IOE Engineering Entrance Examination (Tribhuvan University, Nepal) · Mathematics

Calculus, algebra and coordinate geometry

60 practice questions, each with the answer and an explanation.

Practise Calculus, algebra and coordinate geometry now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 60 questions

Evaluate $\int_{0}^{3} 3 x^{2} d x$ .
What is the value of $lo g_{5} (12 5^{4})$ ?
What is the sum to infinity of the geometric series with first term 3 and common ratio $\frac{1}{3}$ ?
Find the determinant of the matrix with rows $(- 1, 6)$ and $(- 2, - 2)$ .
Find the dot product of the vectors $(- 2, 5, 0)$ and $(1, - 3, 3)$ .
What is the distance between the points $(3, 2)$ and $(8, - 10)$ ?
In how many ways can 3 books be chosen from 6 different books?
What is the modulus of the complex number $8 + 15 i$ ?
If $α$ and $β$ are the roots of $x^{2} - 2 x - 24 = 0$ , what is $α^{2} + β^{2}$ ?
What is the value of $cos 15 0^{\circ}$ ?
What is the sum of the first 23 terms of an arithmetic progression with first term 5 and common difference 5?
Find $lim_{x \to 7} \frac{x ^{2} - 49}{x - 7}$ .
If $f (x) = 3 x^{3} + x^{2}$ , what is $f^{'} (3)$ ?
Evaluate $\int_{0}^{3} 4 x^{3} d x$ .
What is the value of $lo g_{5} (12 5^{3})$ ?
What is the sum to infinity of the geometric series with first term 12 and common ratio $\frac{2}{3}$ ?
Find the determinant of the matrix with rows $(4, - 2)$ and $(0, - 1)$ .
Find the dot product of the vectors $(- 1, 5, 2)$ and $(1, 2, 4)$ .
What is the distance between the points $(1, - 1)$ and $(7, - 9)$ ?
In how many ways can 4 books be chosen from 9 different books?
What is the modulus of the complex number $5 - 12 i$ ?
If $α$ and $β$ are the roots of $x^{2} - 2 x - 15 = 0$ , what is $α^{2} + β^{2}$ ?
What is the value of $sin 13 5^{\circ}$ ?
What is the sum of the first 24 terms of an arithmetic progression with first term 3 and common difference 5?
Find $lim_{x \to 5} \frac{x ^{2} - 25}{x - 5}$ .
A line is given by $y = - 3 x + 5$ . What is the slope of a line perpendicular to it?
If $f (x) = x^{3} + 2 x^{2} - 3$ , what is $f^{'} (4)$ ?
Evaluate $\int_{0}^{2} 4 x^{3} d x$ .
What is the value of $lo g_{2} (3 2^{4})$ ?
What is the sum to infinity of the geometric series with first term 4 and common ratio $\frac{1}{4}$ ?
Find the determinant of the matrix with rows $(- 1, 6)$ and $(1, 4)$ .
Find the dot product of the vectors $(- 1, 0, 4)$ and $(0, - 3, - 3)$ .
What is the distance between the points $(1, 2)$ and $(7, - 6)$ ?
What is the centre of the circle $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$ ?
In how many ways can 2 books be chosen from 7 different books?
What is the modulus of the complex number $7 - 24 i$ ?
If $α$ and $β$ are the roots of $x^{2} + 7 x + 12 = 0$ , what is $α^{2} + β^{2}$ ?
What is the value of $cos 4 5^{\circ}$ ?
What is the sum of the first 20 terms of an arithmetic progression with first term 2 and common difference 5?
A line is given by $y = - 3 x + 2$ . What is the slope of a line perpendicular to it?
If $f (x) = 2 x^{3} + 3 x^{2} - 4$ , what is $f^{'} (4)$ ?
What is the value of $lo g_{5} (2 5^{3})$ ?
What is the sum to infinity of the geometric series with first term 8 and common ratio $\frac{1}{4}$ ?
Find the dot product of the vectors $(- 1, 4, 5)$ and $(5, 5, 4)$ .
What is the distance between the points $(2, - 2)$ and $(7, - 14)$ ?
In how many ways can 4 books be chosen from 10 different books?
What is the value of $cos 12 0^{\circ}$ ?
What is the sum of the first 17 terms of an arithmetic progression with first term 8 and common difference 6?
Find $lim_{x \to 4} \frac{x ^{2} - 16}{x - 4}$ .
A line is given by $y = 4 x - 3$ . What is the slope of a line perpendicular to it?
If $f (x) = 3 x^{3} + 4 x^{2} - 2$ , what is $f^{'} (3)$ ?
Evaluate $\int_{0}^{2} 4 x^{1} d x$ .
What is the value of $lo g_{3} (24 3^{2})$ ?
What is the sum to infinity of the geometric series with first term 2 and common ratio $\frac{1}{2}$ ?
Find the determinant of the matrix with rows $(5, - 4)$ and $(6, 0)$ .
Find the dot product of the vectors $(0, 4, 4)$ and $(5, 3, 2)$ .
What is the distance between the points $(- 1, 1)$ and $(2, - 3)$ ?
In how many ways can 2 books be chosen from 6 different books?
What is the modulus of the complex number $8 - 6 i$ ?
If $α$ and $β$ are the roots of $x^{2} + 5 x + 6 = 0$ , what is $α^{2} + β^{2}$ ?

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