32581 + Interview Questions in Mathematics Page 114 InterviewSolution

5651.	Find the values of k for which the given equation has real and equal roots: [3 MARKS]x2−2x(1+3k)+7(3+2k)=0
Answer» Find the values of k for which the given equation has real and equal roots: [3 MARKS] $x^{2} - 2 x (1 + 3 k) + 7 (3 + 2 k) = 0$

Discussion

5652.	Which among the following pairs of terms have different literal factors?
Answer» Which among the following pairs of terms have different literal factors?

Discussion

5653.	The product of two consecutive positive even number is 48. Select the correct numbers.
Answer» The product of two consecutive positive even number is 48. Select the correct numbers.

Discussion

5654.	Prove that ratio of incircle and circumcircle of an equaliser al triangle is 1:2
Answer» Prove that ratio of incircle and circumcircle of an equaliser al triangle is 1:2

Discussion

5655.	Find the value of loge144.
Answer» Find the value of ${log}_{e} 144$ .

Discussion

5656.	Find the value of sin2θ+cos2θ at θ=30∘ & 60∘.
Answer» $F i n d t h e v a l u e o f s i n^{2} θ + c o s^{2} θ a t θ = 30^{\circ} & 60^{\circ}$ .

Discussion

5657.	Determine whether the given points are collinear.(1) A(0,2), B(1,–0.5), C(2,–3)(2) P1,2, Q2,85, R3,65(3) L(1,2), M(5,3) , N(8,6)
Answer» Determine whether the given points are collinear. (1) A(0,2), B(1,–0.5), C(2,–3) (2) $P (1, 2), Q (2, \frac{8}{5}), R (3, \frac{6}{5})$ (3) L(1,2), M(5,3) , N(8,6)

Discussion

5658.

Find the mean of each of the following frequency distributions : Class interval: 0−8 8−16 16−24 24−32 32−40 Frequency: 6 7 10 8 9

Answer» Find the mean of each of the following frequency distributions :

Class interval:	0−8	8−16	16−24	24−32	32−40
Frequency:	6	7	10	8	9

Discussion

5659.	(1,5,35), (7,5,5), (1, lambda,7) and (2 lambda, 1,2) are coplanar, then the sum of all possible values(1) 39/5(2) 44/5(3) -39/5(4) -44/5
Answer» (1,5,35), (7,5,5), (1, lambda,7) and (2 lambda, 1,2) are coplanar, then the sum of all possible values (1) 39/5 (2) 44/5 (3) -39/5 (4) -44/5

Discussion

5660.	How to find square root of polynomials?
Answer» How to find square root of polynomials?

Discussion

5661.	x^y +y^x =16 dy/dx at (2,2) equal to?
Answer» x^y +y^x =16 dy/dx at (2,2) equal to?

Discussion

5662.	The side of a square is equal to the side of an equilateral triangle. The ratio of their areas is (a) 4:3 (b) 2:√3 (c) 4:√3 (d) none of these
Answer» The side of a square is equal to the side of an equilateral triangle. The ratio of their areas is (a) 4:3 (b) 2: $\sqrt{3}$ (c) 4: $\sqrt{3}$ (d) none of these

5662.

The side of a square is equal to the side of an equilateral triangle. The ratio of their areas is (a) 4:3 (b) 2:√3 (c) 4:√3 (d) none of these

Answer»

The side of a square is equal to the side of an equilateral triangle. The ratio of their areas is

(a) 4:3 (b) 2: $\sqrt{3}$ (c) 4: $\sqrt{3}$ (d) none of these

Discussion

5663.	Two vectors P and Q having values P=(5î+3j) and Q=(5î-5j). The projection of P on Q is?
Answer» Two vectors P and Q having values P=(5î+3j) and Q=(5î-5j). The projection of P on Q is?

Discussion

5664.	In Fig. 7.141 DE \|\| BC such that AE=(14)AC. If AB = 6 cm, find AD.
Answer» In Fig. 7.141 DE \|\| BC such that $A E = (\frac{1}{4}) A C$ . If AB = 6 cm, find AD.

5664.

In Fig. 7.141 DE || BC such that AE=(14)AC. If AB = 6 cm, find AD.

Answer»

In Fig. 7.141 DE || BC such that $A E = (\frac{1}{4}) A C$ . If AB = 6 cm, find AD.

Discussion

5665.	Prove that 4-√3 is irrational
Answer» Prove that 4-√3 is irrational

Discussion

5666.	What is the value of (1 − cos2 θ) cosec2 θ?
Answer» What is the value of (1 − cos² θ) cosec² θ?

Discussion

5667.	In the following figure, shows a kite in which BCD is the shape of a quadrant of a circle of radius 42 cm. ABCD is a square and Δ CEF is an isosceles right angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.
Answer» In the following figure, shows a kite in which BCD is the shape of a quadrant of a circle of radius 42 cm. ABCD is a square and Δ CEF is an isosceles right angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.

Discussion

5668.	In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained by him in the two subjects separately.
Answer» In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained by him in the two subjects separately.

Discussion

5669.	From each of the two opposite corners of a square of side 8 cm, a quadrant of a circle of radius 1.4 cm is cut. Another circle of radius 4.2 cm is also cut from the centre as shown in the following figure. Find the area of the remaining (Shaded) portion of the square. (Use π = 22/7)
Answer» From each of the two opposite corners of a square of side 8 cm, a quadrant of a circle of radius 1.4 cm is cut. Another circle of radius 4.2 cm is also cut from the centre as shown in the following figure. Find the area of the remaining (Shaded) portion of the square. (Use π = 22/7)

Discussion

5670.	Conjugate surds of a+√b?
Answer» Conjugate surds of $a + \sqrt{b}$ ?

Discussion

5671.	If the sides of 4 squares are 4 cm , 3 cm , 2 cm and 1 cm respectively, what is the mean of their areas?
Answer» If the sides of 4 squares are 4 cm , 3 cm , 2 cm and 1 cm respectively, what is the mean of their areas?

Discussion

5672.	Which of the following options is the correct comparison of the coefficients of x2 if a1, a2, and a3 are given as shown below:a1x2:a2x2:a3x2:
Answer» Which of the following options is the correct comparison of the coefficients of $x^{2}$ if $a_{1}$ , $a_{2}$ , and $a_{3}$ are given as shown below: $a_{1} x^{2}$ : $a_{2} x^{2}$ : $a_{3} x^{2}$ :

Discussion

5673.	One leg of a right angled triangle exceeds the other leg by 2 inches. The hypotenuse is 10 inches. Find the length of the shorter leg of the triangle.
Answer» One leg of a right angled triangle exceeds the other leg by 2 inches. The hypotenuse is 10 inches. Find the length of the shorter leg of the triangle.

Discussion

5674.	If ∆ABC and ∆DEF are similar triangles such that AB = 3 cm, BC = 2 cm, CA = 2.5 cm and EF = 4 cm, write the perimeter of ∆DEF.
Answer» If ∆ABC and ∆DEF are similar triangles such that AB = 3 cm, BC = 2 cm, CA = 2.5 cm and EF = 4 cm, write the perimeter of ∆DEF.

Discussion

5675.	There are 5 blue balls, 6 black balls in basket 1 and 7 blue balls and 3 black balls in basket 2 respectively. If we take one ball from each basket, what is the probability of both balls being blue?
Answer» There are 5 blue balls, 6 black balls in basket 1 and 7 blue balls and 3 black balls in basket 2 respectively. If we take one ball from each basket, what is the probability of both balls being blue?

Discussion

5676.	is(1/x)^{-1}a polynomial
Answer» is(1/x)^{-1}a polynomial

Discussion

5677.	Find the area of the sector AOB of angle 120∘ and radius 18 cm.
Answer» Find the area of the sector $A O B$ of angle $120^{\circ}$ and radius $18 cm$ .

Discussion

5678.

Find the mode of the following distribution.(i) Class-interval: 0−10 10−20 20−30 30−40 40−50 50−60 60−70 70−80 Frequency: 5 8 7 12 28 20 10 10 (ii) Class-interval: 10−15 15−20 20−25 25−30 30−35 35−40 Frequency: 30 45 75 35 25 15 (iii) Class-interval: 25−30 30−35 35−40 40−45 45−50 50−55 Frequency: 25 34 50 42 38 14 (iv) Class: 0−10 10−20 20−30 30−40 40−50 50−60 60–70 Frequency: 8 10 10 16 12 6 7

Answer» Find the mode of the following distribution.

(i)

Class-interval:	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	5	8	7	12	28	20	10	10

(ii)

Class-interval:	10−15	15−20	20−25	25−30	30−35	35−40
Frequency:	30	45	75	35	25	15

(iii)

Class-interval:	25−30	30−35	35−40	40−45	45−50	50−55
Frequency:	25	34	50	42	38	14

(iv)

Class:	0−10	10−20	20−30	30−40	40−50	50−60	60–70
Frequency:	8	10	10	16	12	6	7

Discussion

5679.	Find the median of the following data:Class interval25−3535−4545−5555−6565−7575−8585−95Frequency1216171581913 58.33
Answer» Find the median of the following data: $\begin{matrix} Class interval & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 & 75 - 85 & 85 - 95 Frequency & 12 & 16 & 17 & 15 & 8 & 19 & 13 \end{matrix}$ 58.33

Discussion

5680.	ABCD is a trapezium such that BC \|\| AD and AD = 4 cm. If the diagonals AC and BD intersect at O such that AOOC=DOOB=12, then BC =(a) 7 cm(b) 8 cm(c) 9 cm(d) 6 cm
Answer» ABCD is a trapezium such that BC \|\| AD and AD = 4 cm. If the diagonals AC and BD intersect at O such that $\frac{AO}{OC} = \frac{DO}{OB} = \frac{1}{2}$ , then BC = (a) 7 cm (b) 8 cm (c) 9 cm (d) 6 cm

Discussion

5681.	A dealer sells an article for ₹75 and gains as much percent as the cost price of the article. Find the cost price of the article. [CBSE 2011]
Answer» A dealer sells an article for ₹75 and gains as much percent as the cost price of the article. Find the cost price of the article. [CBSE 2011]

Discussion

5682.	If the radius of a sphere is 12 cm, its surface area is . (Take π=3.14)
Answer» If the radius of a sphere is 12 cm, its surface area is . (Take $π = 3.14)$

Discussion

5683.	Prove the following trigonometric identities.cosecAcosecA-1+cosecAcosecA +1=2 sec2A
Answer» Prove the following trigonometric identities. $\frac{cosec A}{cosec A - 1} + \frac{cosec A}{cosec A + 1} = 2 \sec^{2} A$

Discussion

5684.	Find the roots of the equation 5x2−6x−2=0 by the method of completing the square.[3 MARKS]
Answer» Find the roots of the equation $5 x^{2} - 6 x - 2 = 0$ by the method of completing the square. [3 MARKS]

Discussion

5685.	Places a and b are 200 km apart on a highway.one car starts from a and another from b at the same time.if the cars travel in the same direction at different speed, they meet in 10 hours. Find the speed of the two cars.
Answer» Places a and b are 200 km apart on a highway.one car starts from a and another from b at the same time.if the cars travel in the same direction at different speed, they meet in 10 hours. Find the speed of the two cars.

Discussion

5686.	m and radius R is pivotedA uniform disc of massat point P and is free to rotate in vertical plane. Thecentre C of disc is initially in horizontal position withP as shown in figure. if it is released from thisposition, then its angular acceleration when the linePC is inclined to the horizontal at an angle θ is+02g cos θ1) 3Rg sin e2)2R42g sin e(4) 3R2g sin θ
Answer» m and radius R is pivotedA uniform disc of massat point P and is free to rotate in vertical plane. Thecentre C of disc is initially in horizontal position withP as shown in figure. if it is released from thisposition, then its angular acceleration when the linePC is inclined to the horizontal at an angle θ is+02g cos θ1) 3Rg sin e2)2R42g sin e(4) 3R2g sin θ

Discussion

5687.	The volume of used metal in making hemispherical shell with internal and external diameter as 8 cm and 10 cm respectively is
Answer» The volume of used metal in making hemispherical shell with internal and external diameter as 8 cm and 10 cm respectively is

Discussion

5688.	The area of a minor sector of a circle is 3.85 cm2 and the measure of its central angle is 36°. Find the radius of the circle .
Answer» The area of a minor sector of a circle is 3.85 cm²and the measure of its central angle is 36^°. Find the radius of the circle .

Discussion

5689.	A card is accidentally dropped from a pack of 52 cards. What is the probability of it being a card of diamond or a king of spade?
Answer» A card is accidentally dropped from a pack of 52 cards. What is the probability of it being a card of diamond or a king of spade?

Discussion

5690.	Which term of the A.P. 121, 117, 113 … is its first negative term?[Hint: Find n for an < 0]
Answer» Which term of the A.P. 121, 117, 113 … is its first negative term? [Hint: Find n for a_n < 0]

5690.

Which term of the A.P. 121, 117, 113 … is its first negative term?[Hint: Find n for an < 0]

Answer»

Which term of the A.P. 121, 117, 113 … is its first negative term?

[Hint: Find n for a_n < 0]

Discussion

5691.	In the given figure, PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 10 cm and CQ = 2 cm, what is the length PC?
Answer» In the given figure, PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 10 cm and CQ = 2 cm, what is the length PC?

Discussion

5692.	AP = x, PC = y and OP = r, the in radius of the right angled triangle ABC, with B right angled. Find the value of (1 + rx)(1 + ry)
Answer» AP = x, PC = y and OP = r, the in radius of the right angled triangle ABC, with B right angled. Find the value of (1 + $\frac{r}{x}$ )(1 + $\frac{r}{y}$ )

5692.

AP = x, PC = y and OP = r, the in radius of the right angled triangle ABC, with B right angled. Find the value of (1 + rx)(1 + ry)

Answer»

AP = x, PC = y and OP = r, the in radius of the right angled triangle ABC, with B right angled.

Find the value of (1 + $\frac{r}{x}$ )(1 + $\frac{r}{y}$ )

Discussion

5693.	The mean of first ten even natural numbers is
Answer» The mean of first ten even natural numbers is

Discussion

5694.	Prove that (5−2√3) is an irrational number.
Answer» Prove that $(5 - 2 \sqrt{3})$ is an irrational number.

Discussion

5695.	In the given figure, C and D are points on the semi-circle described on AB as diameter. Given angle BAD = 700 and angle DBC= 300. Calculate ∠BDC
Answer» In the given figure, C and D are points on the semi-circle described on AB as diameter. Given angle BAD = $70^{0}$ and angle DBC= $30^{0}$ . Calculate $∠ B D C$

5695.

In the given figure, C and D are points on the semi-circle described on AB as diameter. Given angle BAD = 700 and angle DBC= 300. Calculate ∠BDC

Answer»

In the given figure, C and D are points on the semi-circle described on AB as diameter. Given angle BAD = $70^{0}$ and angle DBC= $30^{0}$ . Calculate $∠ B D C$

Discussion

5696.	Obtain all the zeros of the polynomial x4 + x3 – 14x2 – 2x + 24 if two of its zeros are 2 and -2.
Answer» Obtain all the zeros of the polynomial x⁴+ x³– 14x²– 2x + 24 if two of its zeros are $\sqrt{2} and - \sqrt{2}$ .

Discussion

5697.	Area of the loop of the curve }x=\sqrt{15}(1-t^2),y=\sqrt{15}t(1-t^2),t∈\lbrack-1,1\rbrack
Answer» Area of the loop of the curve }x=\sqrt{15}(1-t^2),y=\sqrt{15}t(1-t^2),t∈\lbrack-1,1\rbrack

Discussion

5698.	If sin3A=cos(A-26°),where 3A is an acute angle find the value of A.
Answer» If sin3A=cos(A-26°),where 3A is an acute angle find the value of A.

Discussion

5699.	Show that x = −3 is a solution of x2 + 6x + 9 = 0.
Answer» Show that x = −3 is a solution of x² + 6x + 9 = 0.

Discussion

5700.	In ΔABC, ADDB=AEEC and ∠ADE = ∠ACB. Then ΔABC is
Answer» In $Δ A B C$ , $\frac{A D}{D B} = \frac{A E}{E C}$ and $∠ A D E$ = $∠ A C B$ . Then $Δ A B C$ is

Discussion

Explore topic-wise InterviewSolutions in .

Find the values of k for which the given equation has real and equal roots: [3 MARKS]x2−2x(1+3k)+7(3+2k)=0

Which among the following pairs of terms have different literal factors?

The product of two consecutive positive even number is 48. Select the correct numbers.

Prove that ratio of incircle and circumcircle of an equaliser al triangle is 1:2

Find the value of loge144.

Find the value of sin2θ+cos2θ at θ=30∘ &amp; 60∘.

Determine whether the given points are collinear.(1) A(0,2), B(1,–0.5), C(2,–3)(2) P1,2, Q2,85, R3,65(3) L(1,2), M(5,3) , N(8,6)

Find the mean of each of the following frequency distributions : Class interval: 0−8 8−16 16−24 24−32 32−40 Frequency: 6 7 10 8 9

(1,5,35), (7,5,5), (1, lambda,7) and (2 lambda, 1,2) are coplanar, then the sum of all possible values(1) 39/5(2) 44/5(3) -39/5(4) -44/5

How to find square root of polynomials?

x^y +y^x =16 dy/dx at (2,2) equal to?

The side of a square is equal to the side of an equilateral triangle. The ratio of their areas is (a) 4:3 (b) 2:√3 (c) 4:√3 (d) none of these

Two vectors P and Q having values P=(5î+3j) and Q=(5î-5j). The projection of P on Q is?

In Fig. 7.141 DE || BC such that AE=(14)AC. If AB = 6 cm, find AD.

Prove that 4-√3 is irrational

What is the value of (1 − cos2 θ) cosec2 θ?

In the following figure, shows a kite in which BCD is the shape of a quadrant of a circle of radius 42 cm. ABCD is a square and Δ CEF is an isosceles right angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.

In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained by him in the two subjects separately.

From each of the two opposite corners of a square of side 8 cm, a quadrant of a circle of radius 1.4 cm is cut. Another circle of radius 4.2 cm is also cut from the centre as shown in the following figure. Find the area of the remaining (Shaded) portion of the square. (Use π = 22/7)

Conjugate surds of a+√b?

If the sides of 4 squares are 4 cm , 3 cm , 2 cm and 1 cm respectively, what is the mean of their areas?

Which of the following options is the correct comparison of the coefficients of x2 if a1, a2, and a3 are given as shown below:a1x2:a2x2:a3x2:

One leg of a right angled triangle exceeds the other leg by 2 inches. The hypotenuse is 10 inches. Find the length of the shorter leg of the triangle.

If ∆ABC and ∆DEF are similar triangles such that AB = 3 cm, BC = 2 cm, CA = 2.5 cm and EF = 4 cm, write the perimeter of ∆DEF.

There are 5 blue balls, 6 black balls in basket 1 and 7 blue balls and 3 black balls in basket 2 respectively. If we take one ball from each basket, what is the probability of both balls being blue?

is(1/x)^{-1}a polynomial

Find the area of the sector AOB of angle 120∘ and radius 18 cm.

Find the median of the following data:Class interval25−3535−4545−5555−6565−7575−8585−95Frequency1216171581913 58.33

ABCD is a trapezium such that BC || AD and AD = 4 cm. If the diagonals AC and BD intersect at O such that AOOC=DOOB=12, then BC =(a) 7 cm(b) 8 cm(c) 9 cm(d) 6 cm

A dealer sells an article for ₹75 and gains as much percent as the cost price of the article. Find the cost price of the article. [CBSE 2011]

If the radius of a sphere is 12 cm, its surface area is . (Take π=3.14)

Prove the following trigonometric identities.cosecAcosecA-1+cosecAcosecA +1=2 sec2A

Find the roots of the equation 5x2−6x−2=0 by the method of completing the square.[3 MARKS]

Places a and b are 200 km apart on a highway.one car starts from a and another from b at the same time.if the cars travel in the same direction at different speed, they meet in 10 hours. Find the speed of the two cars.

The volume of used metal in making hemispherical shell with internal and external diameter as 8 cm and 10 cm respectively is

The area of a minor sector of a circle is 3.85 cm2 and the measure of its central angle is 36°. Find the radius of the circle .

A card is accidentally dropped from a pack of 52 cards. What is the probability of it being a card of diamond or a king of spade?

Which term of the A.P. 121, 117, 113 … is its first negative term?[Hint: Find n for an &lt; 0]

In the given figure, PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 10 cm and CQ = 2 cm, what is the length PC?

AP = x, PC = y and OP = r, the in radius of the right angled triangle ABC, with B right angled. Find the value of (1 + rx)(1 + ry)

The mean of first ten even natural numbers is

Prove that (5−2√3) is an irrational number.

In the given figure, C and D are points on the semi-circle described on AB as diameter. Given angle BAD = 700 and angle DBC= 300. Calculate ∠BDC

Obtain all the zeros of the polynomial x4 + x3 – 14x2 – 2x + 24 if two of its zeros are 2 and -2.

Area of the loop of the curve }x=\sqrt{15}(1-t^2),y=\sqrt{15}t(1-t^2),t∈\lbrack-1,1\rbrack

If sin3A=cos(A-26°),where 3A is an acute angle find the value of A.

Show that x = −3 is a solution of x2 + 6x + 9 = 0.

In ΔABC, ADDB=AEEC and ∠ADE = ∠ACB. Then ΔABC is

Find the value of sin2θ+cos2θ at θ=30∘ & 60∘.

Which term of the A.P. 121, 117, 113 … is its first negative term?[Hint: Find n for an < 0]