Question 1 :
If the lines are represented by the equation $a_1x + b_1y + c_1 =0$ and $a_2x + b_2y + c_2 =0$, then the lines are intersecting when _____________.
Question 2 :
A pair of linear equations which has no solution, is called an __________________ pair of linear equations.
Question 3 :
The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save Rs. 2000 per month, find their monthly incomes.
Question 4 :
Find a quadratic polynomial whose sum and product
respectively of the zeroes are as given: $-\frac{3}{2\sqrt{5}}$, $-\frac{1}{2}$
Question 5 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a53273b230584979921.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a57273b230584979925.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 7 :
(1 + tan θ + sec θ) (1 + cot θ – cosec θ) = ____
Question 8 :
$\sin \theta=\cos \theta$ for all values of $\theta$. True or False?
Question 9 :
Express $\sin 67^{\circ} + \cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$.
Question 10 :
Point P (5, –3) is one of the two points of trisection of the line segment joining the points A (7, – 2) and B (1, – 5). State true or false.
Question 11 :
Name the type of quadrilateral formed, if any, by the following points (-3,5) , (3,1) , (0,3) , (-1,-4).
Question 12 :
The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is :
Question 13 :
A carton consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Jimmy, a trader, will only accept the shirts which are good, but Sujatha, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. What is the probability that it is acceptable to Sujatha?
Question 14 :
Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on consecutive days?
Question 15 :
Who wrote the book on the probability, The Book on Games of Chance?
Question 16 : <img style='object-fit:contain' src='61b19a85273b230584979938' />
Consider the above distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using appropriate method.
Question 17 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bff273b230584979a57.PNG' />
A survey conducted on 20 households in a locality by a group of students resulted in the above frequency table for the number of family members in a household. Find the mode of this data.
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c16273b230584979a72.PNG' />
The above given frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the mode.
Question 19 :
State true or false: The square of any positive integer is either of the form 4q or 4q + 1 for some integer q.
Question 20 :
Choose the correct answer from the given four options in the question: If two positive integers a and b are written as $a = x^3y^2$ and $b = xy^3$; x, y are prime numbers, then HCF (a, b) is ________.
Question 21 :
State True or False, Let p be a prime number. If p divides $a^2$ , then p divides a, where a is a positive integer.
Question 22 :
Justify why the following quadratic equation has no two distinct real roots: $x^2-3x+4=0$
Question 23 :
Find the positive root of the equation $2x^2 + x - 300 = 0$, by factorisation.
Question 24 :
Find the roots of the following quadratic equation (by the factorisation method): $3\sqrt{2}x^2-5x-\sqrt{2}=0$
Question 25 :
In an AP, given $a_n = 4, d = 2, S_n = –14$, find n and a.
Question 26 :
Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Question 27 :
A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the smallest value of the prize.
Question 28 :
$\tan 48^{\circ} \tan 23^{\circ} \tan 42^{\circ} \tan 67^{\circ} = 1$. TRUE or FALSE?
Question 29 :
(sec A + tan A) (1 – sin A) = ______
Question 31 :
Is it true to say that the pair of equations – x + 2y + 2 = 0 and $\frac{1}{2}x-\frac{1}{4}y-1=0$ has a unique solution?
Question 32 :
Solve the following pair of linear equations by the elimination method and the substitution method : $3x – 5y – 4 = 0 ~and ~9x = 2y + 7$
Question 33 :
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs. 155. How much does a person have to pay for travelling a distance of 25 km?
Question 34 :
State True or False. In a grouped frequency distribution, it is not possible to determine the mode by looking at the frequencies. To find the mode of grouped data, locate the class with the maximum frequency. This class is known as the modal class. The mode of the data is a value inside the modal class.
Question 35 : In the following distribution :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b8e273b2305849799c8.PNG' />
The number of families having income range (in Rs) 16000 – 19000 is
Question 36 :
While computing mean of grouped data, we assume that the frequencies are
Question 37 :
Find the sum of the odd numbers between 0 and 50.
