Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Sequences and Series

Short Answer Type

131. Find the sum to n terms of the following series.

space space space 1 cross times 2 cross times 3 plus 2 cross times 3 cross times 4 plus 3 cross times 4 cross times 5 plus........

134 Views

132. Find the sum of n terms of the series 3 + 7 + 13 + 21 + 31 +.......

136 Views

133. The ages of the students in a class form an A.P. whose common difference is 4 months. If the youngest student is 8 years old and the sum of the ages of all the students in the class is 168 years. Find the numbers of students in the class.

787 Views

134.

A man deposited Rs. 10,000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.

241 Views

135. An insect starts from a point and travels in a straight path 1 mm in the first second and half of the distance covered in the previous second in the succeeding second. In what time would it reach a point 3 mm away from its starting point?

Let a mm be the distance travelled in the first second. Since the insect covers half the distance covered in the previous second in the succeeding second.

∴ Distances covered in various seconds are $1 comma space 1 half comma space 1 fourth comma space 1 over 8........$

Let r be the common ratio

∴ $straight r space equals space 1 half$

Let 3 mm distance be covered in n seconds

∴ $straight S subscript straight n space equals space 3$

$rightwards double arrow$ $fraction numerator straight a left parenthesis 1 minus straight r to the power of straight n right parenthesis over denominator 1 minus straight r end fraction space equals space 3 space space rightwards double arrow space space space fraction numerator 1 open square brackets 1 minus open parentheses begin display style 1 half end style close parentheses to the power of straight n close square brackets over denominator 1 minus begin display style 1 half end style end fraction space equals space 3 space rightwards double arrow space space space space 1 space minus space open parentheses 1 half close parentheses to the power of straight n space equals space 3 over 2 space rightwards double arrow space space open parentheses 1 half close parentheses to the power of straight n space equals space fraction numerator negative 1 over denominator 2 end fraction$

which is impossible for any value of n.

Hence, the insect would never reach a point 3 mm away from its starting point.

234 Views

136. The interior angles of a polygon are in A.P. The smallest angle is 120° and the common difference is 5°. Find the number of sides of the polygon.

270 Views

Long Answer Type

137. Shamshad Ali buys a scooter for Rs 22000. He pays Rs. 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

336 Views

Short Answer Type

138. A man buys every year Bank’s cash certificates of value exceeding the last year purchase by Rs. 25. After 20 years, he finds that the total value of the certificates purchased by him is Rs. 7250. Find the values of the certificates purchased by him

(i) In the first year. (ii) In the 13th year.

179 Views

Long Answer Type

139. An odd number of stones lie along a straight path, the distance between any two consecutive stones being 10 m. The stones are to the collected at the place where the middle stone lies. A man can carry only one stone at a time. He starts carrying the stones beginning from the extreme stone. If he covers a path of 3 km, how many stones are there ?

183 Views

Short Answer Type

140. The income of a person is Rs. 3,00,000 in first year and he receives an increase of Rs. 10,000 to his income per year for next 19 years. Find the total amount, he received in 20 years.

126 Views