Algebra Model set 1 by shaalaa.com 2024-2025 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

Two coins are tossed simultaneously. The probability of getting at the most one head is ______.

`1/2`

`1/4`

`3/4`

1

Avnish spends 70% of his income. From the balance amount, he donates ₹ 1000 to an orphanage. He is then left with ₹ 8,000. Find his income.

₹ 60,000

₹ 50,000

₹ 40,000

₹ 30,000

If d = – 5, n = 10, a_n = 68, then find the first term.

113

23

– 113

– 23

Ayush buys a share of FV ₹ 200 for MV of ₹ 250. A company confirmed 20% dividend on the share. What will be the rate of return?

16%

15%

20%

5%

Mr. Dubey's payable amount of income tax is ₹ 7000. He needs to pay education cess at 3% on income tax. Hence how much total income tax will he have to pay?

Find the remainder when p(x) = 3x² + 2x – 7 is divided by 2x + 1.

Find the value of x, if `5^(x - 3) xx 5^(2x – 8)` = 625.

Find the value of x, if `(4/7)^x (7/4)^(2x) = 343/64`.

Fill in the boxes:

Sunita choose a card from a well-shuffled deck of 52 cards.

Total number of cards, S = `square`

Let E be the event that the choosen card is a queen.

Number of queens = `square`

Thus, P(E) = `"Number of queens"/"Total number of cards" = square/square = square`

Fill in the boxes:

Sunita choose a card from a well-shuffled deck of 52 cards.

Let F be the event that the choosen card is an eight of the spade.

Number of the eight of the spade = `square`

Thus, P(F) = `square/square`

= `square/square`

The price of one unit is ₹ 500. To find the numbers of units for the investment of ₹ 6,25,000, fill in the boxes.

Sum invested = `square`

Price of one unit = `square`

Number of units = `square/square`

= `square/square`

= `square` units.

Hence the number of units is `square`.

One of the roots of equation x² + 5x + a = 0 is – 3. To find the value of a, fill in the boxes.

Since, `square` is a root of equation x² + 5x + a = 0

∴ Put x = `square` in the equation

⇒ `square^2 + 5 xx square + a` = 0

⇒ `square + square + a` = 0

⇒ `square + a` = 0

⇒ a = `square`

Shivam Yadav bought a share of FV ₹ 9000 for MV of ₹ 15,000. A company declared 20% dividend on the share. Find the rate of return.

If six times of the 3^rd term is equal to the eight times of 7^th term in an A.P., then what will be the 19^th term?

Which term in the A.P. 60, 56, 52, 48, 44, 40, ...... is the first negative term?

Find the sum of all odd numbers between 351 and 373.

Solve: 7x² – 30x – 25 = 0

Nitin is younger than Nishant by 5 years. Sum of their ages is 45. What is Nishants age?

Let the ages of Nitin and Nishant be x years and y years respectively.

Then, according to the question,

x = `square - 5`  .......(i)

and `x + square` = 45  .......(ii)

Substituting the value of x from equation (i) to equation (ii), we get

`square + square` = 45

`square - square` = 45

`square` = 45 + `square`

`square = square`

y = `square/2 = square`

Hence, the age of Nishant is `square` years.

The sum of the digits in a two-digit number is 7. The number obtained by interchanging the digits exceeds the original number by 27. Find the two-digit number.

Let the units place digit in original number bey and tens place be x.

So, Original number = `square`

Now, from the first condition, x + y = `square`  ...(i)

From the second condition, 10y + x = `square` + `square`

10y + x – `square` = `square`

`square` – `square` = `square`

9(y – `square`) = `square`

y – `square = square/9 = square`  ...(ii)

Adding equation (i) and (ii), we get

2y = `square`

⇒ y = `square`

Putting y = `square` equation (i), we get

x + `square` = 7

⇒ x = `square`

So, Original number = 10x + y = 10 × `square` + `square`

= `square`

If a letter is choosen randomly from all the letters of the word 'MAINTAINANCE', what is the probability that the choosen letter is a vowel

If a letter is choosen randomly from all the letters of the word 'MAINTAINANCE', what is the probability that the choosen letter is a consonant

For arithmetic progression, first term is – 8 and last term is 55. If sum of all these terms is 235, find the number of terms and common difference.

What will be the 6^th, 12^th and 25^th term of the sequence defined by a_n = (n – 2)² + 2n?

Two straight paths are represented by the linear equations 2x – 4y = 4 and – 6x + 12y = 6. Check whether the paths cross each other or not, by using the graphical representation.

The maximum speeds, in km per hour, of 35 cars in a race are given as follows:

Calculate the median speed.

In a right-angled triangle, altitude is 2 cm longer than its base. Find the dimensions of the right-angled triangle given that the length of its hypotenuse is 10 cm.

If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)

X takes 3 hours more than Y to walk 30 km. But, if X doubles his pace, he is ahead of Y by `1 1/2` hours. Find their speed of walking.

Find the values of a and b, if the sum of all the frequencies is 120 and the median of the following data is 55.