32581 + Interview Questions in Mathematics Page 122 InterviewSolution

6051.	Which term of the AP 21, 18, 15, ... is zero?
Answer» Which term of the AP 21, 18, 15, ... is zero?

Discussion

6052.	The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is
Answer» The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is

Discussion

6053.	For what value of ‘n’ would 4n end with zero?
Answer» For what value of ‘n’ would $4^{n}$ end with zero?

Discussion

6054.	Solve the following pair of equations. 7x−2yxy=5 8x+6yxy=15 Here, x ≠ 0 and y ≠ 0.
Answer» Solve the following pair of equations. $\frac{7 x - 2 y}{x y} = 5$ $\frac{8 x + 6 y}{x y} = 15$ Here, x $\neq$ 0 and y $\neq$ 0.

6054.

Solve the following pair of equations. 7x−2yxy=5 8x+6yxy=15 Here, x ≠ 0 and y ≠ 0.

Answer»

Solve the following pair of equations.

$\frac{7 x - 2 y}{x y} = 5$

$\frac{8 x + 6 y}{x y} = 15$

Here, x $\neq$ 0 and y $\neq$ 0.

Discussion

6055.	The diameters of the top and the bottom portions of a bucket are 42 cm and 28 cm respectively. If the height of the bucket is 24 cm, then the cost of painting its outer surface at the rate of 50 paise / cm2 is(a) Rs. 1582.50(b) Rs. 1724.50(c) Rs. 1683(d) Rs. 1642
Answer» The diameters of the top and the bottom portions of a bucket are 42 cm and 28 cm respectively. If the height of the bucket is 24 cm, then the cost of painting its outer surface at the rate of 50 paise / cm² is (a) Rs. 1582.50 (b) Rs. 1724.50 (c) Rs. 1683 (d) Rs. 1642

Discussion

6056.	P is any point inside the circle. A line AB is shifted right to pass through P. Then, what is the line called?
Answer» P is any point inside the circle. A line AB is shifted right to pass through P. Then, what is the line called?

6056.

P is any point inside the circle. A line AB is shifted right to pass through P. Then, what is the line called?

Answer»

P is any point inside the circle. A line AB is shifted right to pass through P. Then, what is the line called?

Discussion

6057.	Question 3 (i)In an AP:(i) Given a = 5, d = 3, an=50, find n and Sn.
Answer» Question 3 (i) In an AP: (i) Given a = 5, d = 3, $a_{n} = 50$ , find n and $S_{n}$ .

Discussion

6058.	32. How many significant figures are present in 100m
Answer» 32. How many significant figures are present in 100m

Discussion

6059.	Find the area of a shaded region in the the following figure,where a circular arc of radius 7 cm has been drawn with vertex A of an equilateral triangle ABC of side 14 cm as centre. (Use π = 22/7 and 3 = 1.73)
Answer» Find the area of a shaded region in the the following figure,where a circular arc of radius 7 cm has been drawn with vertex A of an equilateral triangle ABC of side 14 cm as centre. (Use π = 22/7 and $\sqrt{3}$ = 1.73)

Discussion

6060.	If the centroid of the triangle formed by the points (a, b), (1, a) and (b, 1) is at the origin, then a3+b3+1ab= ____________.
Answer» If the centroid of the triangle formed by the points (a, b), (1, a) and (b, 1) is at the origin, then $\frac{a^{3} + b^{3} + 1}{a b} =$ ____________.

Discussion

6061.	Question 52 To construct a unique rectangle, the minimum number of measurements required is (a) 4 (b) 3 (c) 2 (d) 1
Answer» Question 52 To construct a unique rectangle, the minimum number of measurements required is (a) 4 (b) 3 (c) 2 (d) 1

Discussion

6062.	In an equilateral triangle ABC,D is point on BC such that BD=1/3BC.Prove that 9AD2=7AB2.
Answer» In an equilateral triangle ABC,D is point on BC such that BD=1/3BC.Prove that 9AD²=7AB².

Discussion

6063.	Question 1(iv) Find the roots of the following quadratic equations by factorisation: (iv) 2x2−x+18=0
Answer» Question 1(iv) Find the roots of the following quadratic equations by factorisation: (iv) $2 x^{2} - x + \frac{1}{8} = 0$

Discussion

6064.	Find the roots of the quadratic equation, 3x2 – 5x + 2 = 0, using quadratic formula.
Answer» Find the roots of the quadratic equation, 3x² – 5x + 2 = 0, using quadratic formula.

Discussion

6065.	In a flag race, a pole is placed at the starting point, which is 10m from the first flag and the other flags are placed 6m apart in a straight line. There are 10 flags in the line. Each competitor starts from the pole, picks up the nearest flag, comes back to the pole and continues the same way until all the flags are on the pole. Find the total distance covered.
Answer» In a flag race, a pole is placed at the starting point, which is 10m from the first flag and the other flags are placed 6m apart in a straight line. There are 10 flags in the line. Each competitor starts from the pole, picks up the nearest flag, comes back to the pole and continues the same way until all the flags are on the pole. Find the total distance covered.

Discussion

6066.	How many autosomes and sex chromosomes are there in a somatic cell and in a sex cell?
Answer» How many autosomes and sex chromosomes are there in a somatic cell and in a sex cell?

Discussion

6067.	AT A CERTAIN POINT THE ANGLE OF ELEVATION OF A TOWER IS FOUND TO BE SUCH THAT ITS TANGENT IS 5/2 ON WALKING 35 METERS AWAY FROM THE TOWER THE ANGLE OF ELEVATION HAS ITS TANGENT 5/3 FIND THE HEIGHT OF THE TOWER
Answer» AT A CERTAIN POINT THE ANGLE OF ELEVATION OF A TOWER IS FOUND TO BE SUCH THAT ITS TANGENT IS 5/2 ON WALKING 35 METERS AWAY FROM THE TOWER THE ANGLE OF ELEVATION HAS ITS TANGENT 5/3 FIND THE HEIGHT OF THE TOWER

Discussion

6068.	Why do banks keep a small portion of deposits as cash with themselves?
Answer» Why do banks keep a small portion of deposits as cash with themselves?

Discussion

6069.	IF the zeroes of polynomial ×^3 -3×^2 +×+1 are a-b,a+b,a find value b and a?
Answer» IF the zeroes of polynomial ×^3 -3×^2 +×+1 are a-b,a+b,a find value b and a?

Discussion

6070.	A cube of side 4 cm is cut into cubes of side 1 cm. Calculate the total surface area of all the small cubes.
Answer» A cube of side 4 $c m$ is cut into cubes of side 1 $c m$ . Calculate the total surface area of all the small cubes.

Discussion

6071.	Find the distance between P and S.
Answer» Find the distance between P and S.

Discussion

6072.	The arithmetic mean of 1, 2, 3, ... , n is(a) n+12(b) n-12(c) n2(d) n2+1
Answer» The arithmetic mean of 1, 2, 3, ... , n is (a) $\frac{n + 1}{2}$ (b) $\frac{n - 1}{2}$ (c) $\frac{n}{2}$ (d) $\frac{n}{2} + 1$

Discussion

6073.	In Fig. 4, ABCD is a rectangle. Find the values of x and y.
Answer» In Fig. 4, ABCD is a rectangle. Find the values of x and y.

Discussion

6074.	Question 16In figure, ∠ACB=40∘. Find ∠OAB.
Answer» Question 16 In figure, $∠ A C B = 40^{\circ}$ . Find $∠ O A B$ .

Discussion

6075.	For any positive integer n and prove that n cube minus n is divisible by 6
Answer» For any positive integer n and prove that n cube minus n is divisible by 6

Discussion

6076.

From the following Trial Balance of Sh. Parveen Kumar, prepare Trading and Profit & Loss Account for the year ending 31st March, 2019 and a Balance Sheet as at that date: Dr. Balances (₹) Cr. Balances (₹) Stock at Commencement 40,000 Sales 5,10,000 Purchases 3,20,000 Loan from Mr. Naresh 15% p.a. 40,000 Returns Inward 7,000 Returns Outwards 8,000 Sundry Debtors 80,000 Bank 24,200 Cash 9,400 Provision for Doubtful Debts 2,500 Manufacturing Expenses 44,000 Discount 1,800 Trade Expenses 7,200 Rent of Premises sublet, for the year to 30th Sep., 2019 4,000 Carriage 3,500 Capital 1,20,000 Salaries and Wages 15,800 Sundry Creditors 47,000 Postage 1,500 Stationery 800 Freight Inwards 4,300 Land and Building 2,00,000 Patents 8,000 Furniture 10,000 Insurance Premium 6,000 7,57,500 7,57,500 Informations:-(1) Closing Stock was valued at ₹ 60,000. You are informed that goods valued ₹ 12,000 were sold and despactched on 29th March, 2019, but no entry was passed to this effect.(2) Insurance Premium include ₹ 1,200 paid on 1st October, 2018 to run for one year from Oct. 1, 2018 to Sept. 30, 2019.(3) Loan from Mr. Naresh was taken on 1st July, 2018. Interest has not been paid so far.(4) Create provision for Doubtful Debts at 5% on Sundry Debtors after writing off ₹ 600 as Bad-debts during the year.(5) A bill of ₹ 3,200 for advertisement in newspaper remained unpaid at the end of the year.(6) Purchases include Furniture costing ₹ 5,000 purchased on 1st April, 2018.(7) Charge 10% p.a. depreciation on Furniture and write off 15th of patents.

Answer» From the following Trial Balance of Sh. Parveen Kumar, prepare Trading and Profit & Loss Account for the year ending 31st March, 2019 and a Balance Sheet as at that date:

Dr. Balances	(₹)	Cr. Balances	(₹)
Stock at Commencement	40,000	Sales	5,10,000
Purchases	3,20,000	Loan from Mr. Naresh 15% p.a.	40,000
Returns Inward	7,000	Returns Outwards	8,000
Sundry Debtors	80,000	Bank	24,200
Cash	9,400	Provision for Doubtful Debts	2,500
Manufacturing Expenses	44,000	Discount	1,800
Trade Expenses	7,200	Rent of Premises sublet, for the year to 30th Sep., 2019	4,000
Carriage	3,500	Capital	1,20,000
Salaries and Wages	15,800	Sundry Creditors	47,000
Postage	1,500
Stationery	800
Freight Inwards	4,300
Land and Building	2,00,000
Patents	8,000
Furniture	10,000
Insurance Premium	6,000
	7,57,500		7,57,500

Informations:-

(1) Closing Stock was valued at ₹ 60,000. You are informed that goods valued ₹ 12,000 were sold and despactched on 29th March, 2019, but no entry was passed to this effect.

(2) Insurance Premium include ₹ 1,200 paid on 1st October, 2018 to run for one year from Oct. 1, 2018 to Sept. 30, 2019.

(3) Loan from Mr. Naresh was taken on 1st July, 2018. Interest has not been paid so far.

(4) Create provision for Doubtful Debts at 5% on Sundry Debtors after writing off ₹ 600 as Bad-debts during the year.

(5) A bill of ₹ 3,200 for advertisement in newspaper remained unpaid at the end of the year.

(6) Purchases include Furniture costing ₹ 5,000 purchased on 1st April, 2018.

(7) Charge 10% p.a. depreciation on Furniture and write off

\frac{1}{5} th

of patents.

Discussion

6077.	If the point P (2, 2) is equidistant from the points A (-2, k) and B (-2k, -3), find k. Also, find the length of AP.
Answer» If the point P (2, 2) is equidistant from the points A (-2, k) and B (-2k, -3), find k. Also, find the length of AP.

Discussion

6078.	Find the 27th term of the following A.P.9, 4, –1, –6, –11,...
Answer» Find the 27^th term of the following A.P. 9, 4, –1, –6, –11,...

Discussion

6079.	prove that (4,4),(3,5) and (-1,-1)are the vertices of a right angled triangle.
Answer» prove that (4,4),(3,5) and (-1,-1)are the vertices of a right angled triangle.

Discussion

6080.	If tan A=512, find the value of (sin A + cos A) sec A.
Answer» If $\tan A = \frac{5}{12}$ , find the value of (sin A + cos A) sec A.

Discussion

6081.	If a shopkeeper incurs 10% loss and 25% profit on items sold for ₹ 45 and ₹ 40 respectively, then find his net profit/loss. [4 MARKS]
Answer» If a shopkeeper incurs 10% loss and 25% profit on items sold for ₹ 45 and ₹ 40 respectively, then find his net profit/loss. [4 MARKS]

Discussion

6082.	The area of a quadrilateral whose vertices taken in order are (–4, –2), (–3, –5), (3, –2) and (2, 3) is _______.
Answer» The area of a quadrilateral whose vertices taken in order are (–4, –2), (–3, –5), (3, –2) and (2, 3) is _______.

Discussion

6083.	The 11th term of the A.P.-5,-52, 0, 52,..., is
Answer» The 11th term of the A.P. $- 5, - \frac{5}{2}, 0, \frac{5}{2}$ ,..., is

Discussion

6084.	Let the sequence an be defined as follows:a1=1,an=an−1+2 for n≥2.Find first five terms and write corresponding series.
Answer» Let the sequence $a_{n}$ be defined as follows: $a_{1} = 1, a_{n} = a_{n - 1} + 2$ for $n \geq 2$ . Find first five terms and write corresponding series.

Discussion

6085.	Question 78(iv) Harshna gave her car for service at service station on 27-05-2009 and was charged as follows 3% cess on service tax. Find the bill amount.
Answer» Question 78(iv) Harshna gave her car for service at service station on 27-05-2009 and was charged as follows 3% cess on service tax. Find the bill amount.

6085.

Question 78(iv) Harshna gave her car for service at service station on 27-05-2009 and was charged as follows 3% cess on service tax. Find the bill amount.

Answer»

Question 78(iv)

Harshna gave her car for service at service station on 27-05-2009 and was charged as follows
3% cess on service tax.
Find the bill amount.

Discussion

6086.	A shopkeeper buys a camera at a discount of 20% from a wholesaler. The printed price of the camera is Rs. 1600 and the rate of sales tax is 6%. The shopkeeper sells it to a buyer at the printed price and charges tax at the same rate. Find: (i) The price at which the camera can be bought. (ii) The VAT (Value Added Tax) paid by the shopkeeper.
Answer» A shopkeeper buys a camera at a discount of 20% from a wholesaler. The printed price of the camera is Rs. 1600 and the rate of sales tax is 6%. The shopkeeper sells it to a buyer at the printed price and charges tax at the same rate. Find: (i) The price at which the camera can be bought. (ii) The VAT (Value Added Tax) paid by the shopkeeper.

6086.

A shopkeeper buys a camera at a discount of 20% from a wholesaler. The printed price of the camera is Rs. 1600 and the rate of sales tax is 6%. The shopkeeper sells it to a buyer at the printed price and charges tax at the same rate. Find: (i) The price at which the camera can be bought. (ii) The VAT (Value Added Tax) paid by the shopkeeper.

Answer»

A shopkeeper buys a camera at a discount of 20% from a wholesaler. The printed price of the camera is Rs. 1600 and the rate of sales tax is 6%. The shopkeeper sells it to a buyer at the printed price and charges tax at the same rate. Find:

(i) The price at which the camera can be bought.

(ii) The VAT (Value Added Tax) paid by the shopkeeper.

Discussion

6087.	if sin +cos=under root 3 then prove that cot + tan =1
Answer» if sin +cos=under root 3 then prove that cot + tan =1

Discussion

6088.	Construct a right angled triangle PQR, in which ∠Q=90o,hypotenuse PR=8 cm and QR=4.5 cm. Draw bisector of angle PQR and let it meet PR at point T. Prove that T is equidistant from PQ and QR.
Answer» Construct a right angled triangle PQR, in which $∠ Q = 90^{o}$ ,hypotenuse PR=8 cm and QR=4.5 cm. Draw bisector of angle PQR and let it meet PR at point T. Prove that T is equidistant from PQ and QR.

Discussion

6089.	16. Find the locus of the mid-point of the chords of the parabola y²=4ax such that tangent at the extremities of the chords are perpendicular.
Answer» 16. Find the locus of the mid-point of the chords of the parabola y²=4ax such that tangent at the extremities of the chords are perpendicular.

Discussion

6090.	The value of the expression 16x2+24x+9 for x=0 is ___.
Answer» The value of the expression $16 x^{2} + 24 x + 9$ for $x = 0$ is ___.

Discussion

6091.	Give an example each, of two irrational numbers, whose(iii) sum is a rational number.
Answer» Give an example each, of two irrational numbers, whose (iii) sum is a rational number.

Discussion

6092.	The areas of two similar triangles are in respectively 9 cm2 and 16 cm2. The ratio of their corresponding sides is(a) 3 : 4(b) 4 : 3(c) 2 : 3(d) 4 : 5
Answer» The areas of two similar triangles are in respectively 9 cm² and 16 cm². The ratio of their corresponding sides is (a) 3 : 4 (b) 4 : 3 (c) 2 : 3 (d) 4 : 5

Discussion

6093.	If S(1) is the sum of first n terms, S(2) is the sum of 2n terms, and S(3) is the sum of 3n terms, then prove that S(3) = 3[S(2) - S(2)].
Answer» If S(1) is the sum of first n terms, S(2) is the sum of 2n terms, and S(3) is the sum of 3n terms, then prove that S(3) = 3[S(2) - S(2)].

Discussion

6094.	What is the slope of the line shown in the image below?
Answer» What is the slope of the line shown in the image below?

Discussion

6095.	The coefficient of variation of two series are 58% and 69%. If their standard deviations are 21.2 and 15.6, then their arithmetic means are:
Answer» The coefficient of variation of two series are 58% and 69%. If their standard deviations are 21.2 and 15.6, then their arithmetic means are:

Discussion

6096.	In the figure, PC is the tangent to the circle. A and B are 2 points on the circle. If ∠BPC =600 and ∠APB =550, then find ∠ABP .
Answer» In the figure, PC is the tangent to the circle. A and B are 2 points on the circle. If $∠$ BPC $= 60^{0}$ and $∠$ APB $= 55^{0}$ , then find $∠$ ABP .

6096.

In the figure, PC is the tangent to the circle. A and B are 2 points on the circle. If ∠BPC =600 and ∠APB =550, then find ∠ABP .

Answer»

In the figure, PC is the tangent to the circle. A and B are 2 points on the circle. If $∠$ BPC $= 60^{0}$ and $∠$ APB $= 55^{0}$ , then find $∠$ ABP .

Discussion

6097.	A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is 14 and that of the woman's selection is 13. What is the probability that none of them will be selected.
Answer» A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is $\frac{1}{4}$ and that of the woman's selection is $\frac{1}{3}$ . What is the probability that none of them will be selected.

Discussion

6098.	Which of the following are quadratic equations?(i) x2 + 6x − 4 = 0(ii) 3x2-2x+12=0(iii) x2+1x2=5(iv) x-3x=x2(v) 2x2-3x+9=0(vi) x2-2x-x-5=0(vii) 3x2 − 5x + 9 = x2 − 7x + 3(viii) x+1x=1(ix) x2 − 3x = 0(x) x+1x2=3x+1x+4(xi) (2x + 1) (3x + 2) = 6(x − 1) (x − 2)(xii) x+1x=x2, x≠0(xiii) 16x2 − 3 = (2x + 5) (5x − 3)(xiv) (x + 2)3 = x3 − 4(xv) x(x + 1) + 8 = (x + 2) (x − 2)
Answer» Which of the following are quadratic equations? (i) x² + 6x − 4 = 0 (ii) $\sqrt{3} x^{2} - 2 x + \frac{1}{2} = 0$ (iii) $x^{2} + \frac{1}{x^{2}} = 5$ (iv) $x - \frac{3}{x} = x^{2}$ (v) $2 x^{2} - \sqrt{3 x} + 9 = 0$ (vi) $x^{2} - 2 x - \sqrt{x} - 5 = 0$ (vii) 3x² − 5x + 9 = x² − 7x + 3 (viii) $x + \frac{1}{x} = 1$ (ix) x² − 3x = 0 (x) ${(x + \frac{1}{x})}^{2} = 3 (x + \frac{1}{x}) + 4$ (xi) (2x + 1) (3x + 2) = 6(x − 1) (x − 2) (xii) $x + \frac{1}{x} = x^{2}, x \neq 0$ (xiii) 16x² − 3 = (2x + 5) (5x − 3) (xiv) (x + 2)³ = x³ − 4 (xv) x(x + 1) + 8 = (x + 2) (x − 2)

Discussion

6099.	If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through point ___________.
Answer» If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through point ___________.

Discussion

6100.	Two identical solid cubes of side a are joined end to end. The total surface area of the resulting cuboid is _________.
Answer» Two identical solid cubes of side a are joined end to end. The total surface area of the resulting cuboid is _________.

Discussion

Explore topic-wise InterviewSolutions in .

Which term of the AP 21, 18, 15, ... is zero?

The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is

For what value of ‘n’ would 4n end with zero?

Solve the following pair of equations. 7x−2yxy=5 8x+6yxy=15 Here, x ≠ 0 and y ≠ 0.

The diameters of the top and the bottom portions of a bucket are 42 cm and 28 cm respectively. If the height of the bucket is 24 cm, then the cost of painting its outer surface at the rate of 50 paise / cm2 is(a) Rs. 1582.50(b) Rs. 1724.50(c) Rs. 1683(d) Rs. 1642

P is any point inside the circle. A line AB is shifted right to pass through P. Then, what is the line called?

Question 3 (i)In an AP:(i) Given a = 5, d = 3, an=50, find n and Sn.

32. How many significant figures are present in 100m

Find the area of a shaded region in the the following figure,where a circular arc of radius 7 cm has been drawn with vertex A of an equilateral triangle ABC of side 14 cm as centre. (Use π = 22/7 and 3 = 1.73)

If the centroid of the triangle formed by the points (a, b), (1, a) and (b, 1) is at the origin, then a3+b3+1ab= ____________.

Question 52 To construct a unique rectangle, the minimum number of measurements required is (a) 4 (b) 3 (c) 2 (d) 1

In an equilateral triangle ABC,D is point on BC such that BD=1/3BC.Prove that 9AD2=7AB2.

Question 1(iv) Find the roots of the following quadratic equations by factorisation: (iv) 2x2−x+18=0

Find the roots of the quadratic equation, 3x2 – 5x + 2 = 0, using quadratic formula.

How many autosomes and sex chromosomes are there in a somatic cell and in a sex cell?

AT A CERTAIN POINT THE ANGLE OF ELEVATION OF A TOWER IS FOUND TO BE SUCH THAT ITS TANGENT IS 5/2 ON WALKING 35 METERS AWAY FROM THE TOWER THE ANGLE OF ELEVATION HAS ITS TANGENT 5/3 FIND THE HEIGHT OF THE TOWER

Why do banks keep a small portion of deposits as cash with themselves?

IF the zeroes of polynomial ×^3 -3×^2 +×+1 are a-b,a+b,a find value b and a?

A cube of side 4 cm is cut into cubes of side 1 cm. Calculate the total surface area of all the small cubes.

Find the distance between P and S.

The arithmetic mean of 1, 2, 3, ... , n is(a) n+12(b) n-12(c) n2(d) n2+1

In Fig. 4, ABCD is a rectangle. Find the values of x and y.

Question 16In figure, ∠ACB=40∘. Find ∠OAB.

For any positive integer n and prove that n cube minus n is divisible by 6

If the point P (2, 2) is equidistant from the points A (-2, k) and B (-2k, -3), find k. Also, find the length of AP.

Find the 27th term of the following A.P.9, 4, –1, –6, –11,...

prove that (4,4),(3,5) and (-1,-1)are the vertices of a right angled triangle.

If tan A=512, find the value of (sin A + cos A) sec A.

If a shopkeeper incurs 10% loss and 25% profit on items sold for ₹ 45 and ₹ 40 respectively, then find his net profit/loss. [4 MARKS]

The area of a quadrilateral whose vertices taken in order are (–4, –2), (–3, –5), (3, –2) and (2, 3) is _______.

The 11th term of the A.P.-5,-52, 0, 52,..., is

Let the sequence an be defined as follows:a1=1,an=an−1+2 for n≥2.Find first five terms and write corresponding series.

Question 78(iv) Harshna gave her car for service at service station on 27-05-2009 and was charged as follows 3% cess on service tax. Find the bill amount.

if sin +cos=under root 3 then prove that cot + tan =1

Construct a right angled triangle PQR, in which ∠Q=90o,hypotenuse PR=8 cm and QR=4.5 cm. Draw bisector of angle PQR and let it meet PR at point T. Prove that T is equidistant from PQ and QR.

16. Find the locus of the mid-point of the chords of the parabola y²=4ax such that tangent at the extremities of the chords are perpendicular.

The value of the expression 16x2+24x+9 for x=0 is ___.

Give an example each, of two irrational numbers, whose(iii) sum is a rational number.

The areas of two similar triangles are in respectively 9 cm2 and 16 cm2. The ratio of their corresponding sides is(a) 3 : 4(b) 4 : 3(c) 2 : 3(d) 4 : 5

If S(1) is the sum of first n terms, S(2) is the sum of 2n terms, and S(3) is the sum of 3n terms, then prove that S(3) = 3[S(2) - S(2)].

What is the slope of the line shown in the image below?

The coefficient of variation of two series are 58% and 69%. If their standard deviations are 21.2 and 15.6, then their arithmetic means are:

In the figure, PC is the tangent to the circle. A and B are 2 points on the circle. If ∠BPC =600 and ∠APB =550, then find ∠ABP .

A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is 14 and that of the woman's selection is 13. What is the probability that none of them will be selected.

If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through point ___________.

Two identical solid cubes of side a are joined end to end. The total surface area of the resulting cuboid is _________.