Question 1 :
In an AP, given a = 5, d = 3, $a_n$= 50, find n and $S_n$.

Question 2 :
Find the sum of the following AP: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, . .$ , to 11 terms

Question 3 :
In an AP, given $a = 3, n = 8, S = 192$, find d.

Question 4 :
Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week, her weekly savings become Rs. 20.75, find n.

Question 5 :
Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

Question 6 :
From each corner of a square of side 4 cm, a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in figure. The area of the remaining (shaded) portion is <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b67273b230584979997.PNG' />

Question 7 :
The coordinates of the points P and Q are (4, –3) and (–1, 7). Then the abscissa of a point R on the line segment PQ such that $\frac{PR}{PQ}$ = $\frac{3}{5}$ is

Question 8 :
A letter of English alphabets is chosen at random. The probability that it is a letter of the word ‘MATHEMATICS’ is

Question 9 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b68273b230584979998.PNG' /> In the adjoining figure, PA and PB are tangents from a point P to a circle with centre O. Then the quadrilateral OAPB must be a

Question 10 :
A pair of linear equations $a_1x + b_1y + c_1 = 0$; $a_2x + b_2y + c_2 = 0$ is said to be inconsistent, if

Question 11 :
After how many decimal places will the decimal expansion of the number $\frac{47}{(2^3 \times 5^2)}$ terminate?

Question 12 :
The number of zeroes, the polynomial p (x) = $(x – 2)^2 + 4$ can have, is

Question 13 :
If for some angle θ, cot 2θ = $\frac{1}{\sqrt{3}}$ then the value of sin3θ, where 2θ $\leq$ 90º is

Question 14 :
The smallest value of k for which the equation $x^{2} + kx + 9 = 0$ has real roots, is

Question 15 :
Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where