Take sectional tests or a full 40-question Algebra mock for CUET UG with timers, answer review, and detailed explanations.
This route gives you four sectional sessions and a full mixed mock. Each question runs on a 60-second timer to train both concept clarity and pace.
Polynomials, degree, and linear equations
Simultaneous equations, quadratics, and remainder theorem
Inequalities and modulus
Logarithms and arithmetic progression
1. Solve: $3x + 5 = 20$
Explanation: Move 5 to the right: $3x = 15$. Therefore $x = 5$.
2. Solve: $5x - 7 = 18$
Explanation: Add 7 on both sides: $5x = 25$. Hence $x = 5$.
3. What is the degree of $7x^4 - 3x + 8$?
Explanation: The highest power of $x$ is 4, so the degree is 4.
4. What is the degree of the term $6x^3y^2$?
Explanation: In a multivariable term, add exponents: $3 + 2 = 5$.
5. If $2x + 3 = x + 11$, then $x =$
Explanation: Bring like terms together: $2x - x = 11 - 3$. So $x = 8$.
6. Solve: $4x - 9 = 3$
Explanation: Add 9 to both sides: $4x = 12$. So $x = 3$.
7. Which of the following is a polynomial in $x$?
Explanation: A polynomial has only non-negative integer powers of the variable. So $3x^2 - 5x + 4$ is the valid choice.
8. If $7x + 4 = 46$, then $x =$
Explanation: Subtract 4: $7x = 42$. Therefore $x = 6$.
9. The constant term of $4x^3 - 7x + 9$ is:
Explanation: The constant term is the term without $x$, which is 9.
10. Solve: $\frac{x}{3} + 5 = 9$
Explanation: Subtract 5: $x/3 = 4$. Multiply by 3 to get $x = 12$.
11. If $x + y = 9$ and $x - y = 3$, find $x$.
Explanation: Add the two equations: $2x = 12$, so $x = 6$.
12. If $2x + y = 11$ and $x + y = 7$, find $x$.
Explanation: Subtract the second equation from the first: $x = 4$.
13. Find the roots of $x^2 - 5x + 6 = 0$.
Explanation: Factorize: $x^2 - 5x + 6 = (x-2)(x-3)$. So the roots are 2 and 3.
14. For $x^2 - 7x + 10 = 0$, the sum of roots is:
Explanation: For $ax^2+bx+c=0$, sum of roots $= -b/a$. Here it is $-(-7)/1 = 7$.
15. For $2x^2 - 9x + 4 = 0$, the product of roots is:
Explanation: Product of roots is $c/a = 4/2 = 2$.
16. What is the discriminant of $x^2 - 6x + 9 = 0$?
Explanation: $D = (-6)^2 - 4(1)(9) = 36 - 36 = 0$.
17. If the discriminant of a quadratic is negative, the roots are:
Explanation: When $D
18. Find the remainder when $x^2 + 3x + 2$ is divided by $x + 1$.
Explanation: By the Remainder Theorem, remainder = $f(-1) = 1 - 3 + 2 = 0$.
19. Find the remainder when $2x^2 - 5x + 3$ is divided by $x - 2$.
Explanation: Remainder = $f(2) = 2(4) - 10 + 3 = 1$.
20. Form the quadratic equation whose roots have sum 8 and product 15.
Explanation: If the roots have sum $S$ and product $P$, the equation is $x^2 - Sx + P = 0$. So it becomes $x^2 - 8x + 15 = 0$.
21. Solve: $2x - 5 > 9$
Explanation: Add 5: $2x > 14$. Divide by 2 to get $x > 7$.
22. Solve: $3x + 4 \le 19$
Explanation: Subtract 4: $3x \le 15$. Divide by 3 to get $x \le 5$.
23. Solve: $5 - 2x \ge -7$
Explanation: Subtract 5: $-2x \ge -12$. Divide by -2 and reverse the sign to get $x \le 6$.
24. Which interval represents the solution of $x - 4 < 0$?
Explanation: $x - 4
25. Solve: $|x - 3| = 5$
Explanation: Case 1: $x - 3 = 5$, so $x = 8$. Case 2: $x - 3 = -5$, so $x = -2$.
26. Solve: $|2x| = 18$
Explanation: $|2x| = 18$ gives $2x = 18$ or $2x = -18$. Hence $x = \pm 9$.
27. Solve: $|x + 4| = 2$
Explanation: $x + 4 = 2$ gives $x = -2$, and $x + 4 = -2$ gives $x = -6$.
28. The solution set of $|x - 1| \ge 4$ is:
Explanation: Distance from 1 is at least 4, so move 4 units left and right: $x \le -3$ or $x \ge 5$.
29. Solve: $7 - x > 1$
Explanation: Subtract 7: $-x > -6$. Multiply by -1 and reverse the sign to get $x
30. Solve: $|5x| = 25$
Explanation: $5x = 25$ or $5x = -25$. So $x = \pm 5$.
31. Evaluate $\log_2 32$
Explanation: $2^5 = 32$, so $\log_2 32 = 5$.
32. Evaluate $\log_3 81$
Explanation: $3^4 = 81$, so $\log_3 81 = 4$.
33. Evaluate $\log_{10}(0.01)$
Explanation: $0.01 = 10^{-2}$, so $\log_{10}(0.01) = -2$.
34. Evaluate $\log_5 125$
Explanation: $5^3 = 125$, so $\log_5 125 = 3$.
35. Find the 8th term of the A.P. 5, 8, 11, 14, ...
Explanation: Here $a = 5$ and $d = 3$. So $a_8 = a + 7d = 5 + 21 = 26$.
36. Find the sum of the first 10 terms of the A.P. with $a = 4$ and $d = 3$.
Explanation: $S_n = \frac{n}{2}[2a + (n-1)d]$. So $S_{10} = 5[8 + 27] = 175$.
37. What is the common difference of the A.P. 12, 17, 22, 27, ...?
Explanation: Subtract consecutive terms: $17 - 12 = 5$, so the common difference is 5.
38. If $\log_a m + \log_a n =$
Explanation: The product law says $\log_a m + \log_a n = \log_a(mn)$.
39. Find the 12th term of the A.P. with first term 8 and common difference 3.
Explanation: $a_{12} = 8 + 11 \times 3 = 41$.
40. Evaluate $\log_4 \left(\frac{1}{16}\right)$
Explanation: $\frac{1}{16} = 4^{-2}$, so the logarithm equals -2.
41. If $\frac{2x-3}{5}=7$, then $x =$
Explanation: Multiply by 5: $2x-3=35$. So $2x=38$ and $x=19$.
42. If one root of $x^2-kx+24=0$ is 6, then the other root is:
Explanation: Product of roots = 24. If one root is 6, the other root is $24/6=4$.
43. How many integer solutions satisfy $|x-2|<4$?
Explanation: $|x-2| So $-2
44. In an A.P., the 5th term is 18 and the 11th term is 42. What is the common difference?
Explanation: $a+4d=18$ and $a+10d=42$. Subtracting gives $6d=24$, so $d=4$.
45. If $\log_2 x=6$, then $x =$
Explanation: $\log_2 x=6$ means $x=2^6=64$.