Mathematics Questions

Browse 1,240 Mathematics questions with expert-verified, step-by-step solutions — NCERT, exemplar and previous-year questions, organised by chapter.

Q341

Find the values of $x$ and $y$ in the following rectangle [see Fig. 3.2].
Rectangle with labelled sides

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Q342
Solve the following pairs of equations:
1. (i) $x + y = 3.3$ , $\frac{0.6}{3 x - 2 y} = - 1$ , $3 x - 2 y \neq = 0$ .
2. (ii) $\frac{x}{3} + \frac{y}{4} = 4$ , $\frac{5 x}{6} - \frac{y}{8} = 4$ .
3. (iii) $4 x + \frac{6}{y} = 15$ , $6 x - \frac{8}{y} = 14$ , $y \neq = 0$ .
4. (iv) $\frac{1}{2 x} - \frac{1}{y} = - 1$ , $\frac{1}{x} + \frac{1}{2 y} = 8$ , $x, y \neq = 0$ .
5. (v) $43 x + 67 y = - 24$ , $67 x + 43 y = 24$ .
6. (vi) $\frac{x}{a} + \frac{y}{b} = a + b$ , $\frac{x}{a ^{2}} + \frac{y}{b ^{2}} = 2$ , $a, b \neq = 0$ .
7. (vii) $\frac{2 x y}{x + y} = \frac{3}{2}$ , $\frac{x y}{2 x - y} = \frac{- 3}{10}$ , $x + y \neq = 0, 2 x - y \neq = 0$ .
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Q343

Find the solution of the pair of equations $\frac{x}{10} + \frac{y}{5} - 1 = 0$ and $\frac{x}{8} + \frac{y}{6} = 15$ . Hence, find $λ$ , if $y = λ x + 5$ .

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Q344
By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.
1. (i) $3 x + y + 4 = 0$ and $6 x - 2 y + 4 = 0$
2. (ii) $x - 2 y = 6$ and $3 x - 6 y = 0$
3. (iii) $x + y = 3$ and $3 x + 3 y = 9$ .
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Q345

Draw the graph of the pair of equations $2 x + y = 4$ and $2 x - y = 4$ . Write the vertices of the triangle formed by these lines and the $y$ -axis. Also find the area of this triangle.

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Q346

Write an equation of a line passing through the point representing solution of the pair of linear equations $x + y = 2$ and $2 x - y = 1$ . How many such lines can we find?

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Q347

If $x + 1$ is a factor of $2 x^{3} + a x^{2} + 2 b x + 1$ , then find the values of $a$ and $b$ given that $2 a - 3 b = 4$ .

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Q348

The angles of a triangle are $x$ , $y$ and $4 0^{\circ}$ . The difference between the two angles $x$ and $y$ is $3 0^{\circ}$ . Find $x$ and $y$ .

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Q349

Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?

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Q350

The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

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Q351

Two numbers are in the ratio $5 : 6$ . If $8$ is subtracted from each of the numbers, the ratio becomes $4 : 5$ . Find the numbers.

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Q352

There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to B. But if 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in the two halls.

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Q353

A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs 22 for a book kept for six days, while Anand paid Rs 16 for the book kept for four days. Find the fixed charges and the charge for each extra day.

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Q354

In a competitive examination, one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

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Q355

The angles of a cyclic quadrilateral ABCD are $∠ A = (6 x + 10)^{\circ}$ , $∠ B = (5 x)^{\circ}$ , $∠ C = (x + y)^{\circ}$ , $∠ D = (3 y - 10)^{\circ}$ . Find $x$ and $y$ , and hence the values of the four angles.

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Q356
Which of the following is a quadratic equation? (A) $x^{2} + 2 x + 1 = (4 - x)^{2} + 3$ (B) $- 2 x^{2} = (5 - x) (2 x - \frac{2}{5})$ (C) $(k + 1) x^{2} + \frac{3}{2} x = 7$ , where $k = - 1$ (D) $x^{3} - x^{2} = (x - 1)^{3}$
1. (a) $x^{2} + 2 x + 1 = (4 - x)^{2} + 3$
2. (b) $- 2 x^{2} = (5 - x) (2 x - \frac{2}{5})$
3. (c) $(k + 1) x^{2} + \frac{3}{2} x = 7$ , where $k = - 1$
4. (d) $x^{3} - x^{2} = (x - 1)^{3}$
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Q357
Which of the following is not a quadratic equation?
1. (a) $2 (x - 1)^{2} = 4 x^{2} - 2 x + 1$
2. (b) $2 x - x^{2} = x^{2} + 5$
3. (c) $(2 x + 3)^{2} + x^{2} = 3 x^{2} - 5 x$
4. (d) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{3}$
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Q358
Which of the following equations has $2$ as a root?
1. (a) $x^{2} - 4 x + 5 = 0$
2. (b) $x^{2} + 3 x - 12 = 0$
3. (c) $2 x^{2} - 7 x + 6 = 0$
4. (d) $3 x^{2} - 6 x - 2 = 0$
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Q359
If $\frac{1}{2}$ is a root of the equation $x^{2} + k x - \frac{5}{4} = 0$ , then the value of $k$ is
1. (a)2
2. (b) $- 2$
3. (c) $\frac{1}{4}$
4. (d) $\frac{1}{2}$
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Q360
Which of the following equations has the sum of its roots as 3?
1. (a) $2 x^{2} - 3 x + 6 = 0$
2. (b) $- x^{2} + 3 x - 3 = 0$
3. (c) $2 x^{2} - \frac{3}{2} x + 1 = 0$
4. (d) $3 x^{2} - 3 x + 3 = 0$
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