangent between a pair of parallel tangents to a circle subtend a right angle at the centre of the circle.

Discussion

2793.	A man arranges to pay off a debt of3600 by 40 annual installments which form an arithmeticseries. When 30 installments were paid, he dies leaving one-third of the debt unpaid. Value ofthe first instalment is
Answer» A man arranges to pay off a debt of3600 by 40 annual installments which form an arithmetic series. When 30 installments were paid, he dies leaving one-third of the debt unpaid. Value of the first instalment is

Discussion

2794.	There is a square of side 4 unit. A point in the interior of the square is randomly chosen and a circle of radius 1 unit is drawn centered at the point. Then probability that the circle intersects the square exactly twice is
Answer» There is a square of side $4$ unit. A point in the interior of the square is randomly chosen and a circle of radius $1$ unit is drawn centered at the point. Then probability that the circle intersects the square exactly twice is

Discussion

2795.	In the given figure, if ∠POR=120°,then enter the value of ∠PQR in degrees.120
Answer» $In the given figure, if ∠ P O R = 120 °$ , $then enter the value of ∠ P Q R in degrees.$ 120

Discussion

2796.	The mean of the following distribution is ____.xi10131619fi2576
Answer» The mean of the following distribution is ____. $\begin{matrix} x_{i} & 10 & 13 & 16 & 19 f_{i} & 2 & 5 & 7 & 6 \end{matrix}$

2796.

The mean of the following distribution is ____.xi10131619fi2576

Answer»

The mean of the following distribution is ____.

$\begin{matrix} x_{i} & 10 & 13 & 16 & 19 f_{i} & 2 & 5 & 7 & 6 \end{matrix}$

Discussion

2797.	Three points A, B and C are collinear such that AB = 2BC. If the coordinates of the points A and B are (1, 7) and (6, -3) respectively, then the coordinates of the point C can be
Answer» Three points A, B and C are collinear such that AB = 2BC. If the coordinates of the points A and B are (1, 7) and (6, -3) respectively, then the coordinates of the point C can be

Discussion

2798.	In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
Answer» In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

Discussion

2799.	Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of its two circular faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm (see Fig.). If each cm3 of molasses has a mass of about 1.2 g, find the mass of the molasses that can be poured into each mould( in kg). (Take π = 227)
Answer» Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of its two circular faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm (see Fig.). If each $c m^{3}$ of molasses has a mass of about 1.2 g, find the mass of the molasses that can be poured into each mould( in kg). (Take $π$ = $\frac{22}{7}$ )

2799.

Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of its two circular faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm (see Fig.). If each cm3 of molasses has a mass of about 1.2 g, find the mass of the molasses that can be poured into each mould( in kg). (Take π = 227)

Answer»

Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of its two circular faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm (see Fig.). If each $c m^{3}$ of molasses has a mass of about 1.2 g, find the mass of the molasses that can be poured into each mould( in kg). (Take $π$ = $\frac{22}{7}$ )

Discussion

2800.	Prove that the square of any positive integer is of the form 4q or 4q + 1 for some integer q.
Answer» Prove that the square of any positive integer is of the form 4q or 4q + 1 for some integer q.

Discussion

Explore topic-wise InterviewSolutions in .

If the product of the zeroes of the quadratic polynomial x2 – 3ax + 2a2 – 1 is 7, then a = _______.

Find a cubic polynomial with the sum of the product of its zeroes taken two at a time and product of its zeroes are 5, - 6,-20 respectively.

In ΔABC, ∠B = 35°, ∠C = 65° and the bisector of ∠BAC meets BC in X. Arrange AX, BX and CX in descending order.

Solve the following system of linear equations graphically :3x + y − 11 = 0, x − y − 1 = 0.Shade the region bounded by these lines and y-axis. Also, find the area of the region bounded by the these lines and y-axis.

What is the value of sin45∘sin30∘cos45∘cos30∘?

If sin θ=45 and cos θ=35, then the value of tan θ= .

Find the point on x-axis which is equidistant from points A(−1, 0) and B(5, 0). [CBSE 2013C]

Solve the equation 5x2– 6x– 2 = 0 by the method of completing the square. Find the positive root.

Nick tosses three coins simultaneously. What is the probability of getting at least two heads?

Volume of a right circular cone of radius ′r ′ and height ′h ′ = .

Question 2 (iii)Write whether the given statement is true or false. Justify your answer.Every quadratic equation has at least two roots.

The following graph represents

The value of Δ=∣∣∣cos15∘sin15∘sin75∘cos75∘∣∣∣ is[1 mark]

If the degree of is to be 5, what should be the degree of p(x)?

If a and b are roots of the equations x2−x+1=0, then write the value of a2+b2

PQ is a tangent to a circle with centre O at the point P. If Δ OPQ is an isosceles triangle, then ∠OQP is equal to(a) 30°(b) 45°(c) 60°(d) 90°

Find the sum of all integers between 100 and 550, which are divisible by 9.

Find the algebraic expression to compute the third number of an arithmetic sequence, using the first and the second numbers.

A cone of height 36 cm and base radius 9 cm is reshaped into a sphere. Find the radius of the sphere formed.

If 3 cot A = 4, check whether 1-tan2 A1+tan2 A=cos2 A-sin2 A or not.

The cost of painting the curved surface area of a cylindrical pillar of height 10 m and radius 3.5 m at ₹ 10 per sq. meter is: (Take pi=227)

Determine the degree of each of the following polynomials.(i) 4x−5x2+6x32x(ii) y2(y−y3)(iii) (3x−2)(2x3+3x2)

Equal chords are equidistant from the center. Prove this. In the Proof, which principle are you making use of :

1- Why π is irrational and 22/7 is rational ?

A window of a house is h metre above the ground . From the window , the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be α and β respectively. Prove that the height of the house is h1 + tan α tan β metres.

What portion of a circular paper would form a right circular cone of total surface area 84π cm2 and radius 6 cm?

Q.5If a polynomial G(x), is divided by (x – 14) and (x – 71), then the remainders are 71 and 14 respectively. The remainder when G(x) is divided by (x – 14) (x – 71), is

AD is the median of △ ABC. Area of △ABC : △ADB = ____.

If |z + 2| = |z – 2|, then the locus of z is ____________.

Prove the centroid their of triangles

Let A = [aij] and B = [bij] be a square matrices of order 3 such that bi1 = 2 ai1, bi2 = 3 ai2 and bi3 = 4 ai3, i = 1, 2, 3If |A| = 5, then |B| = _____________.

Pass necessary Journal entries for the issue of debentures in the following cases:(a) ₹ 40,000; 12% Debentures of ₹ 100 each issued at a premium of 5% redeemable at par.(b) ₹ 70,000; 12% Debentures of ₹ 100 each issued at a premium of 5% redeemable at ₹ 110.

The number of points of inflection, number of point of intersections with x−axis and the number of points of local maximum for the curve y=x+tanx are given by l,m and n respectively ∀x∈(−π2,π2), then

In the given figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that AD bisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is(a) 72°(b) 73°(c) 74°(d) 95°

What is the degree of following equation? (k+1)x2+32x=7, where k = -1

Find out the wrong number in the series given below :6,13,27,55,110,223

Choose the correct answer of the following question:The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes is(a) 64 : 27 (b) 16 : 9 (c) 4 : 3 (d) 163 : 93 [CBSE 2013C]

In the given figure, m(arc WY) = 44°, m(arc ZX) = 68°, then(1) Find the measure of ∠ ZTX.(2) If WT = 4.8, TX = 8.0,YT = 6.4, find TZ.(3) If WX = 25, YT = 8,YZ = 26, find WT.

If the lines represented by the equations 3x – y – 5 = 0 and 6x – 2y – p = 0 are parallel, then p is equal to ________.

If α, β are the zeros of the polynomial f(x) = ax2 + bx + c, then 1α2+1β2=(a) b2-2aca2(b) b2-2acc2(c) b2+2aca2(d) b2+2acc2

Let n(U) = 700, n(A) = 200, n(B) = 300 and n(A∩B)=100, Then n(Ac∩Bc)=

29. Prove that the intercepts of a tangent between a pair of parallel tangents to a circle subtend a right angle at the centre of the circle.

A man arranges to pay off a debt of3600 by 40 annual installments which form an arithmeticseries. When 30 installments were paid, he dies leaving one-third of the debt unpaid. Value ofthe first instalment is

There is a square of side 4 unit. A point in the interior of the square is randomly chosen and a circle of radius 1 unit is drawn centered at the point. Then probability that the circle intersects the square exactly twice is

In the given figure, if ∠POR=120°,then enter the value of ∠PQR in degrees.120

The mean of the following distribution is ____.xi10131619fi2576

Three points A, B and C are collinear such that AB = 2BC. If the coordinates of the points A and B are (1, 7) and (6, -3) respectively, then the coordinates of the point C can be

In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

Prove that the square of any positive integer is of the form 4q or 4q + 1 for some integer q.