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What is the largest number that divides 245 and 1029, leaving remainder 5 in each case ?

(a) 15 (b) 16 (c) 9 (d) 5

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

$\begin{array}{cccccccc}\text{Number of plants}& 0-2& 2-4& 4-6& 6-8& 8-10& 10-12& 12-14\\ \text{Number of Houses}& 1& 2& 1& 5& 6& 2& 3\end{array}$

Which method did you use for finding the mean, and why?

Select the meaning of the given phrases/idioms: piece of cake

What are the taxes that never existed in India?

If find the value of “x”.

1. 2

If the sum of the squares of zeros of quadratic polynomial F (X)= x^2 - 8 x + K is 40, find k

If the vertices of a triangle are $A(2,1),B(-2,-2),C(1,0),$ then sum of squares of the lengths of the medians of the triangle is

Determine which of the following polynomials has (x+1) as a factor:
(i) $x^3$+$x^2$+x+1 (ii) $x^4$+$x^3$+$x^2$+x+1

Question 8

Use Euclid’s division algorithm to find the HCF of 441, 567 and 693.

Question 1 (vi)
Solve the following pairs of equations by reducing them to a pair of linear equations:
6x + 3y = 6xy
2x + 4y = 5xy

2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys. How long would it take one man and one boy to do it?

Find the value of k for which the following system of equations has no solution: (20-25):

kx - 5y = 2

6x + 2y = 7

The difference between the maximum and the minimum value of observations in a data-set is called:

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was $3$ more than twice the number of articles produced on that day. If the total cost of production on that day was$Rs.90$, find the number of articles produced and the cost of each article.

Find the roots of the quadratic equation $2x^2-7x+3=0$ using quadratic formula. Select all the correct options.

From the following particulars of Bhomick Brothers, Kathihar, prepare a Trading Account for the year ended 31st March, 2021 and calculate cost of goods sold.

$\begin{array}{cc}& \left(Rs\right)\\ \text{Opening Stock 1.4.21011}& 2,00,000\\ \text{Purchases}& 6,00,000\\ \text{Purchase Returns}& 50,000\\ \text{Sundry Factory Overheads}& 50,000\\ \text{Carriage}& 30,000\\ \text{Royalty on Production}& 20,000\\ \text{Salary to Foreman}& 1,00,000\\ \text{Sales (including Sales Tax Collected Rs 6,000)}& 4,00,000\\ \text{Sales Returns}& 44,000\\ \text{Closing Stock 31.3.2012}& 2,50,000\end{array}$

The distance between the points $(\text{a}cos{35}^{\circ },0)\&(0,\text{a}cos{55}^{\circ })$ is

In the following figure, ABC and AMP are two right triangles, right angled at B and M respectively, prove that:

(i) ΔABC ∼ ΔAMP

(ii)

Question 4

On dividing $x^3-3x^2+x+2$ by a polynomial g(x), the quotient and remainder were $x-2$ and $-2x+4$, respectively. Find g(x).

What is the probability that the minute and hour hands of a clock will form an acute angle at any given time?

If side BC of a triangle ABC is extended to D and $\angle ACD={120}^{\circ }$, then $\angle A+\angle B=$ .