English Medium कक्षा १० - CBSE Question Bank Solutions

What should be subtracted to the polynomial x² − 16x + 30, so that 15 is the zero of the resulting polynomial?

A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is

If two zeroes of the polynomial x³ + x² − 9x − 9 are 3 and −3, then its third zero is

If \[\sqrt{5}\ \text{and} - \sqrt{5}\]   are two zeroes of the polynomial x³ + 3x² − 5x − 15, then its third zero is

If x + 2 is a factor of x² + ax + 2b and a + b = 4, then

The polynomial which when divided by −x² + x − 1 gives a quotient x − 2 and remainder 3, is

For what value of n, the n^th terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?

The 19^th term of an A.P. is equal to three times its sixth term. If its 9^th term is 19, find the A.P.

The 9^th term of an A.P. is equal to 6 times its second term. If its 5^th term is 22, find the A.P.

If the seventh term of an A.P. is  \[\frac{1}{9}\] and its ninth term is \[\frac{1}{7}\] , find its (63)^rd term.

The sum of 5^th and 9^th terms of an A.P. is 30. If its 25^th term is three times its 8^th term, find the A.P.

Find the sum of the first 15 terms of each of the following sequences having nth term as  x_n = 6 − n .

If the sum of a certain number of terms starting from first term of an A.P. is 25, 22, 19, ..., is 116. Find the last term.

Find the sum of all 2 - digit natural numbers divisible by 4.

Find the sum  (−5) + (−8)+ (−11) + ... + (−230) .

Find the sum:  1 + 3 + 5 + 7 + ... + 199 .

Find the sum \[7 + 10\frac{1}{2} + 14 + . . . + 84\]

If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c² = a²(1 + m²).