Algebra Questions

Find the value of x
3
−
x
3

1
​
when x−
x
1
​
=5.

If y+
y
1
​
=5, then the value of y
6
+
y
6

1
​
is:

If P=
x
2
−16
x
2
−100
​
and Q=
x−4
x+10
​
, then the value of
Q
P
​
is:

If p=106, q=105 and r=104, then the value of p
2
+q
2
+r
2
−pq−qr−rp is:

Simplify the expression:
15×15×15+3×15×12×12−3×15×15×12−12×12×12

If x+y=18 and xy=9, then the value of (
y
x
​
+
x
y
​
) will be:

If 4x−5y=−37 and 7x+y=−16, then x−y=________.

If 5x−4≤2−x and 4x+5>2x−5, then x can take which of the following values?

On dividing 111a
2
b
2
c
2
by 37a
2
, we get __________.

The value of x for which the expressions 5x+17 and 17x−5 become equal is __________.

If
7
6
​
th of
5
8
​
th of a number is 192, then
4
3
​
th of that number is __________.

Simplify the following expression:
49a
2
+70ab+25b
2

Factorise x
2
+3x−18.

If 5x−3≥3+
2
x
​
and 4x−2≤6+x, then x can take which of the following values?

If the sum of the roots of a quadratic equation is −7 and the product of the roots is 12, find the quadratic equation.

Coefficient of x in (x+6)(7−3x) is:

Simplify the expression:
(0.2)
3
+(0.3)
3
+(0.5)
3
+3×0.5×0.7×0.8

If $7+3x\ge 5-\frac{x}{2}$ and $2x+3\le 5-2x$; then $x$ can take which of the following values?

If x+
x
4
​
=4, then find the value of x
2
+
x
2

1
​
.

If 2x−2(4−x)<2x−3<3x+3, then x can take which of the following values?

If a+b=10 and a
2
+b
2
=58, then find ab.

The coefficient of x
2
in (x+3)(2−4x)(5x−6) is:

Determine the value of '$r$ ' for which the equation $13x+5=rx+18$ has no solution.

If $2x-3(x+2)<5-2x<-x+2$, then find the range/value of $x$.

Which of the following is not a quadratic equation?

What will be the roots of the quadratic equation $x^2-25x+156=0$?

Square of $(7-4x)$ is:

If $3.352-(9.759-x)-19.64=7.052$, then what is the value of $x$?

What is the value of $\left(2^3+5^2\right)\left(5^2-2^3\right)$?

If $23x+23y=184$, then what is the average of $x$ and $y$?

If $(x+y+z)=23$ and $x^2+y^2+z^2=179$, then find the value of $(xy+yz+zx)$.

If $x+\frac{1}{x}=7$, find the value of $x^3+\frac{1}{x^3}$.

If x
2
+9y
2
=40 and xy=4, where x>0,y>0, then what is the value of (x
3
+27y
3
)?

If x
4
+y
4
+x
2
y
2
=21 and x
2
+y
2
−xy=7, then what is the value of
x
2

1
​
+
y
2

1
​
?

If x−y=
9
7
​
and
x
1
​
−
y
1
​
=
21
11
​
, then what is the value of (x
3
−y
3
)?

The sum of a non-zero number and thrice its reciprocal is
7
52
​
. Find the number.

If 2x−2(3+4x)<−1−2x<−
3
5
​
−
3
x
​
, then x can take which of the following values?

The sum of the ages of a brother and sister at present is 21. Five years ago the product of their ages was 28. What is the age of the brother and the sister?

If 3x−8(2−x)=−19, then the value of x is:

If x−y=6 and xy=40, then find x
2
+y
2
.

If 2x−3(2x−2)>x−1<2+2x; then x can take which of the following values?

Simplify 52×52−48×48.

If 2x+
3x
1
​
+1=0 and x

=0, then find the value of 2x+
3x
1
​
.

If x+y+z=4, xy+yz+zx=1, and x
3
+y
3
+z
3
=34, then what is the value of 6xyz?

If for a non-zero x, 7x
2
+5x+7=0, then x
3
+
x
3

1
​
is ________.

If x
2
+y
2
+z
2
=xy+yz+zx, then the value of (
8x
2
y
2
+6y
2
z
2
+10z
2
x
2

17x
4
+9y
4
+16z
4

​
) is:

Factorise x
2
+5x−14.

If the sum of the roots of a quadratic equation is 1 and the product of the roots is −20, find the quadratic equation.

If 3x−3<3+
2
x
​
and x−2≤6+2x, then x can take which of the following values?

The sum of a non-zero number and twice its reciprocal is
4
33
​
. Find the number.

The value of x for which the expressions 11x+7 and 17x−1 become equal is:

If (x+y):(x−y)=5:2, find the value of
x−4y
4x+5y
​
.

If 2+2x<5−
2
x
​
and 5x+3>5−5x, then x can take which of the following values?

The sum of a non-zero number and thrice its reciprocal is
2
13
​
. Find the number.

Find the sum of 3+3
2
+3
3
+⋯+3
8
.

A number is greater than five times its reciprocal by $\frac{19}{2}$. Find the number.

If $x^4-3x^2-1=0$, then the value of $\left(x^6-3x^2+\frac{3}{x^2}-\frac{1}{x^6}+1\right)$ is:

Find the value of 13
3
+(−8)
3
+(−5)
3
.

The sum of two numbers is 19, while the difference between the two numbers is 3. Find the smaller number out of these two numbers.

If
2
a
​
=
3
b
​
=
4
c
​
=
k
2a−3b+5c
​
, then find the value of k.

The average of $n$ observations is $40$. If two observations $50$ and $60$ are added, then the average of all the observations will be $41$. What is the value of $n$?

On selling a television at a $6\%$ profit and a fridge at a $9\%$ profit, a shopkeeper gains $\text{Rs. }5,100$. However, if the shopkeeper sells the television at a $9\%$ profit and the fridge at a $6\%$ loss, he gains $\text{Rs. }1,800$ on the whole transaction. The cost price (in $\text{Rs.}$) of the fridge is:

If decreasing $70$ by $x\%$ yields the same result as increasing $60$ by $x\%$, then $x\%$ of $91$ is:

Which of the following is correct?

If a−b=−5 and a
2
+b
2
=73, then find ab.

If 2x+2(4+3x)<2+3x>2x+x/2; then x can take which of the following values?

If $3x-10=-(2x+5)$, then the numerical value of $(x-4{)}^3$ is:

If $xy=-30$ and $x^2+y^2=61$, then find the value of $(x+y)$.

If a−b=−7 and a
2
+b
2
=85, then find ab.

If $2x+4(x-3)<-2-x<2x-1$, then find the value of $x$ from the given integer options.

Coefficient of x in (x+9)(8−5x) is:

If x−y=−9 and xy=−20, then find x
2
+y
2
.

If 4x−5(2x−1)>2x+3>2−3x; then x can take which of the following values?

What is the value of xy if x−y=3 and x
2
+y
2
=15?

Find the value of 1006×994.

The sum of 2xy(3x+4y−5z) and 5yz(2x−3y) is:

If 4x−73
2
​
≥3x+1, then x can take which of the following values?

If $(a+b-3{)}^2+(b+c-2{)}^2+(c+a-5{)}^2=0$, then the value of $\sqrt{(b+c{)}^a+(c+a{)}^b-1}$ is:

The solution set of 4x−3y=47 and 3x+y=32 is:

If cos45
∘
−sec60
∘
=x, then the value of x is:

If (9−3x)−(17x−10)=−1, then the value of x is: