32581 + Interview Questions in Mathematics Page 12 InterviewSolution

551.	Solve the following quadratic equations by factorization:x-ax-b+x-bx-a=ab+ba
Answer» Solve the following quadratic equations by factorization: $\frac{x - a}{x - b} + \frac{x - b}{x - a} = \frac{a}{b} + \frac{b}{a}$

Discussion

552.	Choose the correct statement(s). i) A linear polynomial has only one zero. ii ) A quadratic polynomial will have two zeroes. iii) A quadratic polynomial can have a maximum of two zeroes. iv) A cubic polynomial can have a maximum of three zeroes.
Answer» Choose the correct statement(s). i) A linear polynomial has only one zero. ii ) A quadratic polynomial will have two zeroes. iii) A quadratic polynomial can have a maximum of two zeroes. iv) A cubic polynomial can have a maximum of three zeroes.

552.

Choose the correct statement(s). i) A linear polynomial has only one zero. ii ) A quadratic polynomial will have two zeroes. iii) A quadratic polynomial can have a maximum of two zeroes. iv) A cubic polynomial can have a maximum of three zeroes.

Answer»

Choose the correct statement(s).

i) A linear polynomial has only one zero.
ii ) A quadratic polynomial will have two zeroes.
iii) A quadratic polynomial can have a maximum of two zeroes.
iv) A cubic polynomial can have a maximum of three zeroes.

Discussion

553.	The length (in units) of the perpendicular from the point (−1,3,9) to the line x−135=y+8−8=z−311 is:
Answer» The length (in units) of the perpendicular from the point $(- 1, 3, 9)$ to the line $\frac{x - 13}{5} = \frac{y + 8}{- 8} = \frac{z - 31}{1}$ is:

Discussion

554.	Solve the following system of linear equations by using the method of substitution:2x−3y=2,x+2y=8
Answer» Solve the following system of linear equations by using the method of substitution: $2 x - 3 y = 2, x + 2 y = 8$

Discussion

555.	Susan invested certain amount of money in two schemes A and B , which offer interest at the rate of 8% per annum and 9% per annum , respectively . She received ₹1860 as annual interest .However, had she interchanged the amount of investment in the two schemes , she would have received ₹20 more as annual interest . How much money did she invest in each scheme ?
Answer» Susan invested certain amount of money in two schemes A and B , which offer interest at the rate of 8% per annum and 9% per annum , respectively . She received ₹1860 as annual interest .However, had she interchanged the amount of investment in the two schemes , she would have received ₹20 more as annual interest . How much money did she invest in each scheme ?

Discussion

556.	Which measure of central tendency is given by the x-coordinate of the point of intersection of the 'more than' ogive and 'less than' ogive?
Answer» Which measure of central tendency is given by the x-coordinate of the point of intersection of the 'more than' ogive and 'less than' ogive?

Discussion

557.	A sweet shopkeeper prepares 396 gulab jamuns and 342 rasagula.He packs them in containers.Each container consists of either gulab jamuns or rasagulas but have equal no.of pieces.Find the no.of pieces she should put in each box so that the no.of boxes are least.
Answer» A sweet shopkeeper prepares 396 gulab jamuns and 342 rasagula.He packs them in containers.Each container consists of either gulab jamuns or rasagulas but have equal no.of pieces.Find the no.of pieces she should put in each box so that the no.of boxes are least.

Discussion

558.	On Jan. 1, 2017 Neha sold goods for ₹ 20,000 to Muskan and drew upon her a bill of exchange payable after two months. One month before the maturity of the bill Muskan approached Neha to accept the payment against the bill at a rebate 12% p.a. Neha agreed to the request of Muskan and Muskan retired the bill under the agreed rate of rebate.Journalise the above transactions in the books of Neha and Muskan.
Answer» On Jan. 1, 2017 Neha sold goods for ₹ 20,000 to Muskan and drew upon her a bill of exchange payable after two months. One month before the maturity of the bill Muskan approached Neha to accept the payment against the bill at a rebate 12% p.a. Neha agreed to the request of Muskan and Muskan retired the bill under the agreed rate of rebate. Journalise the above transactions in the books of Neha and Muskan.

Discussion

559.	A bag contains 3 red and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is not red.
Answer» A bag contains 3 red and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is not red.

Discussion

560.	Consider the above figure where O is the center of the circle, AB=CD and ∠AOB=30∘. Then, ∠AED = ___ and ∠COD = ___.
Answer» Consider the above figure where O is the center of the circle, AB=CD and $∠ A O B = 30^{\circ} .$ Then, $∠ A E D$ = ___ and $∠ C O D$ = ___.

Discussion

561.	One of the zeros of the polynomial,p(x)=2x3−3kx+5 is −1,find the value of k. −1
Answer» One of the zeros of the polynomial, $p (x) = 2 x^{3} - 3 k x + 5$ is $- 1$ , find the value of $k$ . $- 1$

Discussion

562.	A ladder is placed along a wall of a house such that its upper end is touching the top of the wall. The foot of the ladder is 2 m away from the wall and the ladder is making an angle of 60° with the level of the ground. Determine the height of the wall.
Answer» A ladder is placed along a wall of a house such that its upper end is touching the top of the wall. The foot of the ladder is 2 m away from the wall and the ladder is making an angle of 60° with the level of the ground. Determine the height of the wall.

Discussion

563.	Two unbiased coins are tossed simultaneously. The probability of getting two tails is
Answer» Two unbiased coins are tossed simultaneously. The probability of getting two tails is

Discussion

564.	(i) sin6θ+cos6θ=1−3sin2θcos2θ (ii) sin4θ−cos4θ=sin2θ−cos2θ (iii) cosec4θ−cosec2θ=cot4θ+cot2θ
Answer» (i) $s i n^{6} θ + c o s^{6} θ = 1 - 3 s i n^{2} θ c o s^{2} θ$ (ii) $s i n^{4} θ - c o s^{4} θ = s i n^{2} θ - c o s^{2} θ$ (iii) $c o s e c^{4} θ - c o s e c^{2} θ = c o t^{4} θ + c o t^{2} θ$

564.

(i) sin6θ+cos6θ=1−3sin2θcos2θ (ii) sin4θ−cos4θ=sin2θ−cos2θ (iii) cosec4θ−cosec2θ=cot4θ+cot2θ

Answer»

(i) $s i n^{6} θ + c o s^{6} θ = 1 - 3 s i n^{2} θ c o s^{2} θ$

(ii) $s i n^{4} θ - c o s^{4} θ = s i n^{2} θ - c o s^{2} θ$

(iii) $c o s e c^{4} θ - c o s e c^{2} θ = c o t^{4} θ + c o t^{2} θ$

Discussion

565.	Find a and b for which (a - 1)x + 3y = 2, 6x + (1 - 2b) y = 6 infinite solution.
Answer» Find a and b for which (a - 1)x + 3y = 2, 6x + (1 - 2b) y = 6 infinite solution.

565.

Find a and b for which (a - 1)x + 3y = 2, 6x + (1 - 2b) y = 6 infinite solution.

Answer»

Find a and b for which (a - 1)x + 3y = 2, 6x + (1 - 2b) y = 6 infinite solution.

Discussion

566.	A month is selected at random in a year. The probability that it is March or October, is(a) 112(b) 16(c) 34(d) None of these
Answer» A month is selected at random in a year. The probability that it is March or October, is (a) $\frac{1}{12}$ (b) $\frac{1}{6}$ (c) $\frac{3}{4}$ (d) None of these

Discussion

567.	Give Journal entries to record the following arrangements in the books of the firm:(a) B and C are partners sharing profits in the ratio of 3 : 2. D is admitted paying a premium (goodwill) of ₹ 2,000 for 1/4th share of the profits, shares shares of B and C remain as before.(b) B and C are partners sharing profits in the ratio of 3 : 2. D is admitted paying a premium of ₹ 2,100 for 1/4th share of profits which he acquires 1/6th from B and 1/12th from C.
Answer» Give Journal entries to record the following arrangements in the books of the firm: (a) B and C are partners sharing profits in the ratio of 3 : 2. D is admitted paying a premium (goodwill) of ₹ 2,000 for 1/4th share of the profits, shares shares of B and C remain as before. (b) B and C are partners sharing profits in the ratio of 3 : 2. D is admitted paying a premium of ₹ 2,100 for 1/4th share of profits which he acquires 1/6th from B and 1/12th from C.

Discussion

568.	Find the diagonal of a rectangle whose length is 16 cm and area is 192 sq.cm.
Answer» Find the diagonal of a rectangle whose length is 16 cm and area is 192 sq.cm.

Discussion

569.	Write the value of λ for which x2 + 4x + λ is a perfect square.
Answer» Write the value of λ for which x² + 4x + λ is a perfect square.

Discussion

570.	In a triangle ABC, ∠B = 35∘.What type of angle is this ?
Answer» In a triangle ABC, $∠$ B = 35 $^{\circ}$ .What type of angle is this ?

Discussion

571.	For a frequency distribution, mean is 7 and median is 6. What is the value of mode?4
Answer» For a frequency distribution, mean is 7 and median is 6. What is the value of mode? 4

Discussion

572.	Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: 4x - 3y + 4 = 0, 4x + 3y - 20 = 0.
Answer» Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: 4x - 3y + 4 = 0, 4x + 3y - 20 = 0.

572.

Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: 4x - 3y + 4 = 0, 4x + 3y - 20 = 0.

Answer»

Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis:

4x - 3y + 4 = 0,

4x + 3y - 20 = 0.

Discussion

573.	The rationalising factor of 4 square root 5 . Option A. Square root 5 B. 3 square root 5 C. 4 square root 125
Answer» The rationalising factor of 4 square root 5 . Option A. Square root 5 B. 3 square root 5 C. 4 square root 125

573.

The rationalising factor of 4 square root 5 . Option A. Square root 5 B. 3 square root 5 C. 4 square root 125

Answer»

The rationalising factor of 4 square root 5 .

Option

A. Square root 5

B. 3 square root 5

C. 4 square root 125

Discussion

574.	If the sum of three consecutive numbers is 33. Find the area of the equilateral triangle whose side Lengths is equal to the smallest number of the three.
Answer» If the sum of three consecutive numbers is 33. Find the area of the equilateral triangle whose side Lengths is equal to the smallest number of the three.

Discussion

575.	If A and B are matrices of the same order, then (3A – 2B)T is equal to ______________.
Answer» If A and B are matrices of the same order, then (3A – 2B)^T is equal to ______________.

Discussion

576.	A rectangular courtyard is 18m72cm long and 13m20cm broad.It is to be paved with square tiles of same size.find the least possible number of such tiles.
Answer» A rectangular courtyard is 18m72cm long and 13m20cm broad.It is to be paved with square tiles of same size.find the least possible number of such tiles.

Discussion

577.	Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)
Answer» Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)

Discussion

578.

Balance Sheet of Ram and Shyam who shares profits in the ratio of their capitals as at 31st March, 2019 is: Liabilities Amount (₹) Assets Amount (₹) Capital A/cs: Freehold Premises 20,000 Ram 30,000 Plant and Machinery 13,500 Shyam 25,000 55,000 Fixtures and Fittings 1,750 Current A/cs: Vehicles 1,350 Ram 2,000 Stock 14,100 Shyam 1,800 3,800 Bills Receivable 13,060 Creditors 19,000 Debtors 27,500 Bills Payable 16,000 Bank 1,590 Cash 950 93,800 93,800 On 1st April, 2019, they admitted Arjun into partnership on the following terms:(a) Arjun to bring ₹ 20,000 as capital and ₹ 6,600 for goodwill, which is to be left in the business and he is to receive 1/4th share of the profits.(b) Provision for Doubtful Debts is to be 2% on Debtors.(c) Value of Stock to be written down by 5% .(d) Freehold Premises are to be taken at a value of ₹ 22,400; Plant and Machinery ₹ 11,800; Fixtures and Fittings ₹ 1,540 and Vehicles ₹ 800.You are required to make necessary adjustments entries in the firm, give Balance Sheet of the new firm as at 1st April, 2019 and also determine the ratio in which the partners will share profits, there being no change in the ratio of Ram and Shyam.

Answer» Balance Sheet of Ram and Shyam who shares profits in the ratio of their capitals as at 31st March, 2019 is:


Liabilities		Amount (₹)	Assets	Amount (₹)
Capital A/cs:			Freehold Premises	20,000
Ram	30,000		Plant and Machinery	13,500
Shyam	25,000	55,000	Fixtures and Fittings	1,750
Current A/cs:			Vehicles	1,350
Ram	2,000		Stock	14,100
Shyam	1,800	3,800	Bills Receivable	13,060
Creditors		19,000	Debtors	27,500
Bills Payable		16,000	Bank	1,590
			Cash	950

		93,800		93,800

On 1st April, 2019, they admitted Arjun into partnership on the following terms:

(a) Arjun to bring ₹ 20,000 as capital and ₹ 6,600 for goodwill, which is to be left in the business and he is to receive 1/4th share of the profits.

(b) Provision for Doubtful Debts is to be 2% on Debtors.

(c) Value of Stock to be written down by 5% .

(d) Freehold Premises are to be taken at a value of ₹ 22,400; Plant and Machinery ₹ 11,800; Fixtures and Fittings ₹ 1,540 and Vehicles ₹ 800.

You are required to make necessary adjustments entries in the firm, give Balance Sheet of the new firm as at 1st April, 2019 and also determine the ratio in which the partners will share profits, there being no change in the ratio of Ram and Shyam.

Discussion

579.	ABC is an isosceles triangle, right-angled at B. Similar triangles, △ACD and △ABE are constructed on sides AC and AB. Find the ratio of the areas of ΔABE and ΔACD.
Answer» ABC is an isosceles triangle, right-angled at B. Similar triangles, $△ A C D$ and $△ A B E$ are constructed on sides AC and AB. Find the ratio of the areas of $Δ A B E$ and $Δ A C D$ .

Discussion

580.	Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle. Draw two tangents PA and PB to the given circle and measure the length of each tangent.
Answer» Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle. Draw two tangents PA and PB to the given circle and measure the length of each tangent.

Discussion

581.	Reduce the following radicals into the simplest form and classify them into sets of like radicals.(1) (2) (3) (4)
Answer» Reduce the following radicals into the simplest form and classify them into sets of like radicals. (1) (2) (3) (4)

581.

Reduce the following radicals into the simplest form and classify them into sets of like radicals.(1) (2) (3) (4)

Answer»

Reduce the following radicals into the simplest form and classify them into sets of like radicals.

(1)

(2)

(3)

(4)

Discussion

582.	In the given figure, if the length of the diagonal of a square which is inscribed in the circle is 5 cm, then the area of the shaded region is
Answer» In the given figure, if the length of the diagonal of a square which is inscribed in the circle is $5 cm$ , then the area of the shaded region is

Discussion

583.	Use Euclid's algorithm tof find HCF of 1990 and 1445. Express the HCF in the form 1190m + 1445n.
Answer» Use Euclid's algorithm tof find HCF of 1990 and 1445. Express the HCF in the form 1190m + 1445n.

Discussion

584.	Sum of two numbers is 4 more than the twice of difference of the two numbers. If one of the two numbers is three more than the other number, then find the numbers.
Answer» Sum of two numbers is 4 more than the twice of difference of the two numbers. If one of the two numbers is three more than the other number, then find the numbers.

Discussion

585.	2a - 1,a -2 lies on the graph of equation x-1 = -1 / 2 then the value of a is
Answer» 2a - 1,a -2 lies on the graph of equation x-1 = -1 / 2 then the value of a is

Discussion

586.	Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°(i) sin 59° + cos 56°(ii) tan 65° + cot 49°(iii) sec 76° + cosec 52°(iv) cos 78° + sec 78°(v) cosec 54° + sin 72°(vi) cot 85° + cos 75°(vii) sin 67° + cos 75°
Answer» Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45° (i) sin 59° + cos 56° (ii) tan 65° + cot 49° (iii) sec 76° + cosec 52° (iv) cos 78° + sec 78° (v) cosec 54° + sin 72° (vi) cot 85° + cos 75° (vii) sin 67° + cos 75°

Discussion

587.	To construct a triangle similar to ∆ABC in which BC = 4.5 cm, ∠B = 45º and ∠C = 60º, using a scale factor of 37, BC will be divided in the ratio (a) 3 : 4 (b) 4 : 7 (c) 3 : 10 (d) 3 : 7 [CBSE 2012]
Answer» To construct a triangle similar to ∆ABC in which BC = 4.5 cm, $∠$ B = 45º and $∠$ C = 60º, using a scale factor of $\frac{3}{7}$ , BC will be divided in the ratio (a) 3 : 4 (b) 4 : 7 (c) 3 : 10 (d) 3 : 7 [CBSE 2012]

Discussion

588.	Two right circular cylinders of equal volumes have their heights in the ratio 1 : 2. What is the ratio of their radii?
Answer» Two right circular cylinders of equal volumes have their heights in the ratio 1 : 2. What is the ratio of their radii?

Discussion

589.	Find -5 (mod 3).
Answer» Find -5 (mod 3).

Discussion

590.	From a window 10 m above the ground level the tangent of angle of elevation of the top of a tower is 52 and tangent of depression of the foot of the lower is 14. Find the height of the lower.
Answer» From a window 10 m above the ground level the tangent of angle of elevation of the top of a tower is $\frac{5}{2}$ and tangent of depression of the foot of the lower is $\frac{1}{4}$ . Find the height of the lower.

Discussion

591.	Show that (-3,2) (-5,-5) (2,-3) (4,4) are vertices of a rhombus
Answer» Show that (-3,2) (-5,-5) (2,-3) (4,4) are vertices of a rhombus

Discussion

592.	In Figure 3, PQ \|\| CD and PR \|\| CB. Prove that AQQD=ARRB.
Answer» In Figure 3, PQ \|\| CD and PR \|\| CB. Prove that $\frac{AQ}{QD} = \frac{AR}{RB}$ .

Discussion

593.	If sec θ=54, show that (sin θ−2cos θ)(tan θ−cot θ)=127.
Answer» If $s e c θ = \frac{5}{4}$ , show that $\frac{(s i n θ - 2 c o s θ)}{(t a n θ - c o t θ)} = \frac{12}{7}$ .

Discussion

594.	Places A and B are 160 km apart on a highway. One car starts from A and another car from B at the same time. If they travel in the same direction , they meet in 8 hours. But, if they travel towards each other, they meet in 2 hours. Find the speed of each car.
Answer» Places A and B are 160 km apart on a highway. One car starts from A and another car from B at the same time. If they travel in the same direction , they meet in 8 hours. But, if they travel towards each other, they meet in 2 hours. Find the speed of each car.

Discussion

595.	5x+1/ 5x+1 +2=-2
Answer» 5x+1/ 5x+1 +2=-2

Discussion

596.	The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is(a) x2 + y2 = 9a2(b) x2 + y2 = 16a2(c) x2 + y2 = 4a2(d) x2 + y2 = a2
Answer» The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is (a) x² + y² = 9a² (b) x² + y² = 16a² (c) x² + y² = 4a² (d) x² + y² = a²

Discussion

597.	Solve each of the following systems of equations by the method of cross-multiplication :a2x+b2y=c2b2x+a2y=d2
Answer» Solve each of the following systems of equations by the method of cross-multiplication : $a^{2} x + b^{2} y = c^{2} b^{2} x + a^{2} y = d^{2}$

Discussion

598.	Let α and β be the roots of equation x2−7x−3=0. If an=αn−βn for n≥1,then value of a10−3a83a9 is
Answer» Let α and β be the roots of equation $x^{2} - 7 x - 3 = 0. If a_{n} = α_{n} - β_{n} f o r n \geq 1, then value of \frac{a_{10} - 3 a_{8}}{3 a_{9}}$ is

Discussion

599.	Will division of a rational number by another rational number always give a rational number?
Answer» Will division of a rational number by another rational number always give a rational number?

Discussion

600.

Two sides of a triangle are 8cm and 12cm, and the angle between them is 110∘ as shown in the figure. Area of the triangle is ___ (sin 70∘=0.93)

Answer»

Two sides of a triangle are 8cm and 12cm, and the angle between them is $110^{\circ}$ as shown in the figure.

Area of the triangle is ___ ( $s i n 70^{\circ} = 0.93$ )

Discussion

Explore topic-wise InterviewSolutions in .

Solve the following quadratic equations by factorization:x-ax-b+x-bx-a=ab+ba

Choose the correct statement(s). i) A linear polynomial has only one zero. ii ) A quadratic polynomial will have two zeroes. iii) A quadratic polynomial can have a maximum of two zeroes. iv) A cubic polynomial can have a maximum of three zeroes.

The length (in units) of the perpendicular from the point (−1,3,9) to the line x−135=y+8−8=z−311 is:

Solve the following system of linear equations by using the method of substitution:2x−3y=2,x+2y=8

Which measure of central tendency is given by the x-coordinate of the point of intersection of the 'more than' ogive and 'less than' ogive?

A sweet shopkeeper prepares 396 gulab jamuns and 342 rasagula.He packs them in containers.Each container consists of either gulab jamuns or rasagulas but have equal no.of pieces.Find the no.of pieces she should put in each box so that the no.of boxes are least.

A bag contains 3 red and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is not red.

Consider the above figure where O is the center of the circle, AB=CD and ∠AOB=30∘. Then, ∠AED = ___ and ∠COD = ___.

One of the zeros of the polynomial,p(x)=2x3−3kx+5 is −1,find the value of k. −1

A ladder is placed along a wall of a house such that its upper end is touching the top of the wall. The foot of the ladder is 2 m away from the wall and the ladder is making an angle of 60° with the level of the ground. Determine the height of the wall.

Two unbiased coins are tossed simultaneously. The probability of getting two tails is

(i) sin6θ+cos6θ=1−3sin2θcos2θ (ii) sin4θ−cos4θ=sin2θ−cos2θ (iii) cosec4θ−cosec2θ=cot4θ+cot2θ

Find a and b for which (a - 1)x + 3y = 2, 6x + (1 - 2b) y = 6 infinite solution.

A month is selected at random in a year. The probability that it is March or October, is(a) 112(b) 16(c) 34(d) None of these

Find the diagonal of a rectangle whose length is 16 cm and area is 192 sq.cm.

Write the value of λ for which x2 + 4x + λ is a perfect square.

In a triangle ABC, ∠B = 35∘.What type of angle is this ?

For a frequency distribution, mean is 7 and median is 6. What is the value of mode?4

Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis: 4x - 3y + 4 = 0, 4x + 3y - 20 = 0.

The rationalising factor of 4 square root 5 . Option A. Square root 5 B. 3 square root 5 C. 4 square root 125

If the sum of three consecutive numbers is 33. Find the area of the equilateral triangle whose side Lengths is equal to the smallest number of the three.

If A and B are matrices of the same order, then (3A – 2B)T is equal to ______________.

A rectangular courtyard is 18m72cm long and 13m20cm broad.It is to be paved with square tiles of same size.find the least possible number of such tiles.

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)

ABC is an isosceles triangle, right-angled at B. Similar triangles, △ACD and △ABE are constructed on sides AC and AB. Find the ratio of the areas of ΔABE and ΔACD.

Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle. Draw two tangents PA and PB to the given circle and measure the length of each tangent.

Reduce the following radicals into the simplest form and classify them into sets of like radicals.(1) (2) (3) (4)

In the given figure, if the length of the diagonal of a square which is inscribed in the circle is 5 cm, then the area of the shaded region is

Use Euclid's algorithm tof find HCF of 1990 and 1445. Express the HCF in the form 1190m + 1445n.

Sum of two numbers is 4 more than the twice of difference of the two numbers. If one of the two numbers is three more than the other number, then find the numbers.

2a - 1,a -2 lies on the graph of equation x-1 = -1 / 2 then the value of a is

Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°(i) sin 59° + cos 56°(ii) tan 65° + cot 49°(iii) sec 76° + cosec 52°(iv) cos 78° + sec 78°(v) cosec 54° + sin 72°(vi) cot 85° + cos 75°(vii) sin 67° + cos 75°

To construct a triangle similar to ∆ABC in which BC = 4.5 cm, ∠B = 45º and ∠C = 60º, using a scale factor of 37, BC will be divided in the ratio (a) 3 : 4 (b) 4 : 7 (c) 3 : 10 (d) 3 : 7 [CBSE 2012]

Two right circular cylinders of equal volumes have their heights in the ratio 1 : 2. What is the ratio of their radii?

Find -5 (mod 3).

From a window 10 m above the ground level the tangent of angle of elevation of the top of a tower is 52 and tangent of depression of the foot of the lower is 14. Find the height of the lower.

Show that (-3,2) (-5,-5) (2,-3) (4,4) are vertices of a rhombus

In Figure 3, PQ || CD and PR || CB. Prove that AQQD=ARRB.

If sec θ=54, show that (sin θ−2cos θ)(tan θ−cot θ)=127.

Places A and B are 160 km apart on a highway. One car starts from A and another car from B at the same time. If they travel in the same direction , they meet in 8 hours. But, if they travel towards each other, they meet in 2 hours. Find the speed of each car.

5x+1/ 5x+1 +2=-2

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is(a) x2 + y2 = 9a2(b) x2 + y2 = 16a2(c) x2 + y2 = 4a2(d) x2 + y2 = a2

Solve each of the following systems of equations by the method of cross-multiplication :a2x+b2y=c2b2x+a2y=d2

Let α and β be the roots of equation x2−7x−3=0. If an=αn−βn for n≥1,then value of a10−3a83a9 is

Will division of a rational number by another rational number always give a rational number?

Two sides of a triangle are 8cm and 12cm, and the angle between them is 110∘ as shown in the figure. Area of the triangle is ___ (sin 70∘=0.93)

Consider the above figure where O is the center of the circle, AB=CD and ∠AOB=30∘. Then, ∠AED = _ and ∠COD = _.