Class 10 Mathematics • Sample Paper Set 5

If one zero of the quadratic polynomial $x^2 + 3x + k$ is 2, then the value of $k$ is:

The pair of equations $x = a$ and $y = b$ graphically represents lines which are:

The discriminant of the quadratic equation $2x^2 - 4x + 3 = 0$ is:

The 10th term of the AP: 5, 8, 11, 14, ... is:

If the sum of the zeroes of the polynomial $3x^2 - kx + 6$ is 3, then the value of $k$ is:

The value of $k$ for which the system of equations $x + 2y = 5$ and $3x + ky + 15 = 0$ has no solution is:

Which of the following is a quadratic equation?

If the common difference of an AP is 5, then what is $a_{18} - a_{13}$?

The degree of the polynomial $(x + 1)(x^2 - x - x^4 + 1)$ is:

If $2x + 3y = 12$ and $3x - 2y = 5$, then:

The roots of the equation $x^2 + 7x + 10 = 0$ are:

The sum of first $n$ odd natural numbers is:

If $\alpha$ and $\beta$ are zeroes of $x^2 - 4x + 1$, then $1/\alpha + 1/\beta - \alpha\beta$ is:

The value of $k$ for which the equations $3x - y + 8 = 0$ and $6x - ky = -16$ represent coincident lines is:

If $1/2$ is a root of the equation $x^2 + kx - 5/4 = 0$, then the value of $k$ is:

The 4th term from the end of the AP: -11, -8, -5, ..., 49 is:

A quadratic polynomial, whose zeroes are -3 and 4, is:

The values of $k$ for which the quadratic equation $2x^2 - kx + k = 0$ has equal roots is:

Find the zeroes of the quadratic polynomial $6x^2 - 3 - 7x$ and verify the relationship between the zeroes and the coefficients.

For what value of $k$, the system of equations $kx + 3y = 1$, $12x + ky = 2$ has no solution?

Find the roots of the quadratic equation $3x^2 - 2\sqrt{6}x + 2 = 0$.

Which term of the AP: 3, 8, 13, 18, ... is 78?

Solve for $x$ and $y$: $2x + y = 7$ and $4x - 3y + 1 = 0$.

If $\alpha$ and $\beta$ are the zeroes of the polynomial $f(x) = x^2 - 5x + k$ such that $\alpha - \beta = 1$, find the value of $k$.

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

The sum of the reciprocals of Rehman's ages (in years) 3 years ago and 5 years from now is 1/3. Find his present age.

Find the sum of first 24 terms of the list of numbers whose nth term is given by $a_n = 3 + 2n$.

Solve for $x$: $\frac{1}{x+4} - \frac{1}{x-7} = \frac{11}{30}, x \neq -4, 7$.

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

The sum of the first 7 terms of an AP is 49 and that of 17 terms is 289. Find the sum of first $n$ terms.

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

If the roots of the equation $(a^2 + b^2)x^2 - 2(ac + bd)x + (c^2 + d^2) = 0$ are equal, prove that $a/b = c/d$.

Case Study: Polynomials (Roller Coaster)
A roller coaster track is represented by the polynomial $p(x) = x^2 - 8x + 12$. The track crosses the x-axis at two points which represent the entry and exit points of a tunnel.

Case Study: Arithmetic Progression (Savings)
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner:

Case Study: Linear Equations (Book Store)
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days.