24740 + Interview Questions in Mathematics Page 111 InterviewSolution

5501.	Question 6 For which values of a and b, the zeroes of q(x)=x3+2x2+a are also the zeroes of the polynomial p(x)=x5–x4–4x3+3x2+3x+b? which zeroes of p (x) are not the zeroes of q(x)?
Answer» Question 6 For which values of a and b, the zeroes of $q (x) = x^{3} + 2 x^{2} + a$ are also the zeroes of the polynomial $p (x) = x^{5} - x^{4} - 4 x^{3} + 3 x^{2} + 3 x + b ?$ which zeroes of p (x) are not the zeroes of q(x)?

Discussion

5502.	In given Fig., two chords AB and CD intersect each other at the point P Prove that:(i) ΔAPC~ΔDPB(ii) AP . PB = CP . DP
Answer» In given Fig., two chords AB and CD intersect each other at the point P Prove that: (i) $Δ APC~ Δ DPB$ (ii) AP . PB = CP . DP

Discussion

5503.	The data is given for 62 students in a certain class regarding their mathematics marks out of 100. Take the classes 0-10, 10-20.. and prepare frequency distribution table and cumulative frequency table more than or equal to type.55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 2 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49. From the prepared table, answer the following questions :(i) How many students obtained marks 40 or above 40 ?(ii) How many students obtained marks 90 or above 90 ?(iii) How many students obtained marks 60 or above 60 ?(iv) What is the cumulative frequency of equal to or more than type of the class 0-10?
Answer» The data is given for 62 students in a certain class regarding their mathematics marks out of 100. Take the classes 0-10, 10-20.. and prepare frequency distribution table and cumulative frequency table more than or equal to type. 55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 2 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49. From the prepared table, answer the following questions : (i) How many students obtained marks 40 or above 40 ? (ii) How many students obtained marks 90 or above 90 ? (iii) How many students obtained marks 60 or above 60 ? (iv) What is the cumulative frequency of equal to or more than type of the class 0-10?

Discussion

5504.	74.The perimeter of the right triangle is 60cm. Its hypotenuse is 25cm. Find the area of the triangle
Answer» 74.The perimeter of the right triangle is 60cm. Its hypotenuse is 25cm. Find the area of the triangle

Discussion

5505.	Question 3If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is(A) 6 cm(B) 8 cm(C) 10 cm(D) 12 cm
Answer» Question 3 If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is (A) 6 cm (B) 8 cm (C) 10 cm (D) 12 cm

Discussion

5506.	In what ratio does the X-axis divide the line segment joining the points (-4,-6) and (-1,7)? Find the coordinates of the points of division.
Answer» In what ratio does the X-axis divide the line segment joining the points (-4,-6) and (-1,7)? Find the coordinates of the points of division.

Discussion

5507.	Consider two triangles shown.If ΔABC⩭ΔDEF, what is the measure of angle E?
Answer» Consider two triangles shown. If $Δ A B C ⩭ Δ D E F$ , what is the measure of angle E?

Discussion

5508.	Two circles touch each other externally. The sum of their areas is (106π)cm2 and the distance between their centers is 14 cm. Find the individual diameters of the circles.
Answer» Two circles touch each other externally. The sum of their areas is $(106 π) c m^{2}$ and the distance between their centers is 14 cm. Find the individual diameters of the circles.

Discussion

5509.	How much Percentage of area of an equilateral triangle will increase if it's side is increased 3 times?
Answer» How much Percentage of area of an equilateral triangle will increase if it's side is increased 3 times?

Discussion

5510.	22. If theta=540degree then cot theta equal to
Answer» 22. If theta=540degree then cot theta equal to

Discussion

5511.	The compound interest on₹30000 at 8% per annum is ₹4992. The period (in years) is_____.
Answer» The compound interest on₹30000 at $8 %$ per annum is ₹4992. The period (in years) is_____.

Discussion

5512.	In Fig. PQR is a triangle and S is any point in iits interior. show that SQ+SR<PQ+PR
Answer» In Fig. $P Q R$ is a triangle and $S$ is any point in iits interior. show that $S Q + S R < P Q + P R$

Discussion

5513.	If the median of scores x2,x3,x4,x5 and x6 (where x > 0) is 6, then find the value of x6.
Answer» If the median of scores $\frac{x}{2}, \frac{x}{3}, \frac{x}{4}, \frac{x}{5}$ and $\frac{x}{6}$ (where x > 0) is 6, then find the value of $\frac{x}{6}$ .

Discussion

5514.	10. What is zeros of xx+1
Answer» 10. What is zeros of xx+1

Discussion

5515.	7 log (1615)+5 log(2524)+3 log(8180) =
Answer» $7 l o g (\frac{16}{15}) + 5 l o g (\frac{25}{24}) + 3 l o g (\frac{81}{80})$ =

Discussion

5516.	Question 5 (v) An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below: Monthly income(inRs)Vehicles per family012Above 2Less than 7000101602507000−10000030527210000−13000153529113000−160002469592516000 or more15798288 Suppose a family is chosen, find the probability that the family chosen is (v) owning not more than 1 vehicle.
Answer» Question 5 (v) An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below: $\begin{matrix} M o n t h l y i n c o m e (i n R s) & V e h i c l e s p e r f a m i l y 0 & 1 & 2 & A b o v e 2 L e s s t h a n 7000 & 10 & 160 & 25 & 0 7000 - 10000 & 0 & 305 & 27 & 2 10000 - 13000 & 1 & 535 & 29 & 1 13000 - 16000 & 2 & 469 & 59 & 25 16000 o r m o r e & 1 & 579 & 82 & 88 \end{matrix}$ Suppose a family is chosen, find the probability that the family chosen is (v) owning not more than 1 vehicle.

Discussion

5517.	In a ΔPQR, if PQ = QR and mid-points of three sides PQ, QR and RP are L, M and N respectively. Prove that LN = MN.
Answer» In a ΔPQR, if PQ = QR and mid-points of three sides PQ, QR and RP are L, M and N respectively. Prove that LN = MN.

Discussion

5518.	Solve the following pair of equations: 8v−3u=5uv 6v−5u=−2uv
Answer» Solve the following pair of equations: $8 v - 3 u = 5 u v$ $6 v - 5 u = - 2 u v$

Discussion

5519.	There are 20 non-collinear points in a plane. How many (a) straight lines (b) triangles can be drawn by joining these points?
Answer» There are 20 non-collinear points in a plane. How many (a) straight lines (b) triangles can be drawn by joining these points?

Discussion

5520.	AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of AB and AC from the centre then prove that 4q2=p2+3r2.
Answer» AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of AB and AC from the centre then prove that $4 q^{2} = p^{2} + 3 r^{2}$ .

Discussion

5521.	If a website gets 2,880 hits in a day, what is its average number of hits per hour?
Answer» If a website gets 2,880 hits in a day, what is its average number of hits per hour?

Discussion

5522.	If the value of x for which the matrixA=⎡⎢⎣2070101−21⎤⎥⎦ is the inverse of B=⎡⎢⎣−x14x7x010x−4x−2x⎤⎥⎦ is k, then 10k is
Answer» If the value of $x$ for which the matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦$ is the inverse of $B = ⎡ ⎢ ⎣ \begin{matrix} - x & 14 x & 7 x 0 & 1 & 0 x & - 4 x & - 2 x \end{matrix} ⎤ ⎥ ⎦$ is $k,$ then $10 k$ is

Discussion

5523.	To make a parabola is it necessary to take 9 points
Answer» To make a parabola is it necessary to take 9 points

Discussion

5524.	6. Let ABC be a right-angled triangle with /_B=90 degree. Let I be the incentre of ABC. Let AI extended intersect BC at F. Draw a line perpendicular to AI at I. Let it intersect AC at E. Prove that IE=IF.
Answer» 6. Let ABC be a right-angled triangle with /_B=90 degree. Let I be the incentre of ABC. Let AI extended intersect BC at F. Draw a line perpendicular to AI at I. Let it intersect AC at E. Prove that IE=IF.

Discussion

5525.	In figure AB \|\| CD. Find the value of x.
Answer» In figure AB \|\| CD. Find the value of x.

Discussion

5526.	Divide: f(x)=9x3−3x2+x−5 by g(x)=x−23
Answer» Divide: $f (x) = 9 x^{3} - 3 x^{2} + x - 5$ by $g (x) = x - \frac{2}{3}$

Discussion

5527.	Find the value of 32×3−5.
Answer» Find the value of $3^{2} \times 3^{- 5}$ .

Discussion

5528.	Express the following linear equations in the form ax+by+c=0 and indicate the values of a, b and c in each case:(i) 3x=−7y (ii) y−5=0(iii) 4=3x
Answer» Express the following linear equations in the form $a x + b y + c = 0$ and indicate the values of a, b and c in each case: (i) $3 x = - 7 y$ (ii) $y - 5 = 0$ (iii) $4 = 3 x$

5528.

Express the following linear equations in the form ax+by+c=0 and indicate the values of a, b and c in each case:(i) 3x=−7y (ii) y−5=0(iii) 4=3x

Answer»

Express the following linear equations in the form $a x + b y + c = 0$ and indicate the values of a, b and c in each case:

(i) $3 x = - 7 y$ (ii) $y - 5 = 0$

(iii) $4 = 3 x$

Discussion

5529.	InΔPQR,if ∠P−∠Q=42∘ and ∠Q−∠R=21∘,find ∠P,∠Q and∠R.
Answer» $I n Δ P Q R, i f ∠ P - ∠ Q = 42^{\circ} a n d ∠ Q - ∠ R = 21^{\circ}, f i n d ∠ P, ∠ Q a n d ∠ R .$

5529.

InΔPQR,if ∠P−∠Q=42∘ and ∠Q−∠R=21∘,find ∠P,∠Q and∠R.

Answer»

$I n Δ P Q R, i f ∠ P - ∠ Q = 42^{\circ} a n d ∠ Q - ∠ R = 21^{\circ}, f i n d ∠ P, ∠ Q a n d ∠ R .$

Discussion

5530.	There are 7 observations in the data and their mean is 11. If each observation is multiplied by2, then the mean of new observations is(a) 11 (b) 13 (c) 22 (d) 55
Answer» There are 7 observations in the data and their mean is 11. If each observation is multiplied by 2, then the mean of new observations is (a) 11 (b) 13 (c) 22 (d) 55

Discussion

5531.	Question 86 (xiii)Using suitable identities, evaluate the following:(9.9)2
Answer» Question 86 (xiii) Using suitable identities, evaluate the following: $(9.9)^{2}$

5531.

Question 86 (xiii)Using suitable identities, evaluate the following:(9.9)2

Answer»

Question 86 (xiii)

Using suitable identities, evaluate the following:

$(9.9)^{2}$

Discussion

5532.	The locus of the point for which z = 0, x = 0, is(a) equation of x-axis(b) equation of y-axis(c) equation of z-axis(d) none of these
Answer» The locus of the point for which z = 0, x = 0, is (a) equation of x-axis (b) equation of y-axis (c) equation of z-axis (d) none of these

Discussion

5533.	If the distance between the directrices of an ellipse be three times the distance between its foci, then the eccentricity is ___________.
Answer» If the distance between the directrices of an ellipse be three times the distance between its foci, then the eccentricity is ___________.

Discussion

5534.	The function f : R → R defined by f(x) =(x - 1)(x - 2)(x - 3) is
Answer» The function f : R $\to$ R defined by f(x) =(x - 1)(x - 2)(x - 3) is

Discussion

5535.	What will be the next pattern in the given series?
Answer» What will be the next pattern in the given series?

Discussion

5536.	Express each of the following decimals in the form pq:(i) 0.39(ii) 0.750(iii) 2.15(iv) 7.010(v) 9.90(vi) 1.0001
Answer» Express each of the following decimals in the form $\frac{p}{q} :$ (i) 0.39 (ii) 0.750 (iii) 2.15 (iv) 7.010 (v) 9.90 (vi) 1.0001

Discussion

5537.	What is the meaning of the statement: Reflex of angle AEC
Answer» What is the meaning of the statement: Reflex of angle AEC

5537.

What is the meaning of the statement: Reflex of angle AEC

Answer»

What is the meaning of the statement:

Reflex of angle AEC

Discussion

5538.	(i) Identify the set of triangles with equal area from the figure given below:(ii) What will be the Ar(△ BDG), if Ar(△CDG) is 27 sq.cm.
Answer» (i) Identify the set of triangles with equal area from the figure given below: (ii) What will be the Ar( $△$ BDG), if Ar( $△$ CDG) is 27 sq.cm.

Discussion

5539.	Question 1 Draw the graph of linear equations y = x and y = -x on the same Cartesian plane. What do you observe?
Answer» Question 1 Draw the graph of linear equations y = x and y = -x on the same Cartesian plane. What do you observe?

Discussion

5540.	find the rate of change of the total surface area of a cylinder of radius r and height h , when the radius varies
Answer» find the rate of change of the total surface area of a cylinder of radius r and height h , when the radius varies

Discussion

5541.	Verify whether the following are zeroes of the polynomial, indicated against them.(i) (ii) (iii) p(x) = x2 − 1, x = 1, − 1 (iv) p(x) = (x + 1) (x − 2), x = − 1, 2(v) p(x) = x2 , x = 0 (vi) p(x) = lx + m(vii) (viii)
Answer» Verify whether the following are zeroes of the polynomial, indicated against them. (i) (ii) (iii) p(x) = x² − 1, x = 1, − 1 (iv) p(x) = (x + 1) (x − 2), x = − 1, 2 (v) p(x) = x², x = 0 (vi) p(x) = lx + m (vii) (viii)

5541.

Verify whether the following are zeroes of the polynomial, indicated against them.(i) (ii) (iii) p(x) = x2 − 1, x = 1, − 1 (iv) p(x) = (x + 1) (x − 2), x = − 1, 2(v) p(x) = x2 , x = 0 (vi) p(x) = lx + m(vii) (viii)

Answer»

Verify whether the following are zeroes of the polynomial, indicated against them.

(i) (ii)

(iii) p(x) = x² − 1, x = 1, − 1 (iv) p(x) = (x + 1) (x − 2), x = − 1, 2

(v) p(x) = x², x = 0 (vi) p(x) = lx + m

(vii) (viii)

Discussion

5542.	If log10(x2−21)=2, then find the value of x.
Answer» If $l o g_{10} (x^{2} - 21) = 2$ , then find the value of $x$ .

Discussion

5543.	What is the combined fraction of sweets eaten by John and Alex?
Answer» What is the combined fraction of sweets eaten by John and Alex?

Discussion

5544.	In the adjoining figure, ABCD is a square and ΔEDC is an equilateral triangle. Prove that (i) AE=BE, (ii) ∠DAE=15∘.
Answer» In the adjoining figure, $A B C D$ is a square and $Δ E D C$ is an equilateral triangle. Prove that (i) $A E = B E,$ (ii) $∠ D A E = 15^{\circ}$ .

5544.

In the adjoining figure, ABCD is a square and ΔEDC is an equilateral triangle. Prove that (i) AE=BE, (ii) ∠DAE=15∘.

Answer»

In the adjoining figure, $A B C D$ is a square and $Δ E D C$ is an equilateral triangle. Prove that (i) $A E = B E,$ (ii) $∠ D A E = 15^{\circ}$ .

Discussion

5545.	In what time Rs 800 amount to Rs 882 at 5% p.a. compounded annually?
Answer» In what time Rs 800 amount to Rs 882 at 5% p.a. compounded annually?

Discussion

5546.	In the figure, ABCD is a square of side 14 cm with centres A, B, C, and D four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region. [3 MARKS]
Answer» In the figure, ABCD is a square of side 14 cm with centres A, B, C, and D four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region. [3 MARKS]

5546.

In the figure, ABCD is a square of side 14 cm with centres A, B, C, and D four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region. [3 MARKS]

Answer»

In the figure, ABCD is a square of side 14 cm with centres A, B, C, and D four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region. [3 MARKS]

Discussion

5547.	Factorise = (a^3-b^3)-(a-b)^3
Answer» Factorise = (a^3-b^3)-(a-b)^3

Discussion

5548.	10. If two opposite vertices of a square are (-1,2) and (3,2).Find the other two coordinates
Answer» 10. If two opposite vertices of a square are (-1,2) and (3,2).Find the other two coordinates

Discussion

5549.	A triangle with sides 12, 16 and 20 units is given. Statement 1: To find the area of this triangle, the formula "Area =12×base×height" is the ideal one to be used. Statement 2: To find the area, the formula "Area =√s(s−a)(s−b)(s−c)" is the ideal one to be used. Enter “1” if you feel Statement 1 is correct, or “2” if Statement 2 is correct. ___
Answer» A triangle with sides 12, 16 and 20 units is given. Statement 1: To find the area of this triangle, the formula "Area $= \frac{1}{2} \times base \times height$ " is the ideal one to be used. Statement 2: To find the area, the formula "Area $= \sqrt{s (s - a) (s - b) (s - c)}$ " is the ideal one to be used. Enter “1” if you feel Statement 1 is correct, or “2” if Statement 2 is correct. ___

5549.

A triangle with sides 12, 16 and 20 units is given. Statement 1: To find the area of this triangle, the formula "Area =12×base×height" is the ideal one to be used. Statement 2: To find the area, the formula "Area =√s(s−a)(s−b)(s−c)" is the ideal one to be used. Enter “1” if you feel Statement 1 is correct, or “2” if Statement 2 is correct. ___

Answer»

A triangle with sides 12, 16 and 20 units is given.

Statement 1: To find the area of this triangle, the formula "Area $= \frac{1}{2} \times base \times height$ " is the ideal one to be used.

Statement 2: To find the area, the formula "Area $= \sqrt{s (s - a) (s - b) (s - c)}$ " is the ideal one to be used.

Enter “1” if you feel Statement 1 is correct, or “2” if Statement 2 is correct.
___

Discussion

5550.	If →u=→a−→b and →v=→a+→b and \|→a\|=\|→b\|=2, then \|→u×→v\|=
Answer» $I f \to u = \to a - \to b a n d \to v = \to a + \to b a n d \| \to a \| = \| \to b \| = 2, t h e n \| \to u \times \to v \| =$

Discussion

Explore topic-wise InterviewSolutions in .

Question 6 For which values of a and b, the zeroes of q(x)=x3+2x2+a are also the zeroes of the polynomial p(x)=x5–x4–4x3+3x2+3x+b? which zeroes of p (x) are not the zeroes of q(x)?

In given Fig., two chords AB and CD intersect each other at the point P Prove that:(i) ΔAPC~ΔDPB(ii) AP . PB = CP . DP

74.The perimeter of the right triangle is 60cm. Its hypotenuse is 25cm. Find the area of the triangle

Question 3If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is(A) 6 cm(B) 8 cm(C) 10 cm(D) 12 cm

In what ratio does the X-axis divide the line segment joining the points (-4,-6) and (-1,7)? Find the coordinates of the points of division.

Consider two triangles shown.If ΔABC⩭ΔDEF, what is the measure of angle E?

Two circles touch each other externally. The sum of their areas is (106π)cm2 and the distance between their centers is 14 cm. Find the individual diameters of the circles.

How much Percentage of area of an equilateral triangle will increase if it's side is increased 3 times?

22. If theta=540degree then cot theta equal to

The compound interest on₹30000 at 8% per annum is ₹4992. The period (in years) is_____.

In Fig. PQR is a triangle and S is any point in iits interior. show that SQ+SR&lt;PQ+PR

If the median of scores x2,x3,x4,x5 and x6 (where x > 0) is 6, then find the value of x6.

10. What is zeros of xx+1

7 log (1615)+5 log(2524)+3 log(8180) =

In a ΔPQR, if PQ = QR and mid-points of three sides PQ, QR and RP are L, M and N respectively. Prove that LN = MN.

Solve the following pair of equations: 8v−3u=5uv 6v−5u=−2uv

There are 20 non-collinear points in a plane. How many (a) straight lines (b) triangles can be drawn by joining these points?

AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of AB and AC from the centre then prove that 4q2=p2+3r2.

If a website gets 2,880 hits in a day, what is its average number of hits per hour?

If the value of x for which the matrixA=⎡⎢⎣2070101−21⎤⎥⎦ is the inverse of B=⎡⎢⎣−x14x7x010x−4x−2x⎤⎥⎦ is k, then 10k is

To make a parabola is it necessary to take 9 points

6. Let ABC be a right-angled triangle with /_B=90 degree. Let I be the incentre of ABC. Let AI extended intersect BC at F. Draw a line perpendicular to AI at I. Let it intersect AC at E. Prove that IE=IF.

In figure AB || CD. Find the value of x.

Divide: f(x)=9x3−3x2+x−5 by g(x)=x−23

Find the value of 32×3−5.

Express the following linear equations in the form ax+by+c=0 and indicate the values of a, b and c in each case:(i) 3x=−7y (ii) y−5=0(iii) 4=3x

InΔPQR,if ∠P−∠Q=42∘ and ∠Q−∠R=21∘,find ∠P,∠Q and∠R.

There are 7 observations in the data and their mean is 11. If each observation is multiplied by2, then the mean of new observations is(a) 11 (b) 13 (c) 22 (d) 55

Question 86 (xiii)Using suitable identities, evaluate the following:(9.9)2

The locus of the point for which z = 0, x = 0, is(a) equation of x-axis(b) equation of y-axis(c) equation of z-axis(d) none of these

If the distance between the directrices of an ellipse be three times the distance between its foci, then the eccentricity is ___________.

The function f : R → R defined by f(x) =(x - 1)(x - 2)(x - 3) is

What will be the next pattern in the given series?

Express each of the following decimals in the form pq:(i) 0.39(ii) 0.750(iii) 2.15(iv) 7.010(v) 9.90(vi) 1.0001

What is the meaning of the statement: Reflex of angle AEC

(i) Identify the set of triangles with equal area from the figure given below:(ii) What will be the Ar(△ BDG), if Ar(△CDG) is 27 sq.cm.

Question 1 Draw the graph of linear equations y = x and y = -x on the same Cartesian plane. What do you observe?

find the rate of change of the total surface area of a cylinder of radius r and height h , when the radius varies

Verify whether the following are zeroes of the polynomial, indicated against them.(i) (ii) (iii) p(x) = x2 − 1, x = 1, − 1 (iv) p(x) = (x + 1) (x − 2), x = − 1, 2(v) p(x) = x2 , x = 0 (vi) p(x) = lx + m(vii) (viii)

If log10(x2−21)=2, then find the value of x.

What is the combined fraction of sweets eaten by John and Alex?

In the adjoining figure, ABCD is a square and ΔEDC is an equilateral triangle. Prove that (i) AE=BE, (ii) ∠DAE=15∘.

In what time Rs 800 amount to Rs 882 at 5% p.a. compounded annually?

In the figure, ABCD is a square of side 14 cm with centres A, B, C, and D four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region. [3 MARKS]

Factorise = (a^3-b^3)-(a-b)^3

10. If two opposite vertices of a square are (-1,2) and (3,2).Find the other two coordinates

If →u=→a−→b and →v=→a+→b and |→a|=|→b|=2, then |→u×→v|=

In Fig. PQR is a triangle and S is any point in iits interior. show that SQ+SR<PQ+PR