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P and Q are points on the sides AB and AC respectively of $△$ABC such that PQ || BC and divides $△$ABC into two parts, equal in area. Find PB : AB.

The LCM and HCF of two numbers are 180 and 6 respectively. If one of the numbers is 30, find the other number.

Twenty one lead marbles of even size are recast to form a big sphere. Find the volume of the sphere when the radius of each marbles is 2 cm.

Lines PQ and RS are parallel. It is given that $\angle RSP={52}^{\circ }$, then find $\angle SPQ$.

If the coordinates of a triangle are A(2,1), B(6,1), C(6,5) then find the length of AB.

Find the excluded values of $\frac{2x-1}{x^2+5x+6}.$

In the given figure, PQ = PR and $\angle PRQ={70}^{\circ }$. Find $\angle QAR$.

In an ap it is given that T8 = 31 and t13= 45 find the AP

Question 1 (iii)
Find the sum of the following APs
(iii) 0.6, 1.7, 2.8 ,…….., to 100 terms

Find X if $2X+3Y=\left[\begin{array}{cc}2& 3\\ 4& 0\end{array}\right]and3X+2Y=\left[\begin{array}{cc}7& -2\\ -1& 5\end{array}\right]$

In $\Delta ABC$ given below, AB = 10 cm, AC = 8 cm and $\angle A={45}^{\circ }$. The find the area of $\Delta ABC$.

A bucket is in the form of a frustum of a cone, its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. Find how many litres of water can the bucket hold ? (Take $\pi$ = $\frac{22}{7}$)

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Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1). Find the third vertex. [2 MARKS]

The marks in science of 80 students of class X are given below: Find the mode of the marks obtained by the students in science.
Marks: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
Frequency: 3 5 16 12 13 20 5 4 1 1

A bag contains three green marbles, four blue marbles and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is__.

Question 4

The angle of elevation of the top of a tower from a point on the ground which is 30 m away from the foot of the tower is ${30}^{\circ }$. Find the height of the tower.

How many terms of the geometric progression 1 + 4 + 16 + 64 + ........ must be added to get sum equal to 5461 ?

Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

Each of letters in the word WILLING is on separate cards, face down on the table. If you pick a card at random, what is the probability that its letter will be I or N?

Four cows are tethered at the four corners of a square field of side 50 m such that each can graze the maximum unshared area. What area will be left ungrazed ?

[ Take $\pi =3.14$]

If the angle of elevation of a cloud from a point h metres above a lake is a and the angle of depression of its reflection in the lake be b, prove that the distance of the cloud from the point of observation is $\frac{2hsec\alpha }{tan\beta -tan\alpha }$

Find the value k where x-3id a factor of k²x³-kx²+3kx-k.