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In the given figure, O is the centre of the circle. If BD = DC and ∠DBC=30∘, find the measures of ∠BAC and ∠BOC.

In a triangle ABC , vertices A,B and C are (0,0), (0,2)& (3,0) respectively. The area of triangle ABC is?

I have some tables and chairs. If i place two chair at each table ,i have one extra chair.If I place three chair at each table,I have one table with no chairs.what is the sum of total no. of chair and table ?

What should be subtracted from -4\5 to get 1?

ABCD and CFEG are squares. HF = 5 cm, AH: HF = 3:1 Which of the following could be the value of area of ABCD? (All the sides are integers)

In the diagram, AD = DB and AH = HD. Find the ratio of the area of the shaded portion to that of the triangle DEF, if DE || BC and HG || AE.

What can be the quadratic equation for the situation:Sum of squares of two consecutive numbers is 145.

37. The number of 6 digit natural numbers where each digit if appears, appears at least twice is

How many natural numbers are there such that their factorials are ending with 5 zeroes?

19. Find the least number which when divided by 12, 15 and 18 leaves the remainder 3, 6 and 9 respectively?

Find the number of all natural numbers that lie between 24 and 101, which are divisible by 5.

If + means divide, x means minus, # means multiply and – means plus, then find the value of 9+3# 4 - 8×2.

Which is the year in which the absolute value of population change in Bangalore and Mumbai together is the highest over the previous year?

Who among the following is seated between P and S?

What is the remainder when 1025−7 is divided by 3?

If a+x=b+y=c+z+1, where a,b,c,x,y,z are non-zero distinct real numbers, then ∣∣∣∣xa+yx+ayb+yy+bzc+yz+c∣∣∣∣ is equal to:

12. In the given fig. PT is tangent to circle at T. If PA=4 cm and AB=5 cm, find PT

For all n≥1, Prove that:11⋅2+12⋅3+13⋅4+⋯+1n(n+1)=nn+1

Four equal jugs are filled with the mixture of sprit and water. The ratio of sprit to water in four jugs is 1:3, 3:5, 5:11 and 7:9. The mixture of the four jugs is emptied into a single vessel. What is the proportion of sprit to water in the vessel?

7Pr = 840 and 7Cr = 35. Find r.

Find the no. of non negative integral solutions of: x1+x2+x3=15.

x2 + 9x − 36 = 0, find the positive root of the equation. Ans._____________.___

30% passengers from a train got down at station A, 70% of the remaining got down at station B. If there are still 1050 passengers on the train, how many passengers were there before station A, provided No one boarded the train at station A and B.

∠AEB = 90∘ and BG is the bisector of ∠ABC. DE is parallel to side BC. Find AF: FC.

A committee of 6 is to be chosen from 10 men and 7 women so as to contain at least 3 men and 2 women. The number of different ways this can be done, if two particular women refuse to serve on the same committee is ___________.

If the sum of a,b,c is an even prime number, then find the value of 24a−b−c×24b−c−a×24c−a−b×24c−a−b

A round balloon of radius r subtends an angle α at the eye of the observer while the angle of elevation of its centre is β. Prove that the height of the centre of the balloon from the ground is(r sin β cosecα2)

If x,y,z are non negative integers so that x + y + z = 12, then themaximum value of xyz + xy + yz + zx is

Find the smallest six-digit number which is exactly divisible by 471.

The remainder obtained when 9722 is divided by 1001 is

If midpoints of sides of △ PQR are (1,2), (0,1) (1,0) then find the coordinate of three vertices of △ PQR

The cost of sugar is ₹50 per kg.Find its cost per mole.

In a two digits no the sum of digits is 8 if we add 18 to those digits the digits are inter changed find the no

If (125) raised to x-1 = (5) raised to 3x-2 - 500, then find the value of x

Question 3 (iii)In the following APs, find the missing term in the boxes.(iii) 5,□,□,912

Choose the most appropriate option to replace (?). 5 5 15 75 ? 4725 51975

Normals are drawn to the parabola y^2=4ax from (3,0).if the feet of normals are P , Q and R THEN SHOW THT circumcentre of △ PQR lies on the axis of the parabola ,i.e, y=0

In how many ways can a committee of 5 people be formed, such that it contains at least 1 social worker?

An odometer read 2510 km when Prateek started his car journey from his house to his office. After he reached there in two hours, it was showing 2750 km. Find the average speed of his car.

Consider the following statements: Which of the above statements is/are correct

A smooth plane inclined at an angle 0 with the horizontal is shown in the given figure. A body starts from rest and slides down on the inclined surface. The time taken by the body to reach the bottom is

An aircraft is flying along a horizontal line PQ directly towards the observer A on the ground and maintaining an altitude of 4500 m, the angles of depression of A from P and Q are 30 degree and 60 degree respectively. Find PQ.

The monthly income of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each save Rs. 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value?

11 Calculate the volume of a Ballon i which 4 gram He is filled at 22 and 720 mm Hg.

Express r in terms of p and q if the roots of the equation x2+px+q=0 are α,β and the roots of the equation x2−rx+s=0 are α4,β4

If CODING = 12, AMPLIFIER = 18, INTEREST = 16, then CAR =

Find the eight term of the series: 13−16+112−124....

x2 + 9x − 36 = 0, find the positive root of the equation. Ans.___________._